Microeconomics Book PDF

1.1.1 Concepts of Revenue: TR, AR and MR 1.1.2 Relationship between AR (Demand Curve) and MR curve under Perfect competition 1.1.3 Relationship between AR(Demand curve) and MR curve under imperfect competition 1.1.4 Significance of the Concept of Revenue 1.1.5 Demand-Concept 1.1.6 Determinants of Demand 1.1.7 Law of Demand 1.1.8 Market Demand 1.1.9 Shift in Demand 1.1.10 Elasticity of Demand - concept 1.1.11 Price Elasticity of Demand 1.1.12 Income Elasticity of Demand 1.1.13 Cross Elasticity of Demand 1.1.14 Promotional Elasticity of Demand 1.1.15 Summary 1.1.16 Self Assessment Questions 1.2.1 Consumer Behaviour- Introduction 1.2.2 Concept of Indifference Curve and Marginal Rate of Substitution 1.2.3 Properties of Indifference Curve 1.2.4 The Budget Line or Price Line 1.2.5 1.2.6 Price consumption curve and Price elasticity 1.2.7 Income Consumption Curve and Engle Curve 1.2.8 Price Change and Income and Substitution Effects 1.2.9 Derivation of Individual Demand Curves from IC 1.2.10 Summary 1.2.11 Self Assessment Questions 2.1.1 Production Function 2.1.2 Production Function with one Variable Input (SRPF) 2.1.3 Production Iso-quants & Marginal Rate of Technical Substitution 2.1.4 Iso-cost Line 2.1.5 The Optimal Combination of Resources (Producers Equilibrium LRPF) 2.1.6 The Expansion Path 2.1.7 Economic Region of Production 2.1.8 Returns to Scale Concept 2.1.9 Returns to scale using Iso-quant 2.1.10 Summary 2.1.11 Self-Assessment Questions 2.2.1 Cost of Production: Social and private costs of production 2.2.2 Short run Cost and Cost Curve 2.2.3 Long run Average Cost Curve and its implications. 2.2.4 Summary 2.2.5 Self Assessment Questions 3.1.1 Perfect competition: Concept and Assumptions 3.1.2 Demand Curve of a Firm 3.1.3 Supply Curve of Firm and Industry-Short run and Long-run 3.1.4 Equilibrium of the firm in Short-run 3.1.5 Equilibrium of the Industry in Short-run 3.1.6 Equilibrium of the firm in Long-run 3.1.7 Equilibrium of the Industry in Long-run 3.1.8 Measuring producer surplus under perfect competition 3.1.9 Summary 3.1.10 Selected Questions 4.1.1 Monopoly: Concept 4.1.2 Short-Run Equilibrium under Monopoly 4.1.3 Long-Run Equilibrium under Monopoly 4.1.4 Absence of the Supply Curve in Monopoly 4.1.5 Effect of Shifts in the demand curve in Monopoly 4.1.6 Effect of the change in cost 4.1.7 Measurement of monopoly power and the rule of thumb for pricing, 4.1.8 Horizontal and vertical integration of firms 4.1.9 Differences between Monopoly and Perfect Competition 4.1.10 Summary 4.1.11 Self Assessment Questions 5.1.1 Imperfect Competition 5.1.2 Monopolistic competition 5.1.3 Equilibrium of a firm (Short-run) 5.1.4 Equilibrium of a Group (long-run) and economic efficiency 5.1.5 Summary 5.1.6 Self Assessment Questions 5.2.1 Oligopoly: Concept 5.2.2 Oligopoly and Interdependence (Kinked Demand Curve) 5.2.3 Basic concept of Game Theory 5.2.4 Summary 5.2.5 Self Assessment Questions understand the concepts of revenue/ demand curves under different market conditions define demand and its determinants explain the Law of Demand identify understand the concept and types of elasticity of demand assess the price elasticity of demand as well as the determinants 1.1.17 Concepts of Revenue: TR, AR and MR 1.1.18 Relationship between AR (Demand Curve) and MR curve under Perfect competition 1.1.19 Relationship between AR(Demand curve) and MR curve under imperfect competition 1.1.20 Significance of the Concept of Revenue 1.1.21 Demand-Concept 1.1.22 Determinants of Demand 1.1.23 Law of Demand 1.1.24 Market Demand 1.1.25 Shift in Demand 1.1.26 Elasticity of Demand - concept 1.1.27 Price Elasticity of Demand 1.1.28 Income Elasticity of Demand 1.1.29 Cross Elasticity of Demand 1.1.30 Promotional Elasticity of Demand 1.1.31 Summary 1.1.32 Self Assessment Questions The costs and revenues of a firm determine its nature and the levels of profit. Cost refers to the expenses incurred by a producer for the production of a commodity. Revenue denotes the amount of income, which a firm receives by the sale of its output. The revenue concepts commonly used in economic are total revenue, average revenue and marginal revenue. Total revenue refers to the total sale proceeds of a firm by selling its total output at a given price. Mathematically TR = PQ, where TR = Total Revenue, P = Price, Q = Quantity sold. Suppose a firm sells 100 units of a product at the price of Rs.5 each, the total revenue will be 100 × Rs.5 = Rs.500. Average revenue is the revenue per unit of the commodity sold. It is obtained by dividing the total revenue by the number of units sold. Mathematically AR = TR/Q; where AR = Average revenue, TR = Total revenue and Q = Quantity sold. In our example, average revenue is = 500/100 = Rs.5. Thus, average revenue means price. Marginal revenue is the addition to total revenue by selling one more unit of the commodity. Suppose 5 units of a product are sold at a total revenue of Rs. 50 and 6 units are sold at a total revenue of Rs. 60. The marginal revenue will be (Rs. 60 Rs.50)/(6 - 5) = 10/1= Rs.10. Under perfect competition, a very large number of firms are assumed to be present selling homogeneous products. So any increase or decrease in production by any one firm exerts no perceptible influence on the total supply and on the price in the market. The collective forces of demand and supply determine the price in the market so that only one price tends to prevail for the whole industry. Each firm has to take the market price as given and sell its quantity at the - infinitely elastic (Horizontal in shape). As the firm sells more and more at the given price, its total revenue will increase but the rate of increase in the total revenue will be constant which implies AR = MR. The relationship between AR and MR for a firm under perfect competition has been depicted in Table-1 and Fig.1 given below. 1 10 10 10 2 10 20 10 3 10 30 10 4 10 40 10 5 10 50 10 6 10 60 10 7 10 70 10 The Demand curve (AR) of a Firm under Perfect Competition In figure 1.1.2, OX axis represents the number of units sold and OY axis represents the price per unit. The price of the unit remains constant at P1. Consequently AR and MR curves coincide with each other. Unlike under perfect competition, a firm under imperfect competition such as under monopoly can sell more only by lowering its price. Therefore, the average revenue curve is downward sloping and its corresponding marginal revenue curve lies below it. 1 10 10 10 2 9 20 10 3 8 30 10 4 7 40 10 5 6 50 10 6 5 60 10 Average and Marginal Revenue Curves under Monopoly In figure 1.1.3, OX axis represents the number of units of the commodity sold. OY represents the price. The AR curve as well as the MR curve slope downwards. (i) When MR and AR are straight lines and slope downwards When AR and MR are straight lines, sloping downwards, the marginal revenue falls twice as much as the fall in the average revenue. In other words, the marginal revenue will cut any line perpendicular to the Y- axis at halfway to the average revenue curve. This can be proved mathematically. In the following figure 1.1.3 (a), AB = BC. Relationship between AR & MR Curves under imperfect competition Total Revenue = Average Revenue × Output CM × OM = Area of Rectangle ACMO Also Total Revenue = Area under the marginal revenue curve = RDMO Also ACMO = ABDMO + BCD and RDMO = ABDMO + RAB Therefore, ABDMO + BCD = ABDMO + RAB Or BCD = RAB But RAB = BCD, being right angles And RBA = CBD, being vertically opposite angles. Thus, the two triangles are equal in area and BCD = RAB Therefore, AB = BC Hence, it is proved that marginal revenue curve will cut any line perpendicular to the Y-axis at halfway to the average revenue curve. Mrs. Joan Robinson in empirical relationship between price elasticity, average revenue and marginal revenue. The relationship is expressed in the formula. AR = MR or AR = MR(e/(e-1)) or MR = AR ((e-1)/e); where, AR = Average Revenue, MR = Relationship between AR,MR & Price elasicity under imperfect competition In figure 1.1.3 (b), AR and MR are the average revenue and the marginal revenue curves. Elasticity of demand at point R on the average revenue curve = RT/RS In triangles PSR and MRT, Therefore, Therefore, triangles PSR and MRT are similar. Hence, RT/RS = RM/SP -----------------------------------(1) Now in triangle PSK and KRQ, PK = KR Therefore, triangles PSK and RQK are congruent. Hence, PS = RQ -----------------------------------(2) From (1) and (2), we get, Elasticity at R = (RT/RS) = (RM/SP) = (RM/RQ) But RM/RQ = RM/(RM-RQ) But RM = Average revenue = price QM = Marginal revenue Elasticity at R = Average revenue/(Average revenue Marginal revenue) = AR/(AR-MR) If A stands for Average rev the average revenue curve, then e = A/(A-M). Therefore, e(AR) e(MR) = AR e(AR) AR = e(MR) AR = e(MR)/(e-1) AR = MR(e/(e-1)) MR = AR((e-1)/e) = )= ) A few examples: 1. Suppose the price of a product is $6 and the elasticity of demand is 2. Marginal revenue will be MR = AR((e-1)/e) = $6 × (2-1)/2 = $6 × (1/2) = $3. 2. When the price of the product is $6 and price elasticity of demand is 1, marginal revenue will be MR = AR((e-1)/e) = $6 × (1-1)/1 = $6 × 0 = 0. If MR = 0, it is a case in which the MR curve coincides with the X-axis. Mrs. Joan Robinson has also pointed out many special cases of Marginal and Average revenue curves. average revenue will assume the form of a rectangular hyperbola. This limiting case is possible under pure monopoly where the monopoly product has no substitutes at all. According to the formula MR = AR ((e-1)/e) Putting e=1, we have MR = AR ((1-1)/1) = AR × 0 = 0 Thus, when the price elasticity of demand (e or PED as shown in Figure below) is equal to one or unity, though not the average revenue curve, the marginal revenue curve will be zero. Therefore, the marginal revenue curve coincides with the X-axis. Further, when PED >1, MR is positive (MR > 0) and when PED MC expansion in output will be profitable If MR < MC expansion incurs loss If MC = MR equilibrium output is attained The intersection of MC = MR determines price, output, and the profit or loss of a firm. (b) Concept of excess capacity This concept is helpful to indicate to the entrepreneur whether the firm possesses excess capacity or not. Under perfect competition, production will be carried on up to the minimum point of the LAC. Therefore, excess capacity is not possible. However, under imperfect competition (monopoly or monopolistic competition) the firm can earn more by reducing its output. So, production will not be carried on up to the minimum point of the long-run average cost curve. Thus, imperfect competition leads to idle capacity. It is a (c) Factor-Pricing In fixing the prices of factors in the factor markets, AR and MR concepts are very useful. In factor pricing, the average revenue curve becomes the average revenue productivity curve, and marginal revenue curve becomes the marginal revenue productivity curve, ARP and MRP are Cost) determines the equilibrium level of price, output and profit for a firm under various cost conditions. Demand for a commodity refers to the desire for the commodity backed by willingness and ability to pay for that commodity. So demand includes the desire to buy the commodity accompanied by the willingness to buy it and sufficient purchasing power to purchase it. For instance-Everyone might have willingness to buy Car but only a few have the ability to pay for it. Thus, everyone cannot be said to have a demand for the car. Demand may arise from individuals, household and market. When goods are demanded by individuals, it is called as individual demand. Goods demanded by household constitute household demand. Demand for a commodity by all individuals/households in the market in total constitutes market demand. The Market demand is the horizontal summation of individual demand. Demand function is showing relationship between the quantity demanded of a commodity and the factors influencing demand. In the above equation, Dx = Quantity demanded of a commodity Px = Price of the commodity Py = Price of related goods T = Tastes and preferences of consumer Y = Income level A = Advertising and promotional activities Pp = Population (Size of the market) U = Specific factors affecting demand for a commodity such as seasonal changes, taxation policy, availability of credit facilities, etc. The law of demand states that there is an inverse relationship between quantity demanded of a commodity and its price, other factors being constant. In other words, higher the price, lower the demand and vice versa, other things remaining constant. is a tabular representation of the quantity demanded of a commodity at various prices. For instance, there are four buyers of apples in the market, namely A, B, C and D. PRICE (Rs. Buyer A Buyer B Buyer C Buyer D Market per dozen) (demand in (demand in (demand in (demand in Demand dozen) dozen) dozen) dozen) (dozens) 10 1 0 3 0 4 9 3 1 6 4 14 8 7 2 9 7 25 7 11 4 12 10 37 6 13 6 14 12 45 The demand by Buyers A, B, C and D are individual demands. Total demand by the four buyers is market demand. Therefore, the total market demand is derived by summing up the quantity demanded of a commodity by all buyers at each price.. It is a graphical representation of price- quantity relationship. Demand Curve Demand curve has a negative slope, i.e, it slopes downwards from left to right depicting that with increase in price, quantity demanded falls and vice versa. The reasons for a downward sloping demand curve can be explained as follows- 1. With the fall in price of a commodity, the purchasing power of consumer increases. Thus, he can buy same quantity of commodity with less money or he can purchase greater quantities of same commodity with same money. Similarly, if the price of a commodity rises, it is equivalent to decrease in income of the consumer as now he has to spend more for buying the same quantity as before. This change in purchasing power (real income) due to price change is known as income effect. 2. When price of a commodity falls, it becomes relatively cheaper compared to other commodities whose price have not changed. Thus, the consumer tend to consume more of the commodity whose price has fallen, i.e, they tend to substitute that commodity for other commodities which have not become relatively dear. 3. It is the basic cause of the law of demand. The law of diminishing marginal utility states that as an individual consumes more and more units of a commodity, the utility derived from it goes on decreasing. So as to get maximum satisfaction, an individual purchases in such a manner that the marginal utility of the commodity is equal to the price of the commodity. When the price of commodity falls, a rational consumer purchases more so as to equate the marginal utility and the price level. Thus, if a consumer wants to purchase larger quantities, then the price must be lowered. This is what the law of demand also states. The instances where law of demand is not applicable are as follows- 1. There are certain goods which are purchased mainly for their snob appeal, such as, diamonds, air conditioners, luxury cars, antique paintings, etc. These goods are used as valuable will be they as status symbols and more will be there demand. Thus, such goods are purchased more at higher price and are purchased less at lower prices. Such goods are called as. 2. The law of demand is also not applicable in case of. Giffen goods are those inferior goods, whose income effect is stronger than substitution effect. These are consumed by poor households as a necessity. For instance, potatoes, animal fat oil, low quality rice, etc. An increase in price of such good increases its demand and a decrease in price of such good decreases its demand. 3. The law of demand does not apply in case of expectations of change in price of the commodity, i.e, in case of. Consumers tend to purchase less or tend to postpone the purchase if they expect a fall in price of commodity in future. Similarly, they tend to purchase more at high price expecting the prices to increase in future. Although the behaviour of an individual in respect of selection and purchase of goods forms the basis of demand theory, the aggregate demand or market demand for a good is most important for its producer. The aggregate quantity of a good that the buyers purchase or demand at a particular price and in a particular period is called the market demand for the good at the said price. Also, the curve that gives us the market demand for a good at any particular price is known as its market demand curve. It is obvious from the definition of for a good would give us its market demand curve. The market demand curve for a good would also slope downward towards right, since, owing to the law of demand. Market Demand Curve The market demand curve can be obtained from the individual demand curves with the help of Figure. To make our analysis simple, suppose that the number of buyers of a good is only two and their individual demand curves are respectively d1 and d2.The market demand corresponding to price p1 and p2.has been shown in the figure given above. It is obvious from this that the market demand curve for a good is the horizontal summation of its individual demand curves. The demand curve shift to the right of left to the original demand curve parallelly when we reflex the assumption of other things reaming constant. The shift in demand curve has been shown as follows Shift in Demand There are as many elasticities of demand as its determinants. (a) The price elasticity, (b) The income elasticity, (c) The cross-elasticity of demand. (d) Promotional elasticity of demand The price elasticity measures the degree of responsiveness of the change in quantity demanded for a commodity due to the change in its price, other things remaining constant. If the changes in price are very small the is used to measure the responsiveness of demand. If the changes in price are not small is used as the relevant measure. The point elasticity of demand is defined as the proportionate change in the quantity demanded resulting from a very small proportionate change in price. Symbolically we may write ep = ( or ep = ( If the demand curve is linear i.e. Q = b0 b1P Its slope is = b1. Substituting in the elasticity formula, we get ep = b1. It implies that the elasticity changes at the various points of the linear-demand curve. Graphically the point elasticity of a linear-demand curve is shown by the ratio of the segments of the line to the right and to the left (i.e. ratio of lower segment to upper segment) of the particular point. In figure 1.1.11.1 the elasticity of the linear-demand curve at point F is the ratio of Point elasticity of demand From the above figure it can be proved that point elasticity of a linear-demand curve is the ratio of lower segment to upper segment (i.e. FD FD) P1 P2 = EF P1 P2 = EF P= OP1 Q= OQ1 If we consider very small changes in P and Q, then the point elasticity will be ep = = / =. From the figure also we can see that the triangles FEF Q1D corresponding angle is equal). Hence, = Q1D / FQ1 = Q1D / OP1. Thus, ep = Q1D / OP1 = OP1 / OQ1 = Q1D / OQ1 Further, the triangles and DP1F and FQ1D and hence, Q1D / FD = P1F / FD = OQ1/ FD Rearranging the above equation, we get the point price elasticity at point F as ep = Q1D / OQ1= FD / FD = Lower Segment / Upper Segment Given this graphical measurement of point elasticity it is obvious that at the mid-point of a linear-demand curve ep = 1 (point M in the figure 1.1.11.2 given below). At any point to the right of M the point elasticity is less than unity (ep < 1); finally at any point to the left of M, ep > 1. At point D the ep= p = 0. The price elasticity is always negative because of the negative sign is omitted when writing the formula of the elasticity. Point elasticity of demand The above formula for the price elasticity is applicable only for infinitesimal changes in the price. If the price changes appreciably we use the following formula, which measures the arc elasticity of demand They are elasticity is a measure of the average elasticity, that is, the elasticity at the midpoint of the chord that connects the two points (A and B) on the demand curve defined by the initial and the new price levels (figure 1.1.11.3). It should be clear that the measure of the arc elasticity is an approximation of the true elasticity of the section AB of the demand curve, which is used when we know only the two points A and B from the demand curve, but not the intermediate ones. Clearly the more convex to the origin the demand curve is, the poorer the linear approximation attained by the arc elasticity formula. Arc elasticity of demand The extent of responsiveness of demand with change in the price is not always the same. The demand for a product can be elastic or inelastic, depending on the rate of change in the demand with respect to change in price of a product. Elastic demand is the one when the response of demand is greater with a small proportionate change in the price. On the other hand, inelastic demand is the one when there is relatively a less change in the demand with a greater change in the price. For better understanding the concepts of elastic and inelastic demand, the price elasticity of demand has been divided into five types, which are shown in Figures 1.1.11.4, 1.1.11.5 and 1.1.11.6. Elastic Inelasic Perfectly elastic, inelastic and unitary elastic Perfectly Elastic Given the price, any quantity can be ep = Demand demanded. Perfectly No change in quantity demanded despite ep = 0 Inelastic the changes in price. Demand Unitary Elastic The percentage change in demand is equal ep= 1 Demand to the percentage change in the price Relatively The percentage change in demand is more ep > 1 Elastic Demand than the percentage change in the price of a product A small change in price leads to relatively a larger change in quantity demanded and vice-versa Relatively The percentage change in demand is less ep < 1 Inelastic than the percentage change in the price of a Demand product. It means A greater change in price leads to relatively a larger change in quantity demanded and vice-versa The relationship between Price elasticity and Revenue such as (Marginal Revenue and Total Revenue) has been shown as follows: When, e > 1, MR > 0 e < 1, MR< 0 e = 1, MR= 0 Price change If , e>1 If , e< 1 If , e= 1 Price rises TR decreases TR increases TR unchanged Price falls TR increases TR decreases TR unchanged (1) The availability of substitutes; the demand for a commodity is more elastic if there are close substitutes for it. (2) The nature of the need that the commodity satisfies. In general, luxury goods are price elastic, while necessities are price inelastic. (3) The time period. Demand is more elastic in the long run. (4) The number of uses to which a commodity can be put. The more the possible uses of a commodity the greater its price elasticity will be. (5) The proportion of income spent on the particular commodity. The income elasticity is defined as the proportionate change in the quantity demanded resulting from a proportionate change in income. Symbolically we may write The income elasticity is positive for normal goods. Some experts have used income elasticity in 1. The nature of the need that the commodity covers the percentage of income spent on food times been used as a measure of welfare and of the development stage of an economy). 2. The initial level of income of a country. For example, a TV set is a luxury in an 3. The time period, because consumption patterns adjust with a time-lag to changes in income. The cross-elasticity of demand helps in the classification of commodities into substitutes and complements. The cross-elasticity of demand is defined as the proportionate change in the quantity demanded of x resulting from a proportionate change in the price of y. Symbolically, The sign of the cross-elasticity is negative if x and y are complementary goods, and positive if x and y are substitutes. The higher the value of the cross-elasticity the stronger will be the degree of substitutability or complementarity of x and y. The main determinant of the cross-elasticity is the nature of the commodities relative to their uses. If two commodities can satisfy equally well the same need, the cross- elasticity is high, and vice versa. The cross-elasticity has been used for the definition of the firms which form an in- dustry Advertising Elasticity of Demand (AED) measures degree of change in demand brought about by change in advertising expenditure. It means Proportionate change in demand brought about by a unit change in advertising expenditure. / Where expressed as AED = (% change in Dx) / (% change in AE) Numerical Values of Advertising Elasticity of Demand will vary from zero to infinity. It would mean that if AED is zero, advertising expenditure has no effect on demand at all. If AED > 1, it is relatively elastic demand. It means that demand is more sensitive to the advertising expenditure and proportionately giving more than proportionate increase in demand. If AED < 1, it is relatively inelastic demand. It means that change in advertising expenditure brings about less than proportionate change in demand. If AED = 0 it is Perfectly Inelastic demand. It means that increase in advertising expenditure has no effect at all on demand. Type of product i.e. whether the product is already existing or new product Brand name Number of competitors and substitutes in the market Strategies of competitors Frequency of advertisements Mode of advertisements Time of advertisements Other factors influencing demand like tastes, professions, income etc. Helps in evaluating success of adverting campaign Helps the firms in deciding advertising expenditure or budget Helps in choosing more effective media for promotion Helps in withdrawing ineffective promotional campaigns Helps in strategic management to respond to co Helps in building brands Value of AED does not help in analyzing effect of advertising a single product Difficult to analyze the effectiveness of promotional strategies at a particular period of time, especially when the campaigns are over a long period of time The Purpose of campaigns may be to create brands, rather than only influencing size of demand AED does not take into account effect of other factors influencing demand. Total Revenue (TR) is equal to the total quantity sold multiplied by price per unit. Marginal Revenue (MR) is the slope of total revenue. It means MR is an addition to TR by selling an additional unit of output. Average Revenue (AR) is nothing but the price per unit of output. The relationship between revenue and price elasticity reveals that MR=AR[(e-1)/e]. MR is positive for e>1, negative for e1), relatively less elastic or inelastic (e1) for luxurious goods whereas it is relatively less elastic or inelastic (e 1 (relatively elastic), demand is more sensitive to the advertising expenditure. If AED < 1(relatively inelastic), demand is less sensitive to the advertising expenditure. 1. Define TR, MR and AR. Explain the relationship between AR and MR. 2. Define Demand. State the determinants of demand. Discuss the Law of demand with assumptions and exceptions. 3. Define Price elasticity of demand. Discuss its methods of Measurement and Types. 4. What is Price elasticity of demand? Discuss its relationship with TR and MR. 5. Write short notes on (a) Income elasticity of demand (b) Cross elasticity of demand (c) Promotional elasticity of demand After studying this unit, you should be able to: Understand the ordinal utility approach for analyzing the consumer behavior Define and draw the Indifference Curve Analyze the Substitution effect, Income effect and Price effect of a price change under IC analysis Derive the consumer demand curve from the IC approach 1.2.12 Consumer Behaviour- Introduction 1.2.13 Concept of Indifference Curve and Marginal Rate of Substitution 1.2.14 Properties of Indifference Curve 1.2.15 The Budget Line or Price Line 1.2.16 1.2.17 Price consumption curve and Price elasticity 1.2.18 Income Consumption Curve and Engle Curve 1.2.19 Price Change and Income and Substitution Effects 1.2.20 Derivation of Individual Demand Curves from IC 1.2.21 Summary 1.2.22 Self Assessment Questions There are broadly three approaches in economics to study the consumer behaviour such as Cardinal utility approach (Marginal Utility approach), Ordinal utility approach (Indifference Curve approach) and Behavioural approach (Revealed Preference approach). Here, the equilibrium. The indifference curve is a geometrical device developed by J.R.Hicks and R.G.D. Allen for explaining how choices between two alternatives are made based on ordinal utility approach. It may be viewed as a replacement or improvement over the neo-classical cardinal utility approach or concept. In contrast to the cardinal measurement of utility, the indifference curve measures the utility ordinally. It means, unlike cardinal utility approach, based on preference orderings how the consumers are assumed to select commodities in such a way to be remained indifferent in deriving satisfaction from the consumption of any of the available combination of two goods on the same indifference curve is explained by the indifference curve analysis. An is a graph showing combination of two goods that give the consumer equal satisfaction and utility. Each point on an indicates that a consumer is between the two and all points give him the same utility. The marginal rate of substitution is the amount of a good that a consumer is willing to give up for another good, as long as the new good is equally satisfying. It's used in indifference theory to analyze consumer behaviour. The slope of the indifference curve is called the MRS which is the ratio of the marginal utilities of the two commodities. This is expressed as. The Law of Diminishing Marginal Rates of Substitution states that MRS decreases as one moves down the standard convex-shaped curve, which is the indifference curve. The indifference curves must slope downward from left to right. As the consumer increases the consumption of X commodity, he has to give up certain units of Y commodity in order to maintain the same level of satisfaction. In the following Figure 1.2.3.1, various combinations of commodity X and commodity Y is shown by the points A, B, C and D on the same indifference curve. Thus, the consumer is indifferent towards any of the points as they represent equal level of satisfaction. This is an important property of indifference curves. They are convex to the origin. As the consumer substitutes commodity X for commodity Y, the marginal rate of substitution of X for Y (Slope of IC) diminishes along an indifference curve. In other words, Indifference curves are convex to the origin because the marginal utility of each product consumed decreases with subsequent consumption. The reason that marginal rate of substitution diminishes is due to the principle of diminishing marginal utility. The indifference curve could not be concave, as this would mean that the marginal rate of substitution increases (which is not possible as the consumer gives up one good for another and hence it violets the fundamental feature of consumer behaviour). In the following Figure 1.2.3.2, as the consumer moves from A to B to C to D, the willingness to substitute good X for good Y diminishes. The slope of IC is negative. In this diagram, diminishing MRSxy is depicted as the consumer is giving up AP>BQ>CR units of Y for PB=QC=RD units of X. Thus indifference curve is steeper towards the Y axis and gradual towards the X axis. It is convex to the origin. Indifference curve that lies above and to the right of another indifference curve represents a higher level of satisfaction. The combination of goods which lies on a higher indifference curve will be preferred by a consumer to the combination which lies on a lower indifference curve. In the following Figure 1.2.3.3, there are three indifference curves, IC1, IC2 and IC3 which represents different levels of satisfaction. The indifference curve IC3 shows greater amount of satisfaction and it contains more of both goods than IC2 and IC1.In short it can be interpreted as IC3 > IC2> IC1. The indifference curves cannot intersect each other. It is because at the point of tangency, the higher curve will give as much as of the two commodities as is given by the lower indifference curve. This is absurd and impossible. In the following Figure 1.2.3.4, it is shown that two indifference curves (IC 1 and IC2) intersect at point C. By definition of IC, C = A and C= B but by property III (as above) A > B. So it is obvious that under no circumstances A = B. Thus, due to this inconsistency in consumer behavior which violets the fundamental feature of IC, two indifference curves cannot intersect to each other. Indifference curve cannot e circular as because it violets the property II (i.e. Convexity condition as given above). In the circle as shown in the following figure both the convex and concave portions are present which violets the fundamental principles of IC. The degree of convexity of an indifference curve depends upon the rate of fall in the marginal rate of substitution of X for Y. But when two goods are perfect substitutes of each other, the indifference curve is a straight line on which marginal rate of substitution remains constant. Straight-line indifference curves of perfect substitutes are shown in Fig. 1.2.3 (a) below. In case of perfect substitutes, the indifference curves are parallel straight lines because the consumer equally prefers the two goods and is willing to exchange one good for the other at a constant rate. Indifference curves of Perfect Substitutes Similarly, when two goods cannot at all be substituted for each other, that is, when the two goods are perfect complementary goods, the indifference curve will consist of two straight lines with a right angle bent which is convex to the origin as shown in the following figure 1.2.3 (b). As will be seen in Fig. the left- hand portion of an indifference curve of the perfect complementary goods is a vertical straight line which indicates that an infinite amount of Y is necessary to substitute one unit of X and the right-hand portion of the indifference curve is a horizontal infinite amount of X is necessary to substitute one unit of Y. All this means that the two perfect complements are used in a certain fixed ratio and cannot be substituted for each other. Complements are thus those goods which are used jointly in consumption so that their consumption increases or decreases simultaneously. Pen and ink, right shoe and left shoe, automobile and petrol sauce and hamburger, type writer and typists are some examples of perfect complements. Indifference curves of Perfect Complements A budget line incorporates information on both the limited income of the consumer to spend and the prices of two purchasable goods. A budget line is a locus of points showing alternative combinations of two goods that can be purchased with a fixed amount of money income given prices of the two goods. If we know the budget (or the spending power) of the consumer and his Indifference Map we can find out what quantity of each commodity he will purchase. With the same information we can measure the effect of changes in the prices of commodities and of changes in the income of the consumer. Suppose a consumer has a fixed income M which he spends on two goods X and Y. Suppose Px is the price of X and Py is the price of Y. Let OB be the amount of Y which can be purchased Similarly, let OL be the amount of X which can be purchased with M. Then OL x px = M. Join B and L. BL is called the Price Line or the Budget Line or the Consumption-Possibility Line (See Fig.1.2.4). The line BL has important characteristics. Every point on it shows a possible and Y. OB / OL = M/py / M/px = M/py. py/xy = This is known as the price ratio. The equation of the budget line is M = Px. X + Py. Y. Budget Line A budget line is derived from a given income and given prices. So any change in income or price leads to a new budget line. If the price of one of the purchasable commodities falls there is a change in the slope of the budget line. Given the income and price of good Y, when the price of similar pattern is observed for the price of good Y given the income and price of good X as shown figure 1.2.4.2. A higher income leads to parallel shifts of the budget line outward (without changing its slope lower income leads to parallel shifts the budget line inward (without changing its slope) i.e. in Figure 1.2.4.3 Changes in Budget Line as a Result of Changes in Price of Good X Changes in Budget Line as a Result of Changes in Price of Good Y Shifts in Budget Line as a Result of Changes in Income \ "The term refers to the amount of goods and services which the consumer may buy in the market given his income and given prices of goods in the market". The aim of the consumer is to get maximum satisfaction from his money income. Given the price line or budget line and the indifference map, "A consumer is said to be in equilibrium at a point where the price line is touching the highest attainable indifference curve from below". The consumer is rational. He wants to obtain maximum satisfaction given his income and prices. It is assumed that the consumer can rank his preference according to the satisfaction of each combination of goods. The consumer is supposed to be consistent about his tastes and preference. For example if he prefers A to B and B to C then it follows that he also prefers A to C. This assumption is called Transitivity. Suppose a consumer buys orange and apple. It can be assumed that as more and more of units of apple are substituted for orange, the consumer will be willing to give up fewer and fewer units of orange for additional units of apple. This is called the Principle of Diminishing Marginal Substitutability. The Principle of Diminishing Marginal Substitutability corresponds to the older law of diminishing marginal utility. There is perfect competition in the market from where the consumer is purchasing the goods. A given price line should be tangent to an indifference curve. It means marginal rate of substitution of good X for good Y (MRSxy) must be equal to the price ratio of the two goods. i.e. The second order condition is that indifference curve must be convex to the origin (diminishing ) at the point of tangency. highest attainable indifference curve from below. In the following figure 1.2.5, there are three indifference curves IC1, IC2 and IC3. The price line BA is tangent to the indifference curve IC2 at point C. The consumer gets the maximum satisfaction or is in equilibrium at point E by purchasing ON units of good Y and OM units of good X with the given money income. The consumer cannot be in equilibrium at any other point on indifference curves. For instance, point F and G lie on lower indifference curve IC1 and hence yield less satisfaction. As regards point H on indifference curve IC3, the consumer no doubt gets higher satisfaction but that is position is only at point E where the price line is tangent to the highest attainable indifference curve IC2 from below. Further, At point E the two conditions of equilibrium gets satisfied viz. (1) Slope of the Price Line to be Equal to the Slope of Indifference Curve i.e. Indifference Curve is Convex to the Origin (MRS of X for Y must be diminishing) at the point of equilibrium Equilibrium under IC Analysis In indifference curve technique the price effect is measured along the Price Consumption Curve (PCC). The PCC is the equilibrium points corresponding to the changing slope of price line due money income and other things remaining constant. PCC can be downward or upward or horizontal sloping in case of normal goods but backward-sloping for giffen goods. Let us observe how the price elasticity of demand can be known from different shapes or slopes Price Consumption curve (PCC). In other words, whether price elasticity of demand is more than one (elastic), less than one (inelastic) or equal to one (unitary elastic) can be judged from the slope of price consumption curve (PCC). The downward sloping price consumption curve (PCC) for a good means that demand for the good is elastic, upward-sloping PCC means that demand for the good is inelastic and horizontal straight-line PCC means that demand for the good is unitary elastic. It can be seen from the following figure 1.2.6.1 that PCC is derived by joining the points Q, R, S and T where each of the points represents equilibrium points on different slopes of budget lines due to the decrease in price of good X other things remaining unchanged. The PCC derived in this figure is downward sloping. It indicates that remaining the price of Y and money income unchanged as indicated by the shift in budget line from L 1 to L2 to L3 to L4, the consumer is and small quantity of good Y as shown in this figure. It is evident from it that the price elasticity of demand for Good X is elastic and hence the PCC derived for good X in this case is downward sloping. Downward Sloping PCC showing Elastic Demand It can be seen from the following figure 1.2.6.2 that PCC is derived by joining the points Q, R, S and T where each of the points represents equilibrium points on different slopes of budget lines due to the decrease in price of good X other things remaining unchanged. The PCC derived in this figure is upward sloping. It indicates that remaining the price of Y and money income unchanged as indicated by the shift in budget line from L1 to L2 to L3 to L4, the consumer is demanding more of both good X and good Y but the. It is evident from it that the price elasticity of demand for Good X is inelastic and hence the PCC derived for good X in this case is upward sloping. Upward Sloping PCC showing Inelastic Demand It can be seen from the following figure 1.2.6.3 that PCC is derived by joining the points Q, R, and S where each of the points represents equilibrium points on different slopes of budget lines due to the decrease in price of good X other things remaining unchanged. The PCC derived in this figure is Horizontal. It indicates that remaining the price of Y and money income unchanged as indicated by the shift in budget line from L1 to L2 to L3 to L4, the consumer is. It is evident from it that the price elasticity of demand for Good X is unitary elastic and hence the PCC derived for good X in this case is Horizontal. Horizontal PCC showing unitary elastic Demand In the above analysis the PCC drawn shows either only elastic demand or only inelastic or unitary elastic demand over its entire range. However, since elasticity of demand varies at different prices, an indifference map can also be drawn that yields PCC which shows different elasticities at different price levels. It is depicted in figure 1.2.6.4 where it can be seen that from Q1 to Q2 PCC is downward sloping and hence the demand for the good is elastic (i.e. e > 1). From Q2 to Q3 PCC is horizontal and hence the demand for the good is unitary elastic (i.e. e = 1). From Q3 to Q4 PCC is upward sloping and hence the demand for the good is inelastic (i.e. e < 1). PCC Varying Elasticity of Demand PCC can also be backward sloping as depicted in figure 1.2.6.5. Backward Sloping PCC for good X indicates that when price of good X falls, after a point smaller quantity of it is demanded or purchased. It happens in the case exceptional type of goods called Giffen Goods. Thus the price effect of a price change in case of Giffen goods is positive. Backward Sloping PCC Income effect refers to in his money income which is reflected by the Income Consumption Curve (ICC). The various points (E, E1 & E2 is connected together to get the ICC as shown in figure 1.2.7. The parallel shift in budget line from original budget line MN to M1N1 and M2N2 indicates change in income and the point of tangency of IC1, IC2 and IC3 on the respective budget lines represents equilibrium point as shown in the following figure 1.2.7. The ICC derived in this figure is for Normal goods. e ICC for Normal goods The shapes of ICC based on the nature of the commodity such as inferior and others are depicted in figure 1.2.7 (a) as given below ICC for Inferior and other goods In indifference curve map income consumption curve is the locus of the equilibrium quantities consumed by an individual at different levels of his income. Thus, the income consumption e and the quantity purchased of a commodity by him. A nineteenth century German statistician Ernet Engel (1821-1896) made an empirical study of family budgets to draw conclusions about the pattern of consumption expenditure, that is, expenditure on different goods and services by the households at different levels of income. The conclusions he arrived at are still believed to be generally valid. Though Engel dealt with the relationship between income and expenditure on different goods, in order to keep the analysis simple it can be explained as the relationship between income and quantities purchased of goods. Thus,. Based on this the derivation of Engel curve from income consumption curve can be made. In other words, here Engel curve relates quantity purchased of a commodity to the level of demanded, other factors (such as prices of goods, consumer preferences etc.) remaining the same. The Engel Curve (EC) from Income Consumption Curve (ICC) for necessary goods has been derived as shown in the following figure 1.2.7.1. The panel (b) of the figure depicts EC where the level of income and quantity purchased of commodity X are represented by Y-axis and X- axis are respectively. Given the indifference map (IC1, IC2 and IC3) and the prices of two goods X and Y, Income Consumption Curve (ICC) is showing the equilibrium quantities purchased of commodities by the consumer as his income increases (shown by the parallel shift in budget lines) from Rs. 300 (B1L1)to Rs. 400 (B2L2)and to Rs. 500 (B3L3)as depicted in panel (a) of the figure. It is observed from panel (a) of the figure that R, S and T are representing the equilibrium points where IC is tangential to Budget line and hence the consumer is found buying more of commodity X (OQ1, OQ2 and OQ3) when income increases from Rs. 300 to 400 to 500, given prices of goods X and Y. Derivation of EC from ICC map have been transformed into Engel curve depicting quantity-income relationship. Each point Engel curve EC corresponds to point R on the ICC curve and so on. As seen from panel (b), Engel curve for normal goods is upward-sloping which shows that as income increases, consumer buys more of a commodity. The slope of Engel curve EC drawn in panel (b) of the Figure is equal to the ratio of change in income to change in quantity demanded of good X and has a positive sign. It shows that the slope of the Engel curve is found increasing as income increases. This indicates that with every equal increase in income (i.e. 300 to 400 to 500),. Thus, in Engel curve drawn in panel (b) of the Figure quantity purchased of the commodity increases with the increase in income but at a decreasing rate. This shape of the Engel curve is obtained for necessities. The Engel curve drawn in the following Figure is upward-sloping but is concave. This implies that slope of the Engel curve is declining with the increase in income. In other words, in the Engel curve of a commodity, the equal increments in income result in successively larger increases in the quantity purchased of the commodity. Thus, at income of Rs. 300 the consumer purchases OQ1 quantity of a commodity. The increase in income by Rs. 100 to Rs. 400 results in increase in quantity purchased of the commodity equal to Q1Q2. With the further increase in income by the same amount of Rs. 100 to Rs. 500, the quantity purchased increases by Q2Q3 which is much larger than Q1Q2. This implies that as a consumer becomes richer he purchases relatively more of the commodity. Such commodities are called luxuries. Derivation of EC from ICC for Luxury goods In case of inferior goods, consumption of the commodity declines as income increases. Engel curve of an inferior good as drawn in the following Figure 1.2.7.2 is backward bending indicating a fall in the quantity purchased of the good as income increases. Derivation of EC from ICC for Inferior goods An extreme case of Engel curve is a vertical straight line as drawn in the following Figure. This represents the case of a neutral commodity which is quite unresponsive to the increase in income. The Engel curve of the shape of a vertical straight line shows that a person goes on consuming the same amount of a commodity whatever the level of his income. For example, the quantity of common salt purchased by a family remains the same, determined as it is by food habits, with the increase in their income. Derivation of EC from ICC for neutral goods Economists often separate the impact of a price change into two Components such as the substitution effect and income effect. The substitution effect involves the substitution of good X good Y or vice versa due to a change in relative prices of the two goods. The income effect results from an increase or decrease in th result of the price change. The sum of these two effects is called the price effect. constant) is called the price effect. In indifference curve technique the price effect is measured along the Price Consumption Curve (PCC). The PCC is the equilibrium points corresponding to the changing slope of price line due to changes in the relative prices of the two goods, the Income effect refers to in his money income which is reflected by the Income Consumption Curve (ICC). Thus, the goods. But the purchases of a good By definition, Substitution Effect means the change in the quantity demanded of a commodity resulting from a change in its price relative to the prices of other The Price Effect (PE) or Effect of a price change is the sum of the Substitution Effect (SE) and Income Effect (IE) of a price change i.e. PE= SE + IE = (-) ve for normal goods (where SE outweigh IE of a price change in case of normal goods) can be discussed with the help of two Method as shown below. The Price Effect (PE) or Effect of a price change decomposed into the Substitution Effect (SE) and Income Effect (IE) of a price change can be derived through Hicksian Compensating Variation Method as shown in Figure 1.2.8 given below. Price Effect Split up into Substitution and Income Effects through Compensating Variation Method (for Normal good) In this method of compensating variation (J.R.Hicks), the income of the consumer is adjusted so as to offset the change in satisfaction and bring back the consumer to his original indifference curve i.e. the initial level of satisfaction which he was obtaining before the change in price occurred. This process is otherwise reflected by splitting up of price effect into substitution and income effect of a price change as shown in the figure 1.2.8. It can be seen from the figure 1.2.8 that a fall in the price of good X resulted in an increase in quantity demanded from M to N. This is the total price effect (i.e. Price effect is negative) which can be split into two separate effects such as substitution and income effects. The substitution effect is the increase in the quantity bought as the price of a commodity falls, after adjusting income so as to keep the real purchasing power of the consumer the same as before. This adjustment in income is called Compensating Variation and is shown graphically by a parallel shift of the new budget line (i.e. compensated Budget line AB as shown in figure 1.2.8) until it becomes tangent to the initial Indifference Curve (i.e. IC1). The budget line AB is tangential to IC1 at point S which is at the right side of the original tangential point Q as depicted in figure1.2.8. The movement from point Q to S shows the Substitution Effect of the price change implying the fact that the consumer will buy more of good X (X being cheaper due to fall in its price) now by substituting Y for X. However, the compensating variation is a device which enables the isolation of substitution effect, but does not show the new equilibrium of the consumer. This is defined by point R on higher Indifference curve i.e. IC2. The consumer has in fact a higher purchasing power, and if the commodity is normal, he will spend some moré of his increased real income on good X, thus moving from K to N (as shown in figure 1.2.8).The movement from K to N of point S to R is called as income effect of a price change. The income effect of a price change is negative for normal goods and it reinforces the negative substitution effect. So the total price effect is negative in the case of normal goods. The price effect can be split up into substitution and income effects through an alternative method of equivalent variation in income. The reduction in price of a commodity increases increase in satisfaction can be achieved through bringing about an increase in his income, prices remaining constant. The increase in income of the consumer, prices of goods remaining the same, enables him to move to a higher subsequent indifference curve at which he in fact reaches with reduction in price of a good is called equivalent variation in income because it represents the variation in income that is equivalent in terms of gain in satisfaction to a reduction in price of the good. Thus, in this equivalent income-variation method substitution effect is shown along the subsequent indifference curve rather than the original one. How this price effect is decomposed into income and substitution effects through equivalent variation in income is shown in Fig. 1.2.8 (a). When price of good X falls, the consumer can purchase more of both the goods, that is, the purchasing power of his given money income rises. It means that after the fall in price of X if the consumer buys the same quantities of goods as before, then some amount of money will be left over. In other words, the fall in price of good X will release some amount of money. Money thus released can be spent on purchasing more of both the goods. It therefore follows that a change in price of the good produces an income effect. When the power to purchase goods rises due to the income effect of the price change, the consumer has to decide how this increase in his purchasing power is to be spread over the two goods he is buying. How he will spread the released purchasing power over the two goods depends upon the nature of his income consumption curve which in turn is determined by his preferences about the two goods. From above it follows, that, as a result of the increase in his purchasing power (or real income) due to the fall in price, the consumer will move to a higher indifference curve and will become better off than before. It is as if price had remained the same but his money income was increased. In other words, a fall in price of good X does to the consumer what an equivalent rise in money income would have done to him. As a result of fall in price of X, the consumer can therefore be imagined as moving up to a higher indifference curve along the income consumption curve as if his money income had been increased, prices of X and Y remaining unchanged. Thus, a given change in price can be thought of as an equivalent to an appropriate change in income. Price effect split into Income and Substitution effects through an Equivalent Variation in Income Method It will be seen from Fig. 8.44 that with price line PL1, the consumer is in equilibrium at Q on indifference curve IC1. Suppose price of good X falls, price of Y and his money income remaining unaltered, so that budget line is now PL2. With budget line PL2, he is in equilibrium at R on indifference curve IC2. Now, a line AB is drawn parallel to PL1 so that it touches the indifference curve IC2 at S. It means that the increase in real income or purchasing power of the consumer as a result of the fall in price of X is equal to PA in terms of Y or L1B in terms of X Movement of the consumer from Q on indifference curve IC1 to S on the higher indifference curve IC2 along the income consumption curve is the result of income effect of the price change. But the consumer will not be finally in equilibrium at S. This is because now that X is relatively cheaper than Y, he will substitute X, which has become relatively cheaper, for good Y, which has become relatively dearer. It will be gainful for the consumer to do so. Thus the consumer will move along the indifference curve IC 2 from S to R. This movement from S to R has taken place because of the change in relative prices alone and therefore represents substitution effect. Thus the price effect can be broken up into income and substitution effects, showing in this case substitution along the subsequent indifference curve. In Fig 1.2.8 (a) the magnitudes of the various effects are: Price effect (Q to R) = MN Income effect (Q to S) = MH Substitution effect (S to R) = HN So, Price effect = MH + HN = Income Effect + Substitution Effect of substitution and income effects are slightly different from that of the effect of a price change is shown in the figure 1.2.8.1. Given the price and income initially the consumer is in equilibrium at point Q tangential point of PL1 and IC1) With a fall in price of good X the price line shift to PL2 from the same origin and hence the consumer achieves the equilibrium at point R on IC3. The movement from represents Price Effect. Now, in order to find out the substitution effect the money income of the consumer be reduced by such an amount that he could buy, if so desires, the old combination Q Thus a line AB which is parallel to line PL2 has been so drawn that it passes through point Q Now, the consumer can have at Q if he so desires, but actually he will not buy the combination at Q because good X is now relatively cheaper than before. It will pay him to substitute X for Y and hence he will be in equilibrium at point S on IC2. The movement from to represents money income taken away from the consumer is restored, he will move from S on IC2 to R on IC3. The movement from to represents representing Price Effect can be broken up into to representing Substitution Effect and to representing Substitution effect causes movement from a lower indifference curve to a higher one. Price Effect is decomposed into Substitution and Income Effects The income effect for the inferior commodity is negative. But the income effect of a price change in case of inferior goods is positive. For instance, if good X is an inferior good, the income effect of a fall in the price of good X will be positive because as the real income of the consumer increases, less quantity of X will be demanded. This is so because price and quantity demanded move in the same direction. On the other hand, the negative substitution effect will increase the quantity demanded of good X. The negative substitution effect is stronger than the positive income effect in case of inferior goods so that the total price effect is negative. It means that when the price of inferior good falls, the consumer purchases more of it due to compensating variation in income. The case of good X as an inferior good is depicted in figure 1.2.8.2. It is observed from the figure that initially the consumer is in equilibrium at point R and with the fall in the price of good X he moves to point T. The movement from point R to T (i.e. from B to E on horizontal axis) is the Price Effect. By compensating variation in income, he is in equilibrium at point H on the new budget line MN along the original indifference curve I1.The movement from point R to H (i.e. from B to D on horizontal axis) is the Substitution Effect. To isolate the income effect, return the increased real income to the consumer which was taken from him so that he is again at point T (tangency of PQ1 and I2). The movement from point H to T (i.e. from D to E on horizontal axis) is the Income Effect of a fall in price of good X. The income effect is positive because the fall in the price of inferior good X leads to decrease in the quantity demanded of X by DE via compensating variation in income. However, in case of an inferior good the negative substitution effect is greater than positive income effect so that the total price effect is negative. Thus Price effect (-) BE = (-) BD (substitution effect) + DE (income effect). Thus the slope of demand curve is doward sloping even in the case of inferior good. Price Effect Split up into Substitution and Income Effects through Compensating Variation Method (for Inferior good) The good for which law of demand does not operate is called Giffen good. It is after Robert Giffen who found that potatoes were indispensible food items for the poor peasants of Ireland. He observed during the famine of 1848 that, a rise the price of potato leads to an increase in its quantity demanded. Thereafter, a fall the price of potato leads to an decrease in its quantity demanded. This direct relationship between the price and quantity demanded for the essential food item is called Giffen Paradox. In case of Giffen goods, the positive income effect is stronger than negative substitution effect so that the consumer buys less of it when its price falls. Thus the total price effect is positive as shown in the figure 1.2.8.3. for the Giffen good X. The movement from point R (initial equilibrium) to point T (equilibrium point when price of X falls) is known as Price effect where the consumption of good X is found reduced by BE. To isolate the substitution effect, the increased real income due to fall in the price of good X is withdrawn from the consumer by drawing the budget line MN parallel to PQ1 and tangent to the original indifference curve I1 at point H. Thus the movement from point R to H represents Substitution effect which is negative as the consumer buys BD i.e. more of X due to fall in the price of X, real income being constant. To isolate the income effect, when the income that was taken away from the consumer is returned to him, he moves from point H to T so that he reduces the consumption by a large quantity DE. This is the positive income effect because with the fall in the price of Giffen good X, its quantity demanded is reduced by DE via compensating variation in income. Thus, in the case of a Giffen good the positive income effect is stronger than that of negative substitution effect and hence the total price effect is positive. That is why, the demand curve for a Giffen good has positive slope. Price Effect Split up into Substitution and Income Effects through Compensating Variation Method (for Giffen good) Indifference curve analysis can be applied to show why the demand curve usually slopes downward. To analyse it let us take commo other good remains constant. The top part of Figure 1.2.9 is a conventional indifference curve diagram. The consumer is in equilibrium at point B2 on the original budget line AF and indifference curve I2 consuming OQ2 of good X equilibrium will be able at point B3 on the higher indifference curve I3 consuming more of good X (i.e. OQ3) 1 on the lower indifference curve I1 consuming less of good X (i.e. OQ1). Thus joining the Points B1, B2 and B3 the price consumption curve (PCC) can be obtained which reveals the change in quantity demanded of good X due to the change in price of good X remaining other things constant. The bottom part of the Fig. 1.2.9 is derived from the top part. In both parts, the horizontal axis shows the quantity of good X which will be bought, but in the bottom part of the diagram, the vertical axis shows the price of good X ( whereas the vertical axis of top part of the diagram shows good Y). This bottom part of the diagram is showing a demand curve derived from the PCC. The point G derived from the point B2 of PCC (tangential point of price line AF and IC1 i.e. I1 in the figure) reveals the quantity demanded of good X i.e. OQ2 given the price of X i.e. P2 and other things. When the price of 3 of PCC corresponding to and IC3 i.e. I3 in the figure indicating more of quantity purchased of good X when its price falls. The point H in bottom part of the figure is derived corresponding to the point B3 of PCC indicates increase in the quantity demanded of good X i.e. OQ3 when its price decreases to P3. Similarly, consumer gets equilibrium at point B1 of PCC corresponding to and IC1 i.e. I1 in the figure indicating less of quantity purchased of good X when its price increases. The point E in bottom part of the figure is derived corresponding to the point B1of PCC indicates decrease in the quantity demanded of good X i.e. OQ1 when its price increases to P1. So joining together these points G, H and E the demand curve for good X, which slopes down to the right, is said to be derived from PCC. The slope of the curve will depend on the cons in the top part of the diagram. The indifference curve approach developed by Prof. Hicks discarded the Marshallian assumptions of cardinal measurement of utility and suggested ordinal measurement. An indifference curve (IC) is the locus of various points where each point represents the combination of two goods (e.g. good X and good Y) in such a way that whatever combination the consumer will choose that will give him the same satisfaction. In other words, the consumer is indifference towards the consumption any of the combination of two goods on the same IC. Thus, the IC is slopping downward as some unit of good Y is to be sacrificed to have an additional unit of good X. Hence the slope of IC is also known as Marginal Rate of Substitution of one good for other (e.g. MRSxy). Further IC is convex to the origin (i.e. diminishing MRSxy).Higher IC gives higher Satisfaction and vice versa. Two ICs cannot intersect to each other. IC canot take any other shape other than downward sloping with convexity. The budget line refers to the consumption of any combination with the given budget. It is also sloping downward and its slpe is represented by the ratio of price of good X to price of good Y. The budget line shift to the right and left from the same origin with the fall and rise in price of good X respectively, given the price of goody and money income. However the budget line shifts paralelly to the right or left with the increase or decrease in the level of income. Based on the properties of IC and budget line, the consumer will be at equilibrium provided at equilibrium the two conditions (necessary and sufficient conditions) are satisfied i.e. Slope of IC (i.e. MRSxy) = Slope of Budget line (Px/Py) and IC must be convex (i.e. diminishing MRS xy) to the origin at equilibrium point. The effect of a price change of a commodity on the quantity consumed of that commodity (given the price of other goods and money income) is called Price Effect. So the price effect in case of normal goods is negative and for Giffen goods it is positive. The curve which represents the price effect is called as Price Consumption curve (PCC). The shape or slope of the PCC depends on the price elasticity of demand. In other words, the downward sloping price consumption curve (PCC) for a good means that demand for the good is elastic, upward-sloping PCC means that demand for the good is inelastic and horizontal straight-line PCC means that demand for the good is unitary elastic. Income effect refers to of a change in his money income which is reflected by the Income Consumption Curve (ICC). The shape of ICC for normal goods is positive but it is backward bending for inferior goods. The change in the pattern of consumption expenditure (that is, decline in the proportion of income spent on food and other necessities and increase in the proportion of income spent on Thus, the curve showing the relationship between the levels of income and quantity purchased of particular commodities can be called as Engel curve which can be derived from income consumption curve (ICC). The Engel curve for necessary goods is upward-sloping but for luxury goods it is upward- sloping but concave in shape. The Engel curve for inferior goods is backward bending. The Substitution effect can be derived from the decomposition of price effect into income and substitution effect by Compensating Variation Method (Hicksian method) or Cost Difference Method (Slut price change is negative and substitution effect of a price change is negative in case of normal goods. In case of inferior goods the negative substitution effect outweighs the positive income effect of a price change and hence price effect is negative. But in case of Giffen goods the positive income effect of a price outweigh the negative substitution effect and hence price effect is positive. The law of demand can be established and demand curve can be derived from the Price Consumption Curve. 2. Define Indifference Curve (IC). Discuss its properties. 3. What is IC? How consumer equilibrium is achieved under IC analysis? 4. Define Price Consumption Curve. Discuss its relationship with price elasticity of demand. 5. Define Income Consumption curve (ICC). Discuss how Engel Curve is derived from ICC. 6. Discuss about the Engel Curve. 7. Define substitution effect. Identify substitution effect from the decomposition 0f price effect under compensating variation method. 8. Discuss the breaking up of Price effect in to income and substitution effect by cost difference method. 9. Discuss the derivation of demand curve from the price effect After going through this unit, you should be able to: Understand the economics of production Discuss the production function Understand the set of conditions required for efficient production Understand the estimation of production function Structure 2.1.1 Production Function 2.1.2 Production Function with one Variable Input (SRPF) 2.1.3 Production Iso-quants & Marginal Rate of Technical Substitution 2.1.4 Iso-cost Line 2.1.5 The Optimal Combination of Resources (Producers Equilibrium LRPF) 2.1.6 The Expansion Path 2.1.7 Economic Region of Production 2.1.8 Returns to Scale Concept 2.1.9 Returns to scale using Iso-quant 2.1.10 Summary 2.1.11 Self-Assessment Questions In economics, a relates physical output of a production process to physical inputs or factors of production. Production function denotes an efficient combination of inputs and outputs. The production function is of two types such as Short-run and Long run production is capital input , in short run one factor normally capital (K) is constant (or fixed) and the other i.e. labour is assumed as variable factor. But in long run all the factors of production are variable. The behaviour of short-run production function is explained by Law of Variable Proportion or Law of Diminishing MPL whereas the behaviour of long-run production function is explained by Law of Returns to scale. The law of variable proportion or law of diminishing marginal product of labour studies the behaviour of short run Production function as discussed below. Law of Variable Proportion To simplify the interpretation of a production function, it is common to divide its range into 3 stages. Given the capital, in the variable input is being used with increasing output per unit. Total product (TP), Average Product (AP) and Marginal Product (MP) of variable input (i.e. Labour) are found increasing in this stage. The point at which TP stops to increase at an increasing rate and start to increase at a diminishing ate is called as Point of inflexion. Stage 1 ends at the point of intersection of MP at the highest point of AP. This stage indicates underutilisation of capital. In , output increases at a decreasing rate, and the average and marginal physical product are declining but positive. The optimum input/output combination for the price-taking firm (or rational producer) will be in stage 2. In , too much variable input is being used relative to the available fixed inputs: variable inputs are over-utilized (MP of Labour is negative) in the sense that their presence on the margin obstructs the production process rather than enhancing it. The TP and AP of variable inputs are found decreasing in this state and MP of variable input (i.e. Labour) is found negative in this stage. At the boundary between stage 2 and stage 3, the highest possible output is being obtained from the fixed input. In other words the second stage is preferred by rational producer as optimum stage. The optimal allocation of resources takes place under short-run production function provided the condition Marginal Revenue Product of Labour (MRPL) = Wage (W), where MRPL = Marginal Product of Labour (MPPL) X Price per unit of output (P) is satisfied. Stage-1: Increasing Returns to variable proportion Stage-2: Diminishing Returns to variable proportion Stage-3: Negative Returns to variable proportion a curve that shows the varying combinations of factors of production such as labour and capital that can be used to produce a given quantity of a product with a given state of technology (where factor inputs can be substituted for one another in the production process). The slope of isoquant reflect process which is called Marginal rate of Technical Substitution (MRTS). The isoquant is sloping downward to the right (as shown in figure 1.2.3) as because the two inputs can be substituted for one another in the production process. Further isoquant is convex to the origin indicating the fact that when the quantities of one factor (such as Labour) is increased, the less of another factor is (such as Capital) will be given up, if output level is to be kept constant. Thus MRTSL-K declines as we move down any isoquant from left to right. Isoqant It means when the amount of one factor input is increased that of other input must be decreased in order to maintain a given level of output so that any combination two factors (lying on the same isoquant) chosen will yield the same level of output which is depicted in figure 2.1.3.1. The convexity of isoquant indicates that MRTS is diminishing which means that as the quantities of one factor (such as Labour) is increased, the less of another factor is (such as Capital) will be given up, if output level is to be kept constant as shown in figure 1.2.3.1. The Elasticity of Factor Substitution (ES) refers to the ratio of the percentage change in the ratio of Capital (K) and labour (L) to the percentage change in MRTS L-K which can be shown symbolically as follows. Iso-quant map represents a set of isoquants describing production function of a firm where a higher isoquant represents a larger quantity of output than the lower one as depicted in figure 1.2.3.2. by definition each isoquant represents a specific quantum of output. Therefore, if two isoquants intersect to each other it would involve logical contradiction as a particular isoquant at a time may be representing a small as well as a large quantity of output. Thus two isoquants cannot intersect to each other as shown in figure 1.2.3.3. Isoquant cannot be circular as it contradicts the convexity condition of an isoquant as shown in figure 1.2.3.4. Isoquant-downward sloping & convex to the origin. Isoquant Map Intersection of Two Isoquants Circular shape of Isoquant The line is an important component when analyzing producer's behavior. The line illustrates all the possible combinations of two factors that can be used at given costs and for a given producer's budget. In simple words, an line represents a combination of two inputs that can be purchased for the same total money outlay. Its slope reflects the relative prices of two factors of production (i.e.Ratio of Price of labour to Price of capital= w/r)..Changes in Iso-Cost Line as a Result of Changes in the Price of Labour.Changes in Iso-Cost Line as a Result of Changes in the income combination of factors. A profit maximisation firm faces two choices of optimal combination of factors (inputs). 1. To minimise its cost for a given output; and 2. To maximise its output for a given cost. Thus the least cost combination of factors refers to a firm producing the largest volume of output from a given cost and producing a given level of output with the minimum cost when the factors are combined in an optimum manner. We study these cases separately. In the theory of production, the profit maximisation firm is in equilibrium when, given the cost- price function, it maximises its profits on the basis of the least cost combination of factors. For this, it will choose that combination which minimizes its cost of production for a given output. This will be the optimal combination for it. This analysis is based on the following assumptions: 1. There are two factors, labour and capital. 2. All units of labour and capital are homogeneous. 3. The prices of units of labour (w) and that of capital (r) are given and constant. 4. The cost outlay is given. 5. The firm produces a single product. 6. The price of the product is given and constant. 7. The firm aims at profit maximisation. 8. There is perfect competition in the factor market. Given these assumptions, the point of least-cost combination of factors for a given level of output is here the isoquant curve is tangent to an iso-cost line. In the Figure 2.1.5.1, the iso-cost line GH is tangent to the isoquant 200 at point M. output at point M with the given cost-outlay GH. At this point, the firm is minimising its cost for producing 200 units. Cost-Minimisation for a Given Output Any other combination on the isoquant 200, such as R or T, is on the higher iso-cost line KP which shows higher cost of production. The iso-cost line EF shows lower cost but output 200 cannot be attained with it. Therefore, the firm will choose the minimum cost point M which is the least-cost factor combination for producing 200 units of output. M is thus the optimal combination for the firm. The point of tangency between the iso-cost line and the isoquant is an important first order condition but not a necessary condition for the 1. The first condition is that the slope of the iso-cost line must equal the slope of the isoquant curve. The slope of the iso-cost line is equal to the ratio of the price of labour (w) to the price of capital (r) i.e. r. The slope of the isoquant curve is equal to the marginal rate of technical substitution of labour and capital (MRTSL-K) which is, in turn, equal to the ratio of the marginal product of labour to the marginal product of capital (MP L/MPK). Thus it can be written as: 2. The second condition is that at the point of tangency, the isoquant curve must be convex to the origin. In other words, the marginal rate of technical substitution of labour for capital (MRTS LK) must be diminishing at the point of tangency for equilibrium to be stable. Both the situations are impossibilities because nothing can be produced either with only labour or only capital. Therefore, the firm can produce the same level of output at point M where the isoquant curve IQ is convex to the origin and is tangent to the iso-cost line GH. The analysis assumes that both the isoquants represent equal level of output IQ = IQ1 = 200. The firm also maximises its profits by maximising its output, given its cost outlay and the prices of the two factors. This analysis is based on the same assumptions and conditions for the equilibrium of the firm as given above. The firm is in equilibrium at point P where the isoquant curve 200 is tangent to the iso-cost line CL as shown in the Figure 2.1.5.2. At this point, the firm is maximising its output level of 200 units by employing the optimal combination of OM of capital and ON of labour, given its cost outlay CL. But it cannot be at points E or F on the iso-cost line CL, since both points give a smaller quantity of output, being on the isoquant 100, than on the isoquant 200. Output-Maximisation for a given Cost The firm can reach the optimal factor combination level of maximum output by moving along the iso-cost line CL from either point E or F to point P. This movement involves no extra cost because the firm remains on the same iso-cost line. The firm cannot attain a higher level of output such as isoquant 300 because of the cost constraint. Thus the equilibrium point has to be P with optimal factor combination OM and ON. At point P, the slope of the isoquant curve 200 is equal to the slope of the iso-cost line CL i.e. and the second condition is that the isoquant curve must be convex to the origin at the point of tangency with the iso-cost line. equilibrium. Suppose, after attaining equilibrium, if a producer is willing to increase its production, then he/she needs to determine the combination that is required to reach a new equilibrium state. Let us consider the following figure in which the producer is willing to produce Q1 units of outpu and achieves its equilibrium at point R1. Now, the producer wants to produce Q2 units of output instead of Q1 units. In such a case, the equilibrium would be achieved at the point R2, as shown in the Figure. Similarly, the equilibrium point for producing Q3 is R3. When the points R1 , R2 and R3 are joined, a straight line is obtained, which is called expansion path or scale line. This line is termed as scale line because producer needs to adjust its scale of production according to this line to achieve the output he/she desires. On the other hand, this line is also termed as expansion path because the producer needs to expand his/her output by following this path when the prices of factors remain constant. Producers would prefer to move along the scale line to increase the output to get maximum output at least cost with fixed factor prices. Expansion path The ridge lines are the locus of points of isoquants where the marginal products (MP) of factors are zero. The upper ridge line implies zero MP of capital and the lower ridge line implies zero MP of labour. Production techniques are only efficient inside the ridge lines. Areas outside the economic region of production mean that at least one of the inputs has negative marginal productivity. This region is marked by what are called ridge lines, which are simply the boundaries beyond which one of the two factors is being overused. The feasible economic region of production is depicted in figure 2.1.7 where A and B are representing upper and lower ridge lines respectively. At each point of A (such as A1----A4) Marginal Product of Capital is zero (MPK = 0) and at each point of B(such as B1----B4) Marginal Product of Labour is zero (MPL = 0). The Feasible Economic Region of Production lies between the points A1----A4 and B1----B4. Economic Region of Production The term arises in the context of a firm's production function. It explains the behaviour of the rate of increase in output (production) relative to the associated increase in the inputs (the factors of production) in the long run. In the long run all factors of production are variable and subject to change due to a given increase in size (scale). The returns to scale are of the following three types: Constant Returns to Scale Increasing Returns to Scale, and Decreasing Returns to Scale. If output increases by that same proportional change as all inputs change then there are (CRS). If output increases by more than that proportional change in inputs, there are (IRS). If output increases by less than that proportional change in inputs, there are (DRS). The reflects the relationships between its inputs - namely physical capital and labor - and the amount of output produced. It's a means for calculating the impact of changes in the inputs, the relevant efficiencies, and the yields of a production activity. Here's the basic form of the Cobb-Douglas production function: Q = total production (the real value of all goods produced in a year) L = labour input (the total number of person-hours worked in a year) K = capital input (the real value of all machinery, equipment, and buildings) A = total factor productivity ( i.e Constant) and are the output elasticities of labour and capital respectively. Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus. For example, if = 0.45, a 1% increase in capital usage would lead to approximately a 0.45% increase in output. If, + = 1, Constant Returns to Scale If, + > 1, Increasing Returns to Scale If, + < 1, Decreasing Returns to Scale The return to scale may be shown diagrammatically on an expansion path by the distance -level-of output which are multiples of some base level of output e.g., 100,200,300 etc. The distance between successive multiple isoquants along the expansion path (OR in the figure) is constant (i.e. OD = DE = EF as shown in the diagram). It means Doubling factor inputs (Labour & Capital) achieves double the level of the initial output; trebling inputs achieves treble output and so on. In this case the Production function is homogeneous of degree one. The constant returns to scale as shown in the figure indicate the facts as follows. 100 units of output require 1(2C + 2L) = 2C + 2L where, C=Capital and L= Labour 200 units of output require 2(2C + 2L) = 4C + 4L 300 units of output require 3(2C + 2L) = 6C + 6L Constant Returns to Scale The distance between successive multiple isoquants along the expansion path (OR in the figure) decreases (i.e. OA > AB > BC as shown in the diagram). It means by doubling inputs (Labour & Capital), output is more than doubled. In other words, to get equal increases in output, lesser proportionate increases in both the inputs (labour & Capita) are required. In this case the Production function is homogeneous of degree greater than one. The increasing returns to scale as shown in the figure indicate the facts as follows. 100 units of output require 3C + 3L 200 units of output require 5C + 5L 300 units of output require 6C + 6L Increasing Returns to Scale The distance between successive multiple isoquants along the expansion path (OR in the figure) increases (i.e. OG < GH < HK as shown in the diagram). It means by doubling inputs (Labour & Capital), output increases by less than twice its original level. In other words, to get equal increases in output, larger proportionate increases in both the inputs (labour & Capita) are required. In this case the Production function is homogeneous of degree less than one. The increasing returns to scale as shown in the figure indicate the facts as follows. Decreasing Returns to Scale The production function (PF) is of two types such as Short-run and Long-run. The Law of variable proportion explains the behavior of short-run PF whereas Returns to explain the behavior of long-run PF. The law of variable proportion explains the behavior of TP, MP and AP curve when additional units of labour is employed against the fixed factor ( i.e. Capital) with the help of three stages. Ultimately, a rational producer will choose the second stage of production where MP L is diminishing but positive. The prod -run can be explained using Isoquant and Isocost line. The producer achieves equilibrium level of output corresponding to equilibrium amount of labour and capital used which can be explained under two circumstances such as Minimisation of cost for a Given Output and Maximisation of output for a Given Cost. In both the cases the conditions of equilibrium will be the same such as the necessary condition is Slope of Isoquant i.e. MRTSL-K is equal to Slope of Isocost line i.e.W/r and the sufficient condition is Isoquant must be convex to the origin at equilibrium point. The expansion path explain the equilibrium at its each point. The feasible economic region of production lies between the upper and lower ridge lines. The returns to scale are of three types such as Constant, Increasing and decreasing returns to scale. If the proportionate change in output is equal to the change in inputs it is called constant returns to scale. If the proportionate change in output is greater than the change in inputs it is called increasing returns to scale. If the proportionate change in output is less than the change in inputs it is called decreasing returns to scale. The returns to scale can be explained with the help of Cob-Douglash PF and with the help of distance between the consecutive Isoquants on the expansion path. 1. Discuss the Law of Variable Proportion. 2. der two variable case. 3. -run. 4. Write Short notes on (a) Returns to Scale (b) Iso-cost line (c) Expansion path (d) Economic Region of Production (e) Isoquant Understand the cost of production Estimate the short-run cost and cost curve Draw and analyze the Long-run Average Cost Curve 2.2.6 Cost of Production: Social and private costs of production 2.2.7 Short run Cost and Cost Curve 2.2.8 Long run Average Cost Curve and its implications. 2.2.9 Summary 2.2.10 Self Assessment Questions The distinction between Private and Social costs of production is important to understand for assessing the socially efficient rate of output to be produced in an economy. Private costs refer to direct costs to the producer for producing the good or service. For instance, Private costs for a producer of a good, service, or activity include the costs the firm pays to purchase capital equipment, hire labor, and buy materials or other inputs. Private costs to firms or individuals do not always equate with the total cost to society (social costs) for a product, service, or activity. The difference between private costs and total costs to society of a product, service, or activity is called an external cost (externalities). The pollution (negative externalities) due to production activities is an example of external cost. External costs are directly associated with producing or delivering a good or service, but they are costs that are not paid directly by the producer. In other words, External costs (or externalities) are not reflected on firms' financial statements as it is paid by the third party i.e. the society. So due to external costs ( or Externalities) market failures and economic inefficiencies may result at the local, state, national, and even international level. Thus, the external costs must be included in the social costs to ensure that society operates at a socially efficient rate of output. Hence, Social costs include both the private costs and any other external costs to society arising from the production of a good or service. Private Costs = Social Costs External Costs Social Costs = Private Costs + External Costs If external costs > 0, then private costs < social costs or social costs > private costs A socially efficient output rate in a competitive market is reached when social costs (both private and external costs) are considered in production. The existence of external costs has implications for product prices, output levels, resource usage, and competition. When significant external costs are associated with a good (or service), then the price of the good is too low (because external costs are not being paid) and its output level is too high, relative to the socially efficient rate of output for the good. Thus bottom line, unless costs and prices include external costs, the market will not produce a socially efficient result as shown in the figure 2.2.1. In the figure 2.2.1 the intersection of the demand curve and marginal Social cost curve represents the socially efficient rate of production in a competitive market i.e. at point S corresponding to output Os and price Ps. Here the marginal social cost curve equals the marginal private cost curve plus the marginal external cost curve. The comparison of prices and outputs as to how external costs affect resource allocation reveals that if a firm pays only the private costs and avoids paying the external costs associated with their product, then output and prices would be determined at point P where the marginal private cost curve meets the demand curve. At P price equals Pp and output equals Op. From a resource standpoint, the important point of this comparison is that including the marginal external costs of production and allocating resources based on the full social cost results in a higher price for the good (Ps > Pp) and less output (Os < Op)

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