Micro Economics Textbook PDF - Telangana

 MICRO ECONOMICS B.A. I - Year (1st Semester) Authors Dr. Akkenapally Meenaiah, M.A., M.Phil., Ph.D. Retired HOD Economics : N.G College Nalgonda (Autonomous), President : Nalgonda Economics Forum, Executive member : Telan...

 MICRO ECONOMICS B.A. I - Year (1st Semester) Authors Dr. Akkenapally Meenaiah, M.A., M.Phil., Ph.D. Retired HOD Economics : N.G College Nalgonda (Autonomous), President : Nalgonda Economics Forum, Executive member : Telangana Economics Association Economy Columnist : Velugu, Sakshi, Namaste Telangana & Nava Telangana Daily News Papers. T. Bhasker Reddy, M.A., SET. Asst. Prof. of Economics, GDC (W), Nalgonda. Associate President : Nalgonda Economics Forum M. Shathavahana, M.A. Lecturer in Economics, Sri Raghavendra Degree College, Nalgonda, Vice President: Nalgonda Economics Forum. Sk. Sulthana, M.A., SET. Lecturer in Economics TSWRDC (W) Nalgonda, Secretary: Nalgonda Economics Forum. P. Naresh Kumar, M.A., SET. Faculty of Economics B.C & S.C, T.S Study Circles, Treasurer: Nalgonda Economics Forum. D. Pravalika, M.A., SET Lecturer in Economics TTWRDC (W) Suryapet, Executive Member: Nalgonda Economics Forum. M.Shobha, M.A., SET. Lecturer in Economics TSWRDC (W) Suryapet, Executive Member: Nalgonda Economics Forum. M. Kavitha, M.A., SET. Faculty of Economics, Nalgonda Economics Forum, Executive Member: Nalgonda Economics Forum. (i) Micro Economics (First Year - 1st Semester) by NALGONDA ECONOMICS FORUM First Edition : September, 2019 Copies : 1000 Cover Page by Giri Babu Kathula Publishers : NALGONDA ECONOMICS FORUM PUBLICATIONS (Regd. No. 297/13) Nalgonda - Telangana Cell : 94901 38118, 70137 74141, 74166 51665 Copies Available at P. Naresh Kumar, Treasurer & Academic Co.ordinator Nalgonda Economics Forum, MVN VIGNANA KENDRAM, Near Subash Chandrabose Statue, Doddi Komaraiah Bhavan, Nalgonda - 508 001. Cell : 94901 38118, 70137 74141, 74166 51665 DTP & Printed at SHREERAMA Graphics Prakasham Bazar, Nalgonda -508 001 (TS) Phone : 94906 70002, 9505618383 Price Rs. 100/- ( ii ) Foreword The Nalgonda Economics Forum came into existence on the 12th of January 2007and was subsequently registered on 10th May, 2013 with the registered number 297/ 2013. It is the proudest boast of the Forum that as many as 450 students got selected to PG courses in different universities. And students trained at this Forum stood in the first rank in the PG entrance examinations both at the Osmania and the Kakatiya universities consecutively in 2016, 2017 and 2018 academic years. Most other students of this study forum got through SET, NET and other such examinations, besides as many five Ph. Ds holders to its credit. And recently, five candidates have become lecturers of different Residential Colleges, four have become PGTs, and about 25 candidates are working as faculty members at different colleges. It is also to be particularly mentioned that the Forum, keeping in view the year after year changing examination patterns, is updating itself with a view to catering to the needs of the examination goers. Hence we created a website of our own to help students face the Computer Based Tests, providing study material, and bringing to the doorsteps the latest relevant information that boosts up the students morale and the self-confidence. As to the aims and objectives of the Forum, it is to be added that it has been offering free coaching to candidates taking different competitive examinations like Group Tests, and SI, Police Constable and Banking examinations. To be mentioned next are the debates and seminars being conducted from time to time to enable students develop economic awareness, establishment of a fully equipped library, conducing very frequently quiz and essay-writing competitions, and holding model tests for various competitive examinations and presenting cash awards to developing competitive spirit among our wards. As has already been made apprehensible as regards the purpose behind bringing into existence this Nalgonda Economics Forum, the very spirit of the essential motto of the organizers has all through been seeing to it that all sorts of academic, competitive and other such needs of the students of the subject of Economics are meticulously pinpointed out and duly made available to them the materials as per their requirements. As a component of this goal, the organizers of the Forum have mooted out a project of bringing out Economics Textbooks for the UG students of the universities in the state of Telangana. Also again as part of this programme, in tune with the Choice Based Credit System that has come into vogue with the present academic year 2019-20, the Forum is now publishing a textbook MICRO ECONOMICS both in Telugu and English languages for the First Semester BA Economics students. In the process, the Forum will be bringing out textbooks for the subsequent semesters in due course to meet again the requirements of both Telugu and English media. Dr. Akkenepally Meenaiah President Nalgonda Economics Forum ( iii ) ( iv )  B.A. (ECONOMICS) SYLLABUS Semester - I MICRO ECONOMICS - I Discipline Specific Course - Paper - I MICRO ECONOMICS Module-I : CONSUMER BEHAVIOUR Ordinal utility Analysis: Properties of Indifference curves, concept of budget line, equilibrium of consumer, price consumption curve, income consumption curve, derivation of demand curve with the help of ordinal utility analysis. Concepts of price, income and substitution effects; separation of price effect: compensating variation and cost difference methods. Module-II : PRODUCTION ANALYSIS Concepts of Short run and long run production function; properties of iso-product curves, concept of factor price line, analysis of least cost input combination, concepts of expansion path and economic region of production, concept of returns scale and types of returns to scale. Linear and homogeneous production function, properties of Cobb-Douglas production function. Module-III : COST AND REVENUE ANALYSIS Cost concepts: Accounting, real, opportunity, explicit cost. Total cost, total fixed cost, total variable cost, average cost, average fixed cost, average variable cost, marginal cost and the relationship between average and marginal cost, derivation of long run average cost curve. Economies of scale: internal and external. Revenue concepts: total, average and marginal, relationship between Average revenue & marginal revenue and price elasticity of demand. Module--IV : MARKET STRUCTURE: IMPERFECT COMPETITION Monopoly: Equilibrium of a monopolist with price discrimination, degrees of price discrimination, welfare loss under monopoly. Monopolistic competition: characteristics, concepts of product differentiation and selling cost, analysis of resource wastage under monopolistic competition. Oligopoly: characteristics of oligopoly, reasons for price rigidity in non-collusive oligopoly. Duopoly: Augustin Cournot’s modern version of duopoly. Module-V : ANALYSIS OF BUSINESS FIRM, PROFIT AND PRICING STRATEGIES Characteristics of a business firm, objectives of business firm: profit maximization, sales revenue maximization, market share maximization, growth maximization. Profit concepts: Accounting and economic; break-even point and profit –volume analysis Pricing strategies: Cost plus pricing, marginal cost pricing, rate of return pricing, price skimming, penetration pricing, loss-leader pricing, mark-up pricing and administered prices. (v )  MODEL QUESTION PAPER COMMON CORE SYLLABUS (with effect from 2019-20) (For All Universities In Telangana State) B.A. ECONOMICS : FIRST YEAR - PAPER - I ( Micro Economics ) Time: 3 Hours Max. Marks : 80 PART - A ( 5x4 = 20 MARKS ) Answer any 5 of the following questions 1. Define ordinal utility and explain any two assumptions of ordinal utility analysis 2. Explain briefly about four factors of production 3. Cob-Douglas production function 4. Explain about the concept of opportunity cost 5. Explain any four internal economies of scale 6. Degrees of Price Discrimination 7. Explain any four features of duopoly market 8. Discuss briefly about break-even point PART - B ( 5x12 = 60 MARKS ) Answer all the following questions 9. a) Draw the indifference curve with the help of indifference schedule and explain the properties of indifference curve. (or) b) Explain the separation of price effect into income and substitution effects by compensating variation method. 10. a) Explain producer's equilibrium through iso-product curves. (or) b) Explain the theory of returns to scale. 11. a) Define average cost and marginal cost and explain the relationship between average and marginal cost. (or) b) Define average revenue and marginal revenue and explain the relationship between average revenue, marginal revenue and price elasticity of demand. 12. a) Explain the short run equilibrium of the firm under monopolistic competition market. (or) b) Define price rigidity and explain price rigidity with the help of kinky demand curve. 13. a) Define business firm and explain the characteristics of a business firm. (or) b) Explain the traditional and modern objectives of a business firm. ( v i)  INDEX 1. Consumer Behaviour................................................. 01 - 24 1.1 Ordinal Utility Analysis.................................................... 03 1.2 Indifference Curve Analysis.............................................. 04 1.3 Assumptions of Indifference Curve Analysis................... 04 1.4 Properties of Indifference Curve....................................... 05 1.5 The Marginal Rate of Substitution (MRSxy).................... 09 1.6 Concept of Budget Line..................................................... 10 1.7 Consumer's Equilibrium.................................................... 12 1.8 Price Consumption Curve................................................. 13 1.9 Income Consumption Curve.............................................. 15 1.10 Derivation of Demand Curve............................................ 17 1.11 Deriving Demand Curve for a Giffen Good...................... 18 1.12 The Substitution Effect - Hicks......................................... 19 1.13 Substitution Effect - Slutsky............................................. 20 1.14 Price Effect-Income and Substitution Effects-Hicks.................. 22 1.15 Price Effect-Income and Substitution Effects-Slutsky............... 23 2. Production Analysis................................................. 25 - 46 2.1 Production Function........................................................... 27 2.2 Short Run Production Function......................................... 27 2.3 Long Run Production Function......................................... 28 2.4 The Law of Variable Proportion......................................... 28 2.5 Iso-Quant Curves............................................................... 31 2.6 Properties of Iso-Product Curves....................................... 32 2.7 Concept of Factors Pricing Line- Iso-Cost Line................ 36 2.8 Iso Quant & Iso-Cost Curves............................................. 37 2.9 Least Cost Combination Analysis...................................... 38 2.10 Expansion Path.................................................................. 40 2.11 Economic Region of production (Ridge Lines).................. 41 2.12 Concept and Types of Returns to Scale............................. 42 2.13 Linear Homogeneous Production Function...................... 44 2.14. Properties of Cobb-Douglas Production Function............. 45 3. Cost And Revenue Analysis................................... 47 - 62 3.1 Cost Concepts..................................................................... 49 3.2 Short Run Costs and Cost Curves..................................... 50 3.3 The Relation between the Average and Marginal Cost Curve......... 53 3.4 Derivation of Long Run Average Cost (LAC) Curve................... 54 3.5 Economies of scale.............................................................. 56 3.6 Concepts of Revenue......................................................... 58 3.7 Relation between TR, AR, MR & Elasticity of Demand............. 61 (vii ) 4. Market Structure : Imperfect Competition............. 63 - 80 4.1 Monopoly............................................................................ 65 4.2 Monopoly: Price and Equilibrium..................................... 66 4.3 Price Discrimination under Monopoly.............................. 69 4.4 Degrees of Price Discrimination....................................... 69 4.5 Welfare Loss under Monopoly........................................... 71 4.6 Monopolistic Competition: Characteristics...................... 72 4.7 Equilibrium of a Firm under Monopolistic Competition.................. 73 4.8 Monopolistic competition: Selling Costs........................... 74 4.9 Monopolistic Competition: Product Differentiation................... 75 4.10 Resources Wastage under Monopolistic Competition................. 76 4.11 Characteristics of Oligopoly Market................................. 77 4.12 Non-Collusive Oligopoly.................................................... 78 4.13 Duopoly-Cournot Model..................................................... 79 5. Analysis of Business Firm, Profit And Pricing Strategies 81 - 95 5.1 Profit Maximisation........................................................... 83 5.2 Baumol's Model - Sales maximisation.............................. 85 5.3 Market Share Maximisation............................................. 86 5.4 Growth Maximisation Theory of Marris........................... 87 5.5 Accounting Profit and Economic Profit............................ 88 5.6 Break-Even Point............................................................... 89 5.7 Profit Volume Analysis...................................................... 90 5.8 Cost-Plus Pricing............................................................... 91 5.9 Marginal-cost pricing......................................................... 92 5.10 Rate of Return Pricing....................................................... 92 5.11 Price Skimming.................................................................. 93 5.12 Penetration Pricing............................................................ 93 5.13 Loss Leader Pricing........................................................... 94 5.14 Mark-up Pricing................................................................. 95 5.15 Administered Price............................................................ 95 Reference Books......................................................................... 96 (viii ) 1 John Richard Hicks 8th April 1904 - 20th May, 1989 CONSUMER BEHAVIOUR 1.1 Assumptions of Ordinal Utility Approach 1.2 Indifference Curve Analysis 1.3 Assumptions of Indifference Curve Analysis 1.4 Properties of Indifference Curve 1.5 The Marginal Rate of Substitution (MRSxy) 1.6 Concept of Budget Line 1.7 Consumer's Equilibrium 1.8 Price Consumption Curve 1.9 Income Consumption Curve 1.10 Derivation of Demand Curve 1.11 Deriving Demand Curve for a Giffen Good 1.12 The Substitution Effect - Hicks 1.13 Substitution Effect - Slutsky 1.14 Price Effect-Income and Substitution Effects-Hicks 1.15 Price Effect-Income and Substitution Effects-Slutsky 1 2 1.1 Ordinal Utility Analysis The Ordinal Utility approach is based on the fact that the utility of a commodity cannot be measured in absolute quantity, but however, it will be possible for a consumer to tell subjectively whether the commodity derives more or less or equal satisfaction when compared to another. The modern economists have discarded the concept of cardinal utility and instead applied ordinal utility approach to study the behaviour of the consumers. While the neo- classical economists believed that the utility can be measured and expressed in cardinal numbers, but the modern economists maintain that the utility being the psychological phenomena cannot be measured theoretically, quantitatively and even cardinally. The modern economist, Hicks, in particular, have applied the ordinal utility concept to study the consumer behaviour. He introduced a tool of analysis called “Indifference Curve” to analyze the consumer behaviour. An indifference curve refers to the locus of points each showing different combinations of two substitutes which yield the same level of satisfaction and utility to the consumer. Assumptions of Ordinal Utility Approach : 1. Rationality : It is assumed that the consumer is rational who aims at maximizing his level of satisfaction for given income and prices of goods and services, which he wish to consume. He is expected to take decisions consistent with this objective. 2. Ordinal Utility: The indifference curve assumes that the utility can only be expressed ordinals. This means the consumer can only tell his order of preference for the given goods and services. 3. Transitivity and Consistency of Choice: The consumer’s choice is expected to be either transitive or consistent. The transitivity of choice means, if the consumer prefers commodity X to Y and Y to Z, then he must prefer commodity X to Z. In other words, if X = Y, Y = Z, then he must treat X = Z. The consistency of choice means that if a consumer prefers commodity X to Y at one point of time, he will not prefer commodity Y to X in another period or even will not consider them as equal. 3 4. Nonsatiety: It is assumed that the consumer has not reached the saturation point of any commodity and hence, he prefers larger quantities of all commodities. 5. Diminishing Marginal Rate of Substitution (MRS) : The marginal rate of substitution refers to the rate at which the consumer is ready to substitute one commodity (X) for another commodity (Y) in such a way that his total satisfaction remains unchanged. The MRS is denoted as -ΔY/ΔX. The ordinal approach assumes that -ΔY/ΔX goes on diminishing if the consumer continues to substitute X for Y. 1. 2. Indifference Curve Analysis : Indifference curves are formulated based on ordinal utility analysis. They were originally introduced by British economist F.Y Edgeworth in the book Mathematical Physics - 1881 and American economist Irving Fisher (1892). Indifference curves were improved by the Italian economist Parito in 1906. It was developed by British economists J.R. Hicks and R.G.D. Allen in 1934. The indifference curve is the locus of the points where the customer gets equal satisfaction by consuming different combination of X and Y goods. 1. 3 Assumptions of Indifference Curve Analysis : The indifference curve analysis retains some of the assumptions of the cardinal theory, rejects others and formulates its own. The assumptions of the ordinal theory are the following: 1. The consumer acts rationally so as to maximise satisfaction. 2. There are two goods X and Y. 3. The consumer possesses complete information about the prices of the goods in the market. 4. The prices of the two goods are given. 5. The consumer’s tastes, habits and income remain the same throughout the analysis. 6. The consumer arranges the two goods in a scale of preference which means that he has both ‘preference’ and ‘indifference’ for the goods. He is supposed to rank them in his order of preference and can state if he prefers one combination to the other or is indifferent between them. 7. Both preference and indifference are transitive. 4 1.4. Properties of Indifference Curve 1. The slope of an indifference curve is negative, downward sloping, and from left to right. 2. An indifference curve is convex to the origin. 3. A higher indifference curves to the right gives higher level of satisfaction. 4. In between two indifference curves there can be a number of other indifference curves. 5. The numbers IC1, IC2, IC3, IC4.. etc. given to indifference curves are absolutely arbitrary. 6. Indifference curves can neither touch nor intersect each other. 7. An indifference curve cannot touch either axis. 8. Indifference curves are not necessarily parallel to each other. 9. If the two goods are perfect complements the indifference curve is L shaped. 10. If two goods are perfect substitutes, the indifference curve is a straight line with negative slope. 1. The slope of an indifference curve is negative, downward sloping, and from left to right. It means that the consumer to be indifferent to all the combinations on an indifference curve must leave less units of good Y in order to have more of good X. To prove this property, let us take indifference curves contrary to this assumption. In the below Figure 1.1 (A) combination B of OX1 +OY1 is preferable to combination A which has a smaller amount of the two goods. Therefore, an indifference curve cannot slope upward from left to right. In Figure 1.1 (B) combination B is preferable to combination A, for combination B has more of X and the same quantity of Y. So an indifference curve cannot be horizontal. In Figure 1.1 (C) the indifference curve is shown as vertical and combination B is preferred to A as the consumer has more of Y and the same quantity of X. Therefore, an indifference curve cannot be vertical either. Consequently, an indifference curve will be of negative slope, as shown in Figure (D) where A and B combinations give equal satisfaction to the consumer. As he moves from combination A to B he gives up less quantity of Y in order to have more of X. 5 2. An indifference curve is convex to the origin. The convexity rule implies that as the consumer substitutes X for Y, the marginal rate of substitution diminishes. It means that as the amount X is increased by equal amounts that of Y diminish by smaller amounts. The slope of the curve becomes smaller as we move to the right. To prove this, let us take a concave curve where the marginal rate of substitution of X for Y increases instead of diminishing, i.e., more of Y is given up to have additional units of X. In Figure 1.2 (A), If we take a straight line indifference curve, the marginal rate of substitution between the two goods will be constant, as in figure 1.2 panel (B) Thus an indifference curve cannot be a straight line. In figure 1. 2 panel (C) shows an indifference curve convex to the origin. Here the consumer is giving up less and less units of Y in order to have equal additional units of X Thus an indifference curve is always convex to the origin because the marginal rate of substitution between the two goods declines. 3. A higher indifference curves to the right of another represents a higher level of satisfaction and preferable combination of the two goods. In the adjoining figure 1.3 consider the indifference curves IC1 and IC2 and combinations N and A respectively on them. Since A is on a higher indifference curve and to the right of N. the consumer will be having more of both the goods X and Y. Even if the two points on these curves are on the same plane as M and A, the consumer will prefer the latter combination, because he will be having more of goods X though the quantity of goods Y is the same. 6  4. In between two indifference curves there can be a number of other indifference curves: There are number of indifference curves in between indifference curves like adjoining figure 1.4 5. The Numbers given to indifference curves are obsolutely orbitrary : The numbers IC1, IC2, IC3, IC4 etc. given to indifference curves are absolutely arbitrary. Any numbers can be given to indifference curves. The numbers can be in the ascending order. 6. Indifference curves can neither touch nor intersect each other : Indifference curves can neither touch nor intersect each other so that one indifference curve passes through only one point on an indifference map. What absurdity follows from such a situation can be shown with the help of adjoining figure 1. 5 (A) where the two curves IC1 and lC2 intersect each other. Point A on the IC 1 curve indicates a higher level of satisfaction than point B on the IC2 curve, as it lies farther away from the origin. But point B which lies on both the curves yields the same level of satisfaction as point A and B. Thus on the curve IC1 : A = C and on the curve lC2: B = C, A = B. This is absurd because A is preferred to B, being on a higher indifference curve IC1. Since each indifference curve represents a different level of satisfaction, indifference curves can never intersect at any point. The same reasoning applies if two indifference curves touch each other at point B in panel (B) of the figure 1.5. 7. An indifference curve cannot touch either axis: If it touches X-axis, as IC1; in adjoining figure 1. 6 at M, the consumer will be having OM quantity of good X and none of Y. Similarly, if an indifference curve IC2 touches the Y- axis at L, the consumer will have only OL of Y good and no amount of X. Such curves are in contradiction to the assumption that the consumer buys two goods in combinations. 7 8. Indifference curves are not necessarily parallel to each other : Though they are falling, negatively inclined to the right, yet the rate of fall will not be the same for all indifference curves. In other words, the diminishing marginal rate of substitution between the two goods is essentially not the same in the case of all indifference schedules. The two curves lC1 and lC2shown in adjoining figure 1.7 (A) are not parallel to each other. 9. If the two goods are perfect complements the indifference curve is L shaped : As shown in Figure 7 (B). The vertical portion of the IC1 curve reveals that no amount of reduction in good Y will lead even to a slight increase in good X. For example, point's A, M and B are all on the curve IC1 but point B involves the same amount of Y but more of X than point M. Thus MRSXY is zero. The two goods X and Y are consumed in the desired ratio, as indicated by the slope of the ray OR at point M. Such complementary goods are left and right shoes which are used in the 1:1 fixed ratio. 10. If two goods X and Y are perfect substitutes, the indifference curve is a straight line with negative slope : As shown in Figure 1.7 (C) because the MRSXY is constant. The value of this slope is throughout minus 1, and MRSXY =1. In the figure, ab of Y = bc of X, and cd of Y= de of X. In this case, the consumer does not distinguish between these two goods and regards them as the same commodity, such as two brands of tea. The consumer is obsessed with the purchase of only one good. This is called monomania for that good. 8 1.5 The Marginal Rate of Substitution (MRSxy) The marginal rate of substitution is the rate of exchange between some units of goods X and Y which are equally preferred. The marginal rate of substitution of X for Y (MRS)xy is the amount of Y that will be given up for obtaining each additional unit of X. This rate is explained below in the following indifference schedule of Table and Figure in 1. 8. In the table all the 5 combinations gives same level of satisfaction to the consumer. In the A combination consumer is consuming 1, X commodity and 12, Y commodities. To have the B combination and yet to be at the same level of satisfaction, the consumer is prepared to forgo 4 units of Y for obtaining an extra unit of X. The marginal rate of substitution of X for Y is 4:1. The rate of substitution will then be the number of units of Y for which one unit of X is a substitute. As the consumer proceeds to have additional units of X, he is willing to give away less and less units of Y so that the marginal rate of substitution falls from 4:1 to 1:1. In the above figure at point B on the indifference curve IC1, the consumer is willing to give up 4 units of Y to get an additional unit of X. As he moves along the curve, the consumer acquires more of X and less of Y. The amount of Y he is prepared to give up to get additional units of X becomes smaller and smaller. This behaviour of the consumer is known as the principle of diminishing marginal rate of substitution. The marginal rate of substitution of X for Y (MRSXY) is in fact the slope of the curve at a point on the indifference curve. - ΔY Thus MRSxy = ΔX The principle of diminishing marginal rate of substitution is superior to the law of diminishing marginal utility. Because the Marshallian analysis is based on introspective cardinalism in which utility is measured quantitatively and is a single-commodity analysis. The principle of diminishing marginal rate of substitution is, however, scientific and realistic because it is free from the psychological quantitative measurement of utility analysis. 9 1.6 Concept of Budget Line The knowledge of the concept of budget line is essential for understanding the theory of consumer's equilibrium. A higher indifference curve shows a higher level of satisfaction than a lower one. Therefore, a consumer in his attempt to maximize his satisfaction will try to reach the highest possible indifference curve. But in his pursuit of buying more and more goods and thus obtaining more and more satisfaction he has to work under two constraints; first, he has to pay the prices for the goods and, secondly, he has a limited money income with which to purchase the goods. Thus, how far he would go in for his purchases depends upon the prices of the goods and the money income which he has to spend on the goods. In order to explain consumer's equilibrium there is also the need for introducing into the indifference diagram the budget line which represents the prices of the goods and consumer's money income. Suppose our consumer has got income of Rs. 50 to spend on goods X and Y. Let the price of the good X in market be Rs. 10 per unit and that of Y Rs. 5 per unit. If the consumer spends his whole income of Rs. 50 on good X, he would buy 5 units of X; if he spends his whole income of Rs. 50 on good Y he would buy 10 units of Y. If a straight line joining 5X and 10Y is drawn, we will get what is called the price line or the budget line. This budget line shows all those combinations of two goods which the consumer can buy spending his given money income on the two goods at their given prices. In the figure 1.9 with Rs. 50 and the prices of X and Y being Rs. 10 and Rs. 5 respectively the consumer can buy 10 - Y and 0 (zero) - X, or 8 - Y and 1 - X; or 6 - Y and 2 - X, or 4 - Y and 3 -X etc. In other words, he can buy any combination that lies on the budget line with his given money income and given prices of the goods. It is also important to remember that the intercept OB on the Y-axis in Fig. equals the amount of his entire income divided by the price of commodity Y. That is, OB = M/Py. Likewise, the intercept OL on the X-axis measures the total income divided by the price of commodity X. Thus OL = M/Px. 10  The budget line can be written algebraically as follows: PxX + PyY = M , Where Px and Py denote prices of goods X and Y respectively and M stands for money income. The budget-line equation implies that, given the money income of the consumer and prices of the two goods, every combination lying on the budget line will cost the same amount of money and can therefore be purchased with the given income. The budget line can be defined as a set of combinations of two commodities that can be purchased if whole of a given income is spent on them and its slope is equal to the negative of the price ratio. Slope of the Budget Line and Prices of two Goods : It is also important to remember that the slope of the budget line is equal to the ratio of the prices of two goods. This can be proved with the aid of figure 1.9. Suppose the given income of the consumer is M and the given prices of goods X and Y are Px and Py respectively. The slope of the budget line BL is OB/OL. We intend to prove that slope OB/OL is equal to the ratio of the price of goods X and Y. The quantity of good X purchased if whole of the given income M is spent on it is OL. Therefore, OL × Px = M OL = M/( Px) …..(i) Now, the quantity of good Y purchased if whole of the given income M is spent on it is OB. OB × Py =M OB = M/( Py) ….(ii) Dividing( ii) by (i) OB/OL = M/Py ÷ M/Px = M/Py × Px/M = Px/Py Thus slope of budget line = OB/OL = Px/Py It is thus proved that the slope of the budget line BL represents the ratio of the prices of two goods. 11 1.7 Consumer's Equilibrium Consumer equilibrium refers to a situation, in which a consumer derives maximum satisfaction, with no intention to change it and subject to given prices and his given income. The point of maximum satisfaction is achieved by studying indifference map and budget line together. On an indifference map, higher indifference curve represents a higher level of satisfaction than any lower indifference curve. So, a consumer always tries to remain at the highest possible indifference curve, subject to his budget constraint. Conditions of Consumer's Equilibrium: The consumer's equilibrium under the indifference curve theory must meet the following two conditions: (i) MRSXY = Ratio of prices or PX/PY : Let the two goods be X and Y. The first condition for consumer's equilibrium is that, MRSXY = PX/PY (ii) MRS continuously falls: The second condition for consumer's equilibrium is that MRS must be diminishing at the point of equilibrium, i.e. the indifference curve must be convex to the origin at the point of equilibrium. Unless MRS continuously falls, the equilibrium cannot be established. Thus, both the conditions need to be fulfilled for a consumer to be in equilibrium. Let us now understand this with the help of a diagram: In the figure 1.10, IC1, IC2 and IC3 are the three indifference curves and AB is the budget line. With the constraint of budget line, the highest indifference curve, which a consumer can reach, is IC2. The budget line is tangent to indifference curve IC2 at point 'E'. This is the point of consumer equilibrium, where the consumer purchases OM quantity of commodity 'X' and ON quantity of commodity 'Y. The other points on the budget line to the left (F) or right (G) of point 'E' will lie on lower indifference curve IC1 and thus indicate a lower level of satisfaction. Whereas point (H) on IC 3 indifference curve is far away from consumer budget line AB. The budget line AB is tangent to IC2 indifference curve at point 'E', consumer maximizes his satisfaction at this point, when both the conditions of consumer's equilibrium are satisfied. 12 1.8 Price Consumption Curve When, the price of good changes, the consumer would be either better off or worse off than before, depending upon whether the price falls or rises. In other words, as a result of change in price of a good, his equilibrium position would lie at a higher indifference curve in case of the fall in price and at a lower indifference curve in case of the rise in price. Price effect is shown in adjoining figure 1.11. With given prices of goods X and Y, and a given money income as represented by the budget line PL1, the consumer is in equilibrium at Q on indifference curve IC1. In this equilibrium position at Q, he is buying OM1 of X and ON1 of Y. Let price of good X fall, price of Y and his money income remaining unchanged. As a result of this price change, budget line shifts to the position PL2. The consumer is now in equilibrium at R on a higher indifference curve IC2 and is buying OM2 of X and ON2 of Y. He has thus become better off, that is, his level of satisfaction has increased as a consequence of the fall in the price of good X. Suppose that price of X further falls so that PL3 is now the relevant price line. With budget line PL3 the consumer is in equilibrium at S on indifference curve IC3 where he has OM3 of X and ON3 of Y. If the price of good X falls still further so that budget line now takes the position of PL4, the consumer now attains equilibrium at T on indifference curve IC4 and has OM4 of X and ON4 of Y. When all the equilibrium points such as Q, R, S, and T are joined together, we get what is called Price Consumption Curve (PCC). Price consumption curve traces out the price effect. It shows how the changes in price of good X will affect the consumer's purchases of X, price of Y, his tastes and money income remaining unaltered. In figure price consumption curve (PCC) is sloping downward. Downward sloping price consumption curve for good X means that as the price of good X falls, the consumer purchases a larger quantity of good X and a smaller quantity of good Y. This is quite evident from figure. In elasticity of demand, we obtain downward-sloping price consumption curve for good X when demand for it is elastic (i.e., price elasticity is greater than one). But downward sloping is one possible shape of price consumption curve. Price consumption curve can have other shapes also. 13  In adjoining figure 1.12 upward-sloping price consumption curve is shown. Upward-sloping price consumption curve for X means that when the price of good X falls, the quantity demanded of both goods X and Y rises. We obtain the upward-sloping price consumption curve for good X when the demand for good is inelastic, (i.e., price elasticity is less than one). Price consumption curve can also have a backward- sloping shape, which is depicted in adjoining figure 1.13. Backward-sloping price consumption curve for good X indicates that when price of X falls, after a point smaller quantity of it is demanded or purchased. This is true in case of exceptional type of goods called Giffen Goods. Price consumption curve for a good can take horizontal shape too. It means that when the price of the good X declines, its quantity purchased rises proportionately but quantity purchased of Y remains the same. Horizontal price consumption curve is shown in figure 1.14. We obtain horizontal price consumption curve of good X when the price elasticity of demand for good X is equal to unity. It is rarely found that price consumption curve slopes downward throughout or slopes upward throughout or slopes backward throughout. More generally, price consumption curve has different slopes at different price ranges. At higher price levels it generally slopes downward, and it may then have a horizontal shape for some price ranges but ultimately it will be sloping upward. For some price ranges it can be backward sloping as in case of Giffen goods. A price consumption curve which has different shapes or slopes at different price ranges is drawn in figure 1.15 14 1.9 Income Consumption Curve : With given money income to spend on goods, given prices of the two goods and given an indifference map, the consumer will be in equilibrium at a point in an indifference map. We are interested in knowing how the consumer will react in regard to his purchases of the goods when his money income changes, prices of the goods and his tastes and preferences remaining unchanged. Income effect shows this reaction of the consumer. Thus, the income effect means the change in consumer's purchases of the goods as a result of a change in his money income. Income effect is illustrated in adjoining figure 1.16 With given prices and a given money income as indicated by the budget line P1L1 the consumer is initially in equilibrium at point Q 1 on the indifference curve IC1 and is having OM1 of X and ON1 of Y. Now suppose that income of the consumer increases. With his increased income, he would be able to purchase larger quantities of both the goods. As a result, budget line will shift upward and will be parallel to the original budget line P1L1. Let us assume that the consumer's money income increases by such an amount that the new budget line is P2L2, the consumer is in equilibrium at point Q2 on indifference curves IC2 and is buying OM2 of X and ON2 of Y. Thus as a result of the increase in his income the consumer buys more quantity of both the goods Since he is on the higher indifference curve IC2 he will be better off than before i.e., his satisfaction will increase. If his income increases further so that the budget line shifts to P3L3, the consumer is in equilibrium at point Q3 on indifference curve IC3 and is having greater quantity of both the goods than at Q2. Consequently, his satisfaction further increases. In the figure the consumer's equilibrium is shown at a still further higher level of income and it will be seen that the consumer is in equilibrium at Q4 on indifference curves IC4 when the budget line shifts to P4L4. As the consumer's income increases, he switches to higher indifference curves and as a consequence enjoys higher levels of satisfaction. If now various points Q1, Q2, Q3 and Q4 showing consumer's equilibrium at various levels of income are joined together, we will get what is called Income Consumption Curve (ICC). Income consumption curve is thus the locus of equilibrium points at various levels of consumer's income. Income effect can either be positive or negative. Income effect for a good is said to be positive when with the increase in income of the consumer, his consumption of the good also increases. This is the normal good case. When the income effect of both the goods represented on the two axes of the figure is positive, the income consumption curve ICC will slope upward to the right as in the figure. Only the upward- sloping income consumption curve can show rising consumption of the two goods as income increases. 15  However, for some goods, income effect is negative. Income effect for a good is said to be negative when with the increases in his income, the consumer reduces his consumption of the good. Such goods for which income effect is negative are called Inferior Goods. This is because the goods whose consumption falls as income of the consumer rises are considered to be some way 'inferior' by the consumer and therefore he substitutes superior goods for them when his income rises. In case of inferior goods, indifference map would be such as to yield income consumption curve which either slopes backward (i.e., toward the left) or downward to the right as in figure 1.17. It would be noticed from the figure that income effect becomes negative only after a point. If income effect for good X is negative, income consumption curve will slope backward to the left as ICC1 in figure. If good Y happens to be an inferior good and income consumption curve will bend towards X-axis as shown by ICC2 in figure. Normal goods can be either necessities or luxuries depending upon whether the quantities purchased of the goods by the consumers increase less than or more than proportionately to the increases in income. If the quantity purchased of a commodity rises less than proportionately to the increases in consumer's income, the commodity is known as a necessity. On the other hand, if the quantity purchased of a commodity increases more than proportionately to the increases in income, it is called a luxury. In figure 1.18, the slope of income consumption curve ICC1 is increasing which implies that the quantity purchased of the commodity X increases less than proportionately to the increases in consumer's income. Therefore, in this case of ICC1 good X is a necessity and good Y is luxury. On the other hand, the slope of income consumption curve ICC3 is decreasing which implies that the quantity purchased of good X increases more than proportionately to increases in income and therefore in this case good X is luxury and good Y is necessity. It will be seen from figure that the income consumption curve ICC2 is a linear curve passing through the origin which implies that the increases in the quantities purchased of both the goods are rising in proportion to the increase in income and therefore neither good is a luxury or a necessity. 16 1.10 Derivation of Demand Curve : A demand curve shows how much quantity of a good will be purchased or demanded at various prices, assuming that tastes and preferences of a consumer, his income, prices of all related goods remain constant. This demand curve showing relationship between price and quantity demanded can be derived from price consumption curve of indifference curve analysis. Let us suppose that a consumer has got income of Rs. 300 to spend on goods. In Fig. 1.19 money is measured on the Y-axis, while the quantities of the good X whose demand curve is to be derived is measured on the X-axis. An indifference map of a consumer is drawn along with the various budget lines showing different prices of the good X. Budget line PL1 shows that price of the good X is Rs. 15 per unit. As price of good X falls from Rs. 15 to Rs. 10, the budget line shifts to PL2. Budget line PL2 shows that price of good X is Rs. 10. With a further fall in price to Rs. 7.5 the budget line takes the position PL3. Thus PL3 shows that price of good X is Rs. 7.5. When price of good X fall further Rs. 6, PL4 is the relevant budget line. With the budget line PL 1 the consumer is in equilibrium at point Q1 on the price consumption curve PCC at which the budget line PL 1 is tangent to indifference curve IC1. In his equilibrium position at Q1 the consumer is buying OA units of the good X. In other words, it means that the consumer demands OA units of good X at price Rs. 15. When price falls to Rs. 10 and thereby the budget line shifts to PL2, the consumer comes to be in equilibrium at point Q2 the price-consumption curve PCC where the budget line PL2 is tangent to indifference curve IC2. At Q2, the consumer is buying OB units of good X. Likewise, with budget lines PL3 and PL4, the consumer is in equilibrium at points Q3 and Q4 of price consumption curve and is demanding OC units and OD units of good X at price Rs. 7.5 and Rs. 6 respectively. It is thus clear that from the price consumption curve we can get information which is required to draw the demand curve showing directly the amounts demanded of the good X against various prices. 17 1.11 Deriving Demand Curve for a Giffen Good 1.11 The demand curve DD in Fig. 1.19 is sloping downward. The demand curve slopes downward because of two forces, namely, income effect and substitution effect. Both the income effect and substitution effect usually work towards increasing the quantity demanded of the good when its price falls and this makes the demand curve slope downward. But in case of Giffen good, the demand curve slopes upward from left to right. This is because in case of a Giffen good income effect, which is negative and works in opposite direction to the substitution effect, outweighs the substitution effect. This results in the fall in quantity demanded of the Giffen good when its price falls and therefore the demand curve of a Giffen good slopes upward from left to right. In Fig. 1.20 the derivation of demand curve of a Giffen good from indifference curves diagram is explained. In Fig. 1.20 the Indifference curves of a Giffen good are drawn along with the various budget lines showing various prices of the good. Price consumption curve of a Giffen good slopes backward. In order to simplify the discussion in this figure we have avoided the numerical values of prices and have instead used symbols such as, P1, P2, P3 and P4 for various levels of the price of good X. It is evident from Fig. 1.20 (the upper portion) that with budget line PL1 (or price P1) the consumer is in equilibrium at Q1 on the price consumption curve PCC and is purchasing OM1 amount of the good. With the fall in price from P1 to P2 and shifting of budget line from PL1to PL2, the consumer goes to the equilibrium position Q3 at which he buys OM2 amount of the good. OM2 is less than OM1. Thus with the fall in price from P1 to P2 the quantity demanded of the good falls. Likewise, the consumer is in equilibrium at Q3 with price line PL3 and is purchasing OM3 at price P3. With this information we can draw the demand curve, as is done in the lower portion of Fig. 1.20 It will be seen from Fig. 1.20 (lower part) that the demand curve of a Giffen good slopes upward to the right indicating that the quantity demanded varies directly with the changes in price. With the rise in price, quantity demanded increases and with the fall in price quantity demanded decreases. 18 1.12 The Substitution Effect - Hicks The substitution effect relates to the change in the quantity demanded resulting from a change in the price of good due to the substitution of relatively cheaper good for a dearer one, while keeping the price of the other good and real income and tastes of the consumer as constant. Prof. Hicks has explained the substitution effect independent of the income effect through compensating variation in income. "The substitution effect is the increase in the quantity bought as the price of the 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 variations and is shown graphically by a parallel shift of the new budget line until it become tangent to the initial indifference curve." Thus on the basis of the methods of compensating variation, the substitution effect measure the effect of change in the relative price of a good with real income constant. The increase in the real income of the consumer as a result of fall in the price of, say good X, is so withdrawn that he is neither better off nor worse off than before. The substitution effect is explained in Figure 1.21 where the original budget line is PQ with equilibrium at point R on the indifference curve IC1. At R, the consumer is buying OB of X and BR of Y. Suppose the price of X falls so that his new budget line is PQ1. With the fall in the price of X, the real income of the consumer increases. To make the compensating variation in income or to keep the consumer's real income constant, take away the increase in his income equal to PM of good Y or Q1N of good X so that his budget line PQ1 shifts to the left as MN and is parallel to it. At the same time, MN is tangent to the original indifference curve lC1 but at point H where the consumer buys OD of X and DH of Y. Thus PM of Y or Q 1 N of X represents the compensating variation in income, as shown by the line MN being tangent to the curve IC1 at point H. Now the consumer substitutes X for Y and moves from point R to H or the horizontal distance from B to D. This movement is called the substitution effect. The substitution affect is always negative, the relation between price and quantity demanded being inverse, the substitution effect is negative. 19 1.13 Substitution Effect - Slutsky The concept of substitution effect put forward by J.R. Hicks. There is another important version of substitution effect put forward by E. Slutsky. The treatment of the substitution effect in these two versions has a significant difference. In Slutsky's version of substitution effect when the price of good changes and consumer's real income or purchasing power increases, the income of the consumer is changed by the amount equal to the change in its purchasing power which occurs as a result of the price change. His purchasing power changes by the amount equal to the change in the price multiplied by the number of units of the good which the individual used to buy at the old price. In other words, in Slutsky's approach, income is reduced or increased (as the case may be), by the amount which leaves the consumer to be just able to purchase the same combination of goods, if he so desires, which he was having at the old price. That is, the income is changed by the difference between the cost of the amount of good X purchased at the old price and the cost of purchasing the same quantity if X at the new price. Income is then said to be changed by the cost difference. Thus, in Slutsky substitution effect, income is reduced or increased not by compensating variation as in case of the Hicksian substitution effect but by the cost difference. Now, an important question is how to determine the exact magnitude of cost difference by which money income of the consumer has to be adjusted to arrive at Slutsky substitution effect. The reduction in price of a commodity, say X, can be represented as ?Px. If the consumer is buying quantity Qx of commodity X before the reduction in price of the commodity, then ΔPx. Qx will represents the cost difference by which money income of the consumer is to be adjusted so as to enable him to buy the quantity Qx of commodity X (and the same original quantity of Y) which he was buying before the change in price. Suppose, with a given money income, a consumer is buying Qx of X and Qy of Y at given prices of Px1 and Py1 respectively. Now, if the price of X falls from Px1 to Px2, the money income and price of Y remaining the same, the cost difference will thus be equal to Px1Qx - Px2Qx = ΔPx Qx Let us give a numerical example. If at a price of Rs. 10, a consumer is buying 15 units of the commodity X along with a certain quantity of Y at the given price of Y. If now the price of X falls to Rs. 8, the cost difference will be 10 × 15 - 8 × 15 = 2 × 15 = 30 20  Slutsky substitution effect is illustrated in adjoining Fig. 1.22. With given money income and the given prices of two goods as represented by the price line PL1 the consumer is in equilibrium at Q on the indifference curve IC1 buying OM of X and ON of Y. Now suppose that price of X falls, price of Y and money income of the consumer remaining un- changed. As a result of this fall in price of X, the price line will shift to PL1 and the real income or the purchasing power of the consumer will increase. Now, in order to find out the Slutsky substitution effect, consumer's money income must be reduced by the cost- difference or, in other words, by the amount which will leave him to be just able to purchase the old combination Q, if he so desires. For this, a price line GH parallel to PL1 has been drawn which passes through the point Q. It means that income equal to PG in terms of Y or L1H in terms of X has been taken away from the consumer and as a result he can buy the combination Q, if he so desires, since Q also lies on the price line GH. Actually, he will not now buy the combination Q since X has now become relatively cheaper and Y has become relatively dearer than before. The change in relative prices will induce the consumer to rearrange his purchases of X and Y. He will substitute X for Y. But in this Slutsky substitution effect, he will not move along the same indifference curve IC1, since the price line GH, on which the consumer has to remain due to the new price-income circumstances is nowhere tangent to the indifference curve IC1. The price line GH is tangent to the indifference curve IC2 at point S. Therefore, the consumer will now be in equilibrium at a point S on a higher indifference curve IC2. This movement from Q to S represents Slutsky substitution effect according to which the consumer moves not on the same indifference curve, but from one indifference curve to another. A noteworthy point is that movement from Q to S as a result of Slutsky substitution effect is due to the change in relative prices alone, since the effect due to the gain in the purchasing power has been eliminated by making a reduction in money income equal to the cost-difference. At S, the consumer is buying OK of X and O W of Y; MK of X has been substituted for NW of Y. Therefore, Slutsky substitution effect on X is the increase in its quantity purchased by MK and Slutsky substitution effect on Y is the decrease in its quantity purchased by NW. 21 1.14 Price Effect - Income and Substitution Effects - Hicks Hicks has separated the substitution effect and the income effect from the price effect through compensating variation in income by changing the relative price of a good while keeping the real income of the consumer constant. Suppose initially the consumer is in equilibrium at point R on the budget line PQ where the indifference curve IC1, is tangent to it at point R in Figure 1.23. Let the price of good X fall. As a result, his budget line rotates outward to PQ, where the consumer is in equilibrium at point T on the higher indifference curve IC2.The movement from R to T or B to E on the horizontal axis is the price effect of the fall in the price of X. With the fall in the price of X, the consumer's real income increases. To make the compensating variation in income in order to isolate the substitution effect, the consumer's money income is reduced equivalent to PM of Y or Q1N of X by drawing the budget line MN parallel to PQ1, so that it is tangent to the original indifference curve IC1 at point H. The movement from R to H on the IC1, curve is the substitution effect whereby the consumer increases his purchases of X from B to D on the horizontal axis by substituting X for Y because it is cheaper. It may be noted that when there is a fall (or rise) in the price of good X, the substitution effect always leads to an increase (or decrease) in its quantity demanded. Thus the relation between price and quantity demanded being inverse, the substitution effect of a price change is always negative, real income being held constant. 22 1.15 Price Effect - Income and Substitution Effects - Slutsky In our discussion of substitution effect we explained that Slutsky presented a slightly different version of the substitution and income effects of a price change from the Hicksian one. His way of breaking up the price effect is shown in figure 1.24. With a certain price- income situation, the consumer is in equilibrium at Q on indifference curve IC1. With a fall in price of X, other things remaining the same, budget line shifts to PL2. With budget line PL2, the consumer would now be in equilibrium at R on the indifference curve IC3. This movement from Q to R represents the price effect (PCC). As a result of this he buys MN quantity of good X more than before. Now, in order to find out the substitution effect his money income be reduced by such an amount that he can buy, if he so desires, the old combination Q. Thus, a line AB, which is parallel to PL2, has been so drawn that it passes through point Q. Thus PA in terms of good Y, L2B in terms of X represents the cost difference. With budget line AB, the consumer can have combination Q if he so desires, but actually he will not buy combination Q because X is now relatively cheaper than before. It will pay him to substitute X for Y. With budget line AB he is in equilibrium at S on indifference curve IC2. The movement from Q to S represents Slutsky substitution effect which induces the consumer to buy MH quantity more of good X. If now the money taken away from him is restored to him, he will move from S on indifference curve IC2 to R on indifference curve IC3. This movement from S to R represents income effect (ICC). Thus, movement from Q to R as a result of price effect can be divided into two steps. First, movement from Q to S as a result of substitution effect and secondly, movement from S to R as a result of income effect. It may be pointed out here again that, unlike the Hicksian method, Slutsky substitution effect causes movement from a lower indifference curve to a higher one. 23 24 2 Alfred Marshall 26 July 1842 - 13th July, 1924 th PRODUCTION ANALYSIS 2.1 Production Function 2.2 Short Run Production Function 2.3 Long Run Production Function 2.4 The Law of Variable Proportions 2.5 Iso-Quant Curves 2.6 Properties of Iso-Product Curves 2.7 Concept of Factors Pricing Line- Iso-Cost Line 2.8 Iso Quant & Iso-Cost Curves 2.9 Least Cost Combination Analysis 2.10 Expansion Path 2.11 Economic Region of production (Ridge Lines) 2.12 Concept and Types of Returns to Scale 2.13 Linear Homogeneous Production Function 2.14. Properties of Cobb-Douglas Production Function 25 26 2.1 Production Function The processes and methods used to transform tangible inputs (raw materials, semi- finished goods, subassemblies) and intangible inputs (ideas, information, knowledge) into goods or services. Resources are used in this process to create an output that is suitable for use or has exchange value. Production function is the technological relationship between inputs and output in physical terms. It specifies the maximum quantity of a commodity that can be produced per unit of time with given quantities of inputs and technology. A production function may take the form of a schedule, a graphical line or curve, an algebraic equation or a mathematical model. The general form a production function may be algebraically expressed as: Q = f (K, L, N, O) Where Q = the quantity of output K = capital, and L = labour. N = Land O = Organisation 2.2 Short Run Production Function The short run production function is one in which at least is one factor of production is thought to be fixed in supply, i.e. it cannot be increased or decreased, and the rest of the factors are variable in nature. In general, the firm's capital inputs are assumed as fixed, and the production level can be changed by changing the quantity of other inputs such as labour, raw material, labour and so on. Therefore, it is quite difficult for the firm to change the capital equipment, to increase the output produced, among all factors of production. In such circumstances, the law of variable proportion operates, which states the consequences when extra units of a variable input are combined with a fixed input. In short run, increasing returns are due to the indivisibility of factors and specialization, whereas diminishing returns are due to the perfect elasticity of substitution of factors. 27 2.3 Long Run Production Function Long run production function refers to that time period in which all the inputs of the firm are variable. It can operate at various activity levels because the firm can change and adjust all the factors of production and level of output produced according to the business environment. So, the firm has the flexibility of switching between two scales. In such a condition, the law of returns to scale operates which discusses, in what way, the output varies with the change in production level, i.e. the relationship between the activity level and the quantities of output. The increasing returns to scale is due to the economies of scale and decreasing returns to scale is due to the diseconomies of scale. 2.4. The Law of Variable Proportions Variable The law of variable proportions states that as the quantity of one factor is increased, keeping the other factors fixed, the marginal product of that factor will eventually decline. This means that up to the use of a certain amount of variable factor, marginal product of the factor may increase and after a certain stage it starts diminishing. When the variable factor becomes relatively abundant, the marginal product may become negative. Assumptions : 1. Constant Technology : The state of technology is assumed to be given and constant. Technology If there is an improvement in technology the production function will move upward. 2. Factor Proportions are V ariable : The law assumes that factor proportions are Variable variable. If factors of production are to be combined in a fixed proportion, the law has no validity. 3. Homogeneous Factor Units : The units of variable factor are homogeneous. Each unit is identical in quality and amount with every other unit. 4. Short-Run : The law operates in the short-run when it is not possible to vary all factor inputs. 28  The law of variable proportion is illustrated in the following table 2.1 (A) and figure. 2.1(A). Suppose there is a given amount of land in which more and more labour (variable factor) is used to produce wheat. It can be seen from the table that up to the use of 3rd units of labour, total product increases at an increasing rate and beyond the 3rd unit total product increases at a diminishing rate. This fact is shown by the marginal product which addition is made to Total Product as a result of increasing the variable factor i.e. labour. It can be seen from the table that the marginal product of labour initially rises and beyond the use of 3rd units of labour, it starts diminishing. The use of 6th units of labour does not add anything to the total production of wheat. Hence, the marginal product of labour has fallen to zero. Beyond the use of 6th units of labour, total product diminishes and therefore marginal product of labour becomes negative. Regarding the average product of labour, it rises up to the use of 3rd unit of labour and beyond that it is falling throughout. 29 Three Stages of the Law of Variable Proportions : These stages were illustrated Variable in figure 2.1 (A) where labour is measured on the X-axis and output on the Y-axis. 1st Stage of Increasing Returns : In this stage, total product increases at an increasing rate up to a point. This is because the efficiency of the fixed factors increases as additional units of the variable factors are added to it. In the figure, from the origin to the point F, slope of the total product curve TP is increasing i.e. the curve TP is concave upwards upto the point F, which means that the marginal product MP of labour rises. The point F where the total product stops increasing at an increasing rate and starts increasing at a diminishing rate is called the point of inflection. Corresponding vertically to this point of inflection marginal product of labour is maximum, after which it diminishes. This stage is called the stage of increasing returns because the average product of the variable factor increases throughout this stage. This stage ends at the point where the average product curve reaches its highest point. 2nd Stage of Diminishing Returns : In this stage, total product continues to increase but at a diminishing rate until it reaches its maximum point H where the second stage ends. In this stage both the marginal product and average product of labour are diminishing but are positive. This is because the fixed factor becomes inadequate relative to the quantity of the variable factor. At the end of the second stage, i.e., at point M marginal product of labour is zero which corresponds to the maximum point H of the total product curve TP. This stage is important because the firm will seek to produce in this range. 3rd Stage of Negative Returns : In stage 3, total product declines and therefore the TP curve slopes downward. As a result, marginal product of labour is negative and the MP curve falls below the X-axis. In this stage the variable factor (labour) is too much relative to the fixed factor. Importance and Applicability of the Law of Variable Proportion : Variable The Law of Variable Proportion has universal applicability in any branch of production. It forms the basis of a number of doctrines in economics. The Malthusian theory of population stems from the fact that food supply does not increase faster than the growth in population because of the operation of the law of diminishing returns in agriculture. Ricardo also based his theory of rent on this principle. According to him rent arises because the operation of the law of diminishing return forces the application of additional doses of labour and capital on a piece of land. Similarly the law of diminishing marginal utility and that of diminishing marginal physical productivity in the theory of distribution are also based on this theory. 30 2. 5 Iso-Quant Curves The term Iso-quant or Iso-product is composed of two words, Iso means equal, and quant means quantity or product. Thus it means equal quantity or equal product. Different factors are needed to produce a good. These factors may be substituted for one another. A given quantity of output may be produced with different combinations of factors. Iso-quant curves are also known as Equal-product or Iso-product or Production Indifference curves. Thus, an Iso-product or Iso-quant curve is that curve which shows the different combinations of two factors yielding the same total product. Like, indifference curves, Iso- quant curves also slope downward from left to right. The slope of an Iso-quant curve expresses the marginal rate of technical substitution (MRTS). Assumptions : 1. Only two factors are used to produce a commodity. 2. Factors of production can be divided into small parts. 3. Technique of production is constant or is known before hand. 4. The substitution between the two factors is technically possible. That is, production function is of 'variable proportion' type rather than fixed proportion. 5. Under the given technique, factors of production can be used with maximum efficiency. 31 Iso-Product Schedule: Let us suppose that there are two factor inputs-labour and capital. An Iso-product schedule shows the different combination of these two inputs that yield the same level of output as shown in table 2.1. The table shows that the five combinations of labour units and units of capital yield the same level of output, i.e., 200 meters of cloth. Iso-Quant (Product) Curve: From the above schedule iso-product curve can be drawn with the help of the table 2.1 in figure 2.1. An equal product curve represents all those combinations of two inputs which are capable of producing the same level of output. The Figure 2.1 shows the various combinations of labour and capital which give the same amount of output i.e. 200 meters of cloth at points A, B, C, D and E. 2.6 Properties of Iso-Product Curves 1. Iso-Product Curves Slope Downward from Left to Right. 2. Iso-quants are Convex to the Origin. 3. Two Iso-Product Curves Never Cut Each Other. 4. A higher iso-product curve represents a higher level of output. 5. Iso-quants Need Not be Parallel to Each Other. 6. No Iso-quant can Touch Either Axis. 7. Each Iso-quant is Oval-Shaped. 1. Iso-Product Curves Slope Downward from Left to Right : They slope downward because MTRS of labour for capital diminishes. When we increase labour, we have to decrease capital to produce a given level of output. The downward sloping iso-product curve can be explained with the help of the following figure: The Figure 2.2 shows that when the amount of labour is increased from OL to OL1, the amount of capital has to be decreased from OK to OK1, The iso-product curve (IQ) is falling as shown in the figure. 32 The possibilities of horizontal, vertical, upward sloping curves can be ruled out with the help of the following figure 2. 3 The figure 2.3 (A) shows that the amounts of both the factors of production are increased- labour from L to L1 and capital from K to K1. When the amounts of both factors increase, the output must increase. Hence the IQ curve cannot slope upward from left to right. The figure 2.3 (B) shows that the amount of labour is kept constant while the amount of labour is increased. The amount of capital is increased from K to K1. Then the output must increase. So, IQ curve cannot be a vertical straight line. The figure 2.3 (C) shows a horizontal curve. If it is horizontal the quantity of labour increases, although the quantity of capital remains constant. When the amount of capital is increased, the level of output must increase. Thus, an IQ curve cannot be a horizontal line. 2. Iso-quants are Convex to the Origin : Like indifference curves, iso-quants are convex to the origin. In order to understand this fact, we have to understand the concept of diminishing marginal rate of technical substitution (MRTS), because convexity of an iso-quant implies that the MRTS diminishes along the iso-quant. The marginal rate of technical substitution between L and K is defined as the quantity of K which can be given up in exchange for an additional unit of L. It can also be defined as the slope of an iso-quant. It can be expressed as : MRTSLK = _ ΔK/ΔL = _ dK/ dL Where ΔK is the change in capital and ΔL is the change in labour. 33  Equation states that for an increase in the use of labour, fewer units of capital will be used. In other words, a declining MRTS refers to the falling marginal product of labour in relation to capital. To put it differently, as more units of labour are used, and as certain units of capital are given up, the marginal productivity of labour in relation to capital will decline. This fact can be explained in Fig.2.4 As we move from point A to B, from B to C and from C to D along an iso-quant, the marginal rate of technical substitution (MRTS) of capital for labour diminishes. Every time labour units are increasing by an equal amount (LL1) but the corresponding decrease in the units of capital (KK1) decreases. Thus it may be observed that due to falling MRTS, the iso-quant is always convex to the origin. 3. Two Iso-Product Curves Never Cut Each Two Other : As two indifference curves cannot cut each other, two iso-product curves cannot cut each other. In Fig.2.5 two Iso-product curves intersect each other. Both curves IQ1 and IQ2 represent two levels of output. But they intersect each other at point A. Then combination A = B and combination A= C. Therefore B must be equal to C. This is absurd. B and C lie on two different iso-product curves. Therefore two curves which represent two levels of output cannot intersect each other. 4. A higher iso-product curve represents a higher level of output : A higher iso-product curve represents a higher level of output as shown in the figure 2.6 given below. In the Fig. 2.6 units of labour have been taken on OX axis while on OY, units of capital. IQ1 represents an output level of 100 units whereas IQ2 represents 200 units of output. 34 5. Iso-quants Need not be Para llel to Each Other : It so happens because the rate of Parallel substitution in different iso-quant schedules need not be necessarily equal. Usually they are found different and, therefore, iso-quants may not be parallel as shown in Fig. 2.7. We may note that the iso-quants Iq1 and Iq2 are parallel but the iso-quants Iq3 and Iq4 are not parallel to each other. 6. No Iso-quant can touch Either Axis : If an iso-quant touches X-axis, it would mean that the product is being produced with the help of labour alone without using capital at all. These logical absurdities for OL units of labour alone are unable to produce anything. Similarly, OC units of capital alone cannot produce anything without the use of labour. Therefore as seen in figure 2.8, IQ and IQ1 cannot be iso-quants. 7. Each Iso-quant is Oval-Shaped : It means that at some point it begins to recede from each axis. This shape is a consequence of the fact that if a producer uses more of capital or more of labour or more of both than is necessary, the total product will eventually decline. The firm will produce only in those segments of the iso-quants which are convex to the origin and lie between the ridge lines. This is the economic region of production. In Figure 2.9 oval shaped iso-quants are shown. Curves OA and OB are the ridge lines and in between them only feasible units of capital and labour can be employed to produce 100, 200, 300 and 400 units of the product. For example, OT units of labour and ST units of the capital can produce 100 units of the product, but the same output can be obtained by using the same quantity of labour OT and less quantity of capital VT. 35 2.7 Concept of Factors Pricing Line - Iso - Cost Line A firm can produce a given level of output using efficiently different combinations of two inputs. For choosing efficient combination of the inputs, the producer selects that combination of factors which has the lower cost of production. The information about the cost can be obtained from the iso-cost lines. An iso-cost line is also called outlay line or price line or factor cost line. An iso-cost line shows all the combinations of labour and capital that are available for a given total cost to the producer. Just as there are infinite numbers of iso-quants, there are infinite numbers of iso-cost lines, one for every possible level of a given total cost. The greater the total cost, the further from origin is the iso-cost line. The iso-cost line is similar to the price or budget line of the indifference curve analysis. It is the line which shows the various combinations of factors that will result in the same level of total cost. It refers to those different combinations of two factors that a firm can obtain at the same cost. Just as there are various iso-quant curves, so there are various iso-cost lines, corresponding to different levels of total output. Explanation : The concept of iso-cost line can be explained with the help of the following table 2. 2 and Figure 2.10 Suppose the producer's budget for the purchase of labour and capital is fixed at Rs. 100. Further suppose that a unit of labour cost the producer Rs. 10 while a unit of capital Rs. 20. From the table cited above, the producer can adopt the following options : 1. Spending all the money on the purchase of labour, he can hire 10 units of labour. 2. Spending all the money on the capital he may buy 5 units of capital. 3. Spending the money on both labour and capital, he can choose between various possible combinations of labour and capital such as (4, 3) (2, 4) etc. 36  In Fig. 2.10 labour is given on OX-axis and capital on OY-axis. The points A, B, C and D convey the different combinations of two factors, capital and labour which can be purchased by spending Rs. 100. Point A indicates 5 units of capital and no unit of labour, while point D represents 10 units of labour and no unit of capital. Point B indicates 4 units of capital and 2 units of labour. Likewise, point C represents 4 units of labour and 3 units of capital. 2. 8 Iso-Quant & Iso-Cost Curves After knowing the nature of isoquant which represent the output possibilities of a firm from a given combination of two inputs. We further extend it to the prices of the inputs as represented on the isoquant map by the iso-cost curves. These curves are also known as outlay lines, price lines, input-price lines, factor-cost lines, constant-outlay lines, etc. Each iso-cost curve represents the different combinations of two inputs that a firm can buy for a given sum of money at the given price of each input. Figure 2.11(A) shows three iso-cost curves each represents a total outlay of 50, 75 and 100 respectively. The firm can hire OC of capital or OD of labour with Rs. 75. The line CD represents the price ratio of capital and labour. Prices of factors remaining the same, if the total outlay is raised, the iso-cost curve will shift upward to the right as EF parallel to CD, and if the total outlay is reduced it will shift downwards to the left as AB. The iso-costs are straight lines because factor prices remain the same whatever the outlay of the firm on the two factors. The iso-cost curves represent the locus of all combinations of the two input factors which result in the same total cost. If the unit cost of labour (L) is w and the unit cost of capital (K) is r, then the total cost: TC = wL + rK. The slope of the iso-cost line is the ratio of prices of labour and capital i.e., w/r. 37  The point where the iso-cost line is tangent to an isoquant shows the least cost combination of the two factors for producing a given output. If all points of tangency like LMN are j