Theory Of Consumer Behaviour PDF

Chapter Three Theory of Consumer Behaviour Introduction In our day –to- day life, we buy different goods and services for consumption. As consumer, we act to derive satisfaction by using goods and services. But, have ever thought of how your mother or any other person who...

Chapter Three Theory of Consumer Behaviour Introduction In our day –to- day life, we buy different goods and services for consumption. As consumer, we act to derive satisfaction by using goods and services. But, have ever thought of how your mother or any other person whom you know decides to buy those consumption goods and services? Consumer theory is based on what people like, so it begins with something that we can‘t directly measure, but must infer. That is, consumer theory is based on the premise that we can infer what people like from the choices they make. Consumer behaviour can be best understood in three steps. First, by examining consumer‘s preference, we need a practical way to describe how people prefer one good to another. Second, we must take into account that consumers face budget constraints – they have limited incomes that restrict the quantities of goods they can buy. Third, we will put consumer preference and budget constraint together to determine consumer choice. Chapter objectives After successful completion of this chapter, you will be able to:  explain consumer preferences and utility  differentiate between cardinal and ordinal utility approach  define indifference curve and discuss its properties  derive and explain the budget line  describe the equilibrium condition of a consumer 3.1 Consumer preferences A consumer makes choices by comparing bundle of goods. Given any two consumption bundles, the consumer either decides that one of the consumption bundles is strictly better than the other, or decides that she is indifferent between the two bundles. In order to tell whether one bundle is preferred to another, we see how the consumer behaves in choice situations involving two bundles. If she always chooses X when Y is available, then it is natural to say that this consumer prefers X to Y. We use the symbol ≻ to mean that one bundle is strictly preferred to another, so that X ≻Y should be interpreted as saying that the consumer strictly prefers X to Y, in the sense that she definitely wants the X-bundle rather than the Y-bundle. If the consumer is indifferent between two bundles of goods, we use the symbol 40 ∼ and write X~Y. Indifference means that the consumer would be just as satisfied, according to her own preferences, consuming the bundle X as she would be consuming bundle Y. If the consumer prefers or is indifferent between the two bundles we say that she weakly prefers X to Y and write X ⪰ Y. The relations of strict preference, weak preference, and indifference are not independent concepts; the relations are themselves related. For example, if X ⪰ Y and Y ⪰ X, we can conclude that X ~Y. That is, if the consumer thinks that X is at least as good as Y and that Y is at least as good as X, then she must be indifferent between the two bundles of goods. Similarly, if X ⪰ Y but we know that it is not the case that X~ Y, we can conclude that X≻Y. This just says that if the consumer thinks that X is at least as good as Y, and she is not indifferent between the two bundles, then she thinks that X is strictly better than Y. 3.2 The concept of utility Economists use the term utility to describe the satisfaction or pleasure derived from the consumption of a good or service. In other words, utility is the power of the product to satisfy human wants. Given any two consumption bundles X and Y, the consumer definitely wants the X-bundle than the Y-bundle if and only if the utility of X is better than the utility of Y. Do you think that utility and usefulness are synonymous? Do two individuals always derive equal satisfaction from consuming the same level of a product? In defining utility, it is important to bear in mind the following points.  ‗Utility’ and ‘Usefulness’ are not synonymous. For example, paintings by Picasso may be useless functionally but offer great utility to art lovers. Hence, usefulness is product centric whereas utility is consumer centric.  Utility is subjective. The utility of a product will vary from person to person. That means, the utility that two individuals derive from consuming the same level of a product may not be the same. For example, non-smokers do not derive any utility from cigarettes.  Utility can be different at different places and time. For example, the utility that we get from drinking coffee early in the morning may be different from the utility we get during lunch time. 41  3.3 Approaches of measuring utility How do you measure or compare the level of satisfaction (utility) that you obtain from goods and services? There are two major approaches to measure or compare consumer‘s utility: cardinal and ordinal approaches. The cardinalist school postulated that utility can be measured objectively. According to the ordinalist school, utility is not measurable in cardinal numbers rather the consumer can rank or order the utility he derives from different goods and services. 3.3.1 The cardinal utility theory According to the cardinal utility theory, utility is measurable by arbitrary unit of measurement called utils in the form of 1, 2, 3 etc. For example, we may say that consumption of an orange gives Bilen 10 utils and a banana gives her 8 utils, and so on. From this, we can assert that Bilen gets more satisfaction from orange than from banana. 3.3.1.1 Assumptions of cardinal utility theory The cardinal approach is based on the following major assumptions. 1. Rationality of consumers. The main objective of the consumer is to maximize his/her satisfaction given his/her limited budget or income. Thus, in order to maximize his/her satisfaction, the consumer has to be rational. 2. Utility is cardinally measurable. According to the cardinal approach, the utility or satisfaction of each commodity is measurable. Utility is measured in subjective units called utils. 3. Constant marginal utility of money. A given unit of money deserves the same value at any time or place it is to be spent. A person at the start of the month where he has received monthly salary gives equal value to 1 birr with what he may give it after three weeks or so. 4. Diminishing marginal utility (DMU). The utility derived from each successive units of a commodity diminishes. In other words, the marginal utility of a commodity diminishes as the consumer acquires larger quantities of it. 5. The total utility of a basket of goods depends on the quantities of the individual commodities. If there are n commodities in the bundle with quantities X 1 , X 2 ,... X n , the total utility is given by TU = f ( X 1 , X 2...... X n ). 42  3.3.1.2 Total and marginal utility Total Utility (TU) is the total satisfaction a consumer gets from consuming some specific quantities of a commodity at a particular time. As the consumer consumes more of a good per time period, his/her total utility increases. However, there is a saturation point for that commodity beyond which the consumer will not be capable of enjoying any greater satisfaction from it. Marginal Utility (MU) is the extra satisfaction a consumer realizes from an additional unit of the product. In other words, marginal utility is the change in total utility that results from the consumption of one more unit of a product. Graphically, it is the slope of total utility. Mathematically, marginal utility is: TU MU  Q where, TU is the change in total utility, and Q is the change in the amount of product consumed. To explain the relationship between TU and MU, let us consider the following hypothetical example. Table 3.1: Total and marginal utility Quantity Total utility (TU) Marginal utility (MU) 0 0 - 1 10 10 2 18 8 3 24 6 4 28 4 5 30 2 6 30 0 7 28 -2 The total utility first increases, reaches the maximum (when the consumer consumes 6 units) and then declines as the quantity consumed increases. On the other hand, the marginal utility continuously declines (even becomes zero or negative) as quantity consumed increases. 43 Graphically, the above data can be depicted as follows. TU 30 TU 18 0 2 6 Quantity Consumed MU 8 Quantity Consumed 0 2 6 Figure 3.1: Total and marginal utility curves As it can be observed from the above figure,  When TU is increasing, MU is positive.  When TU is maximized, MU is zero.  When TU is decreasing, MU is negative. 3.3.1.3 Law of diminishing marginal utility (LDMU) Is the utility you get from consumption of the first orange the same as the second or the third orange? The law of diminishing marginal utility states that as the quantity consumed of a commodity increases per unit of time, the utility derived from each successive unit decreases, consumption of all other commodities remaining constant. In other words, the extra satisfaction that a consumer derives declines as he/she consumes more and more of the product in a given period of time. This gives sense in that the first banana a person consumes gives him more marginal utility than the second and the second banana also gives him higher marginal utility than the third and so on (see figure 3.1). 44 The law of diminishing marginal utility is based on the following assumptions.  The consumer is rational  The consumer consumes identical or homogenous product. The commodity to be consumed should have similar quality, color, design, etc.  There is no time gap in consumption of the good  The consumer taste/preferences remain unchanged 3.3.1.4 Equilibrium of a consumer The objective of a rational consumer is to maximize total utility. As long as the additional unit consumed brings a positive marginal utility, the consumer wants to consumer more of the product because total utility increases. However, given his limited income and the price level of goods and services, what combination of goods and services should he consume so as to get the maximum total utility? a) the case of one commodity The equilibrium condition of a consumer that consumes a single good X occurs when the marginal utility of X is equal to its market price. MU X  PX Proof Given the utility function U  f (X ) If the consumer buys commodity X, then his expenditure will be. The consumer maximizes the difference between his utility and expenditure. Max(U  QX PX ) The necessary condition for maximization is equating the derivative of a function to zero. Thus, dU d (Q X PX )  0 dQ X dQ X dU  PX  0  MU X  PX dQ X 45  MUX A PX C B MUX QX Figure 3.2: Equilibrium condition of consumer with only one commodity At any point above point C (like point A) where MUX > PX, it pays the consumer to consume more. When MUX < PX (like point B), the consumer should consume less of X. At point C where MUX = PX the consumer is at equilibrium. b) the case of two or more commodities For the case of two or more goods, the consumer‘s equilibrium is achieved when the marginal utility per money spent is equal for each good purchased and his money income available for the purchase of the goods is exhausted. That is, = and + =M where, M is the income of the consumer. Example: Suppose Saron has 7 Birr to be spent on two goods: banana and bread. The unit price of banana is 1 Birr and the unit price of a loaf of bread is 4 Birr. The total utility she obtains from consumption of each good is given below. Table 3.2: Utility schedule for two commodities Income = 7 Birr, Price of banana = 1 Birr, Price of bread = 4 Birr Banana Bread Quantity TU MU MU/P Quantity TU MU MU/P 0 0 - - 0 0 - - 1 6 6 6 1 12 12 3 2 11 5 5 2 20 8 2 3 14 3 3 3 26 6 1.5 4 16 2 2 4 29 3 0.75 5 16 0 0 5 31 2 0.5 6 14 -2 -2 6 32 1 0.25 46  Recall that utility is maximized when the condition of marginal utility of one commodity divided by its market price is equal to the marginal utility of the other commodity divided by its market price. MU 1 MU 2  P1 P2 In table 3.2, there are two different combinations of the two goods where the MU of the last birr spent on each commodity is equal. However, only one of the two combinations is consistent with the prices of the goods and her income. Saron will be at equilibrium when she consumes 3 units of banana and 1 loaf of bread. At this equilibrium, i) MU1/P1 = MU2/P2 MU banana MU bread 3 12    3 Pbanana Pbread 1 4 ii) P1.Q1+ P2.Q2= M (1*3) + (4*1) = 7 The total utility that Saron derives from this combination can be given by: TU= TU1 + TU2 TU= 14 + 12 TU= 26 Given her fixed income and the price level of the two goods, no combination of the two goods will give her higher TU than this level of utility. Limitation of the cardinal approach 1. The assumption of cardinal utility is doubtful because utility may not be quantified. Utility cannot be measured absolutely (objectively). 2. The assumption of constant MU of money is unrealistic because as income increases, the marginal utility of money changes. 3.3.2 The ordinal utility theory In the ordinal utility approach, it is not possible for consumers to express the utility of various commodities they consume in absolute terms, like 1 util, 2 utils, or 3 utils but it is possible to express the utility in relative terms. The consumers can rank commodities in the order of their preferences as 1st, 2nd, 3rd and so on. Therefore, the consumer need not know in specific units the utility of various commodities to make his choice. It suffices for him to be able to rank the various baskets of goods according to the satisfaction that each bundle gives him. 47  3.3.2.1 Assumptions of ordinal utility theory The ordinal approach is based on the following assumptions.  Consumers are rational - they maximize their satisfaction or utility given their income and market prices. ]  Utility is ordinal - utility is not absolutely (cardinally) measurable. Consumers are required only to order or rank their preference for various bundles of commodities.  Diminishing marginal rate of substitution: The marginal rate of substitution is the rate at which a consumer is willing to substitute one commodity for another commodity so that his total satisfaction remains the same. The rate at which one good can be substituted for another in consumer‘s basket of goods diminishes as the consumer consumes more and more of the good.  The total utility of a consumer is measured by the amount (quantities) of all items he/she consumes from his/her consumption basket.  Consumer’s preferences are consistent. For example, if there are three goods in a given consumer‘s basket, say, X, Y, Z and if he prefers X to Y and Y to Z, then the consumer is expected to prefer X to Z. This property is known as axioms of transitivity. The ordinal utility approach is explained with the help of indifference curves. Therefore, the ordinal utility theory is also known as the indifference curve approach. 3.3.2.2 Indifference set, curve and map Indifference set/ schedule is a combination of goods for which the consumer is indifferent. It shows the various combinations of goods from which the consumer derives the same level of satisfaction. Consider a consumer who consumes two goods X and Y (table 3.3). Table 3.3: Indifference schedule Bundle (Combination) A B C D Orange 1 2 4 7 Banana 10 6 3 1 In table 3.3 above, each combination of good X and Y gives the consumer equal level of total utility. Thus, the individual is indifferent whether he consumes combination A, B, C or D. Indifference curve: When the indifference set/schedule is expressed graphically, it is called an indifference curve. An indifference curve shows different combinations of two goods which yield the same utility (level of satisfaction) to the consumer. A set of indifference curves is called indifference map. 48  10 A Banana Banana B 6 C IC3 3 D IC2 1 IC1 Orange 1 2 4 7 Orange i) Indifference curve ii) Indifference map Figure 3.3: Indifference curve and indifference map 3.3.2.3 Properties of indifference curves 1. Indifference curves have negative slope (downward sloping to the right). Indifference curves are negatively sloped because the consumption level of one commodity can be increased only by reducing the consumption level of the other commodity. In other words, in order to keep the utility of the consumer constant, as the quantity of one commodity is increased the quantity of the other must be decreased. 2. Indifference curves are convex to the origin. This implies that the slope of an indifference curve decreases (in absolute terms) as we move along the curve from the left downwards to the right. The convexity of indifference curves is the reflection of the diminishing marginal rate of substitution. This assumption implies that the commodities can substitute one another at any point on an indifference curve but are not perfect substitutes. 3. A higher indifference curve is always preferred to a lower one. The further away from the origin an indifferent curve lies, the higher the level of utility it denotes. Baskets of goods on a higher indifference curve are preferred by the rational consumer because they contain more of the two commodities than the lower ones. 4. Indifference curves never cross each other (cannot intersect). The assumptions of consistency and transitivity will rule out the intersection of indifference curves. Figure 3.4 shows the violations of the assumptions of preferences due to the intersection of indifference curves. 49  Good Y A B IC2 C IC1 Good X Figure 3.4: Intersection of indifference curves In the above figure, the consumer prefers bundle B to bundle C. On the other hand, following indifference curve 1 (IC1), the consumer is indifferent between bundle A and C, and along indifference curve 2 (IC2) the consumer is indifferent between bundle A and B. According to the principle of transitivity, this implies that the consumer is indifferent between bundle B and C which is contradictory or inconsistent with the initial statement where the consumer prefers bundle B to C. Therefore, indifference curves never cross each other. 22 3.3.2.4 Marginal rate of substitution (MRS) Marginal rate of substitution is a rate at which consumers are willing to substitute one commodity for another in such a way that the consumer remains on the same indifference curve. It shows a consumer‘s willingness to substitute one good for another while he/she is indifferent between the bundles. Marginal rate of substitution of X for Y is defined as the number of units of commodity Y that must be given up in exchange for an extra unit of commodity X so that the consumer maintains the same level of satisfaction. Since one of the goods is scarified to obtain more of the other good, the MRS is negative. Hence, usually we take the absolute value of the slope. Number of units of Y given up Y MRS X ,Y   Number of units of X gained X To understand the concept, consider the following indifference curve. Good Y 30 A 20 B 12 C 8 D IC 5 10 15 20 Good X Figure 3.5: Indifference curve for two products X and Y 50 From the above graph, MRSX,Y associated with the movement from point A to B, point B to C and point C to D is 2.0,1.6, and 0.8 respectively. That is, for the same increase in the consumption of good X, the amount of good Y the consumer is willing to scarify diminishes. This principle of marginal rate of substitution is reflected by the convex shape of the indifference curve and is called diminishing marginal rate of substitution. It is also possible to derive MRS using the concept of marginal utility. MRS X ,Y is related to MUX and MUY as follows. MU X MRS X ,Y  MU Y Proof: Suppose the utility function for two commodities X and Y is defined as: U  f ( X ,Y ) Since utility is constant along an indifference curve, the total differential of the utility function will be zero. U U dU  dX  dY  0 X Y MU X dX  MU Y dY  0 MU X dY MU Y dX   MRS X ,Y Similarly,   MRS Y , X MU Y dX MU X dY Example: Suppose a consumer‘s utility function is given by U ( X ,Y )  X 4Y 2. Find MRSX,Y MU X Solution: MRS X ,Y  MU Y U U MU X 4 X 3Y 2 2Y MU X   4 X 3Y 2 and MU Y   2 X 4Y Hence, MRS X ,Y    X Y MU Y 2 X 4Y X 3.3.2.5 The budget line or the price line Do you think that the indifference curve discussed in the previous section tells us whether a given combination of goods is affordable to the consumer? If no, what are the major constraints to the consumer in maximizing his/her total utility? Indifference curves only tell us about consumer preferences for any two goods but they cannot show which combinations of the two goods will be bought. In reality, the consumer is constrained by his/her income and prices of the two commodities. This constraint is often presented with the help of the budget line. 51 The budget line is a set of the commodity bundles that can be purchased if the entire income is spent. It is a graph which shows the various combinations of two goods that a consumer can purchase given his/her limited income and the prices of the two goods. In order to draw a budget line facing a consumer, we consider the following assumptions.  There are only two goods bought in quantities, say, X and Y.  Each consumer is confronted with market determined prices, PX and PY.  The consumer has a known and fixed money income (M). Assuming that the consumer spends all his/her income on the two goods (X and Y), we can express the budget constraint as: M  PX X  PY Y By rearranging the above equation, we can derive the following general equation of a budget line. M PX Y  X PY PY Graphically, Good Y M/PY B A Good X M/PX Figure 3.6: The budget line Note that: PX  The slope of the budget line is given is by  (the ratio of the prices of the two goods). PY  Any combination of the two goods within the budget line (such as point A) or along the budget line is attainable.  Any combination of the two goods outside the budget line (such as point B) is unattainable (unaffordable). 52 Example: A consumer has $100 to spend on two goods X and Y with prices $3 and $5 respectively. Derive the equation of the budget line and sketch the graph. Solution: The equation of the budget line can be derived as follows. PX X  PY Y  M Y 3 X  5Y  100 5Y  100  3 X 20 100 3 Y  X 5 5 3 Y  20  X X 5 33.3 When the consumer spends all of her income on good Y, we get the Y- intercept (0,20). Similarly, when the consumer spends all of her income on good X, we obtain the X- intercept (33.3,0). Using these two points we can sketch the graph of the budget line. Recall that a budget is drawn for given prices and fixed consumer‘s income. Hence, the changes in prices or income will affect the budget line. Change in income: If the income of the consumer changes (keeping the prices of the commodities unchanged), the budget line also shifts (changes). Increase in income causes an upward/outward shift in the budget line that allows the consumer to buy more goods and services and decreases in income causes a downward/inward shift in the budget line that leads the consumer to buy less quantity of the two goods. It is important to note that the slope of the budget line (the ratio of the two prices) does not change when income rises or falls. Good Y M/Py Good X M/Px Figure 3.7: Effects of increase (right) and decrease (left) in income on the budget line 53 Change in prices: An equal increase in the prices of the two goods shifts the budget line inward. Since the two goods become expensive, the consumer can purchase the lesser amount of the two goods. An equal decrease in the prices of the two goods, one the other hand, shifts the budget line out ward. Since the two goods become cheaper, the consumer can purchase the more amounts of the two goods. Good Y M/Py Good X M/Px Figure 3.8: Effect of proportionate increase (inward) and decrease (out ward) in the prices of both goods An increase or decrease in the price of one of the two goods, keeping the price of the other good and income constant, changes the slope of the budget line by affecting only the intercept of the commodity that records the change in the price. For instance, if the price of good X decreases while both the price of good Y and consumer‘s income remain unchanged, the horizontal intercept moves outward and makes the budget line flatter. The reverse is true if the price of good X increases. On the other hand, if the price of good Y decreases while both the price of good X and consumer‘s income remain unchanged, the vertical intercept moves upward and makes the budget line steeper. The reverse is true for an increase in the price of good Y. Good Y Good X Figure 3.9: Effect of decrease in the price of only good X on the budget line 54  3.3.2.6 Equilibrium of the consumer The preferences of a consumer (what he/she wishes to purchase) are indicated by the indifference curve. The budget line specifies different combinations of two goods (say X and Y) the consumer can purchase with the limited income. Therefore, a rational consumer tries to attain the highest possible indifference curve, given the budget line. This occurs at the point where the indifference curve is tangent to the budget line so that the slope of the indifference curve ( MRS XY ) is equal to the slope of the budget line ( PX / PY ). In figure 3.10, the equilibrium of the consumer is at point ‗E‘ where the budget line is tangent to the highest attainable indifference curve (IC2). Y Y* E IC3 IC2 IC1 X X* Figure 3.10: Consumer equilibrium under indifference curve approach Mathematically, consumer optimum (equilibrium) is attained at the point where: Slope of indifference curve = Slope of the budget line PX MRS XY  PY MU X PX   MU Y PY Example: A consumer consuming two commodities X and Y has the utility function U ( X ,Y )  XY  2 X. The prices of the two commodities are 4 birr and 2 birr respectively. The consumer has a total income of 60 birr to be spent on the two goods. a) Find the utility maximizing quantities of good X and Y. b) Find the MRS X ,Y at equilibrium. 55  Solution a) The budget constraint of the consumer is given by: PX.X+ PY.Y = M 4X+2Y= 60 …………….…………. (i) Moreover, at equilibrium MU X P  X MU Y PY Y 2 4  X 2 Y 2 2 X Y  2 X  2 ………….………… (ii) Substituting equation (ii) into (i), we obtain Y  14 and X  8. b) MRS X ,Y  MU X  Y  2  14  2  2 MU Y X 8 (At the equilibrium, MRS can also be calculated as the ratio of the prices of the two goods) 56 Chapter summary A consumer makes choices by comparing bundle of goods. Given any two consumption bundles, the consumer either decides that one of the consumption bundles is strictly better than the other, or decides that he is indifferent between the two bundles. Economists use the term utility to describe the satisfaction or pleasure derived from consumption of a good or service. In other words, utility is the power of the product to satisfy human wants. There are two approaches to measure or compare consumer‘s utility derived from consumption of goods and services. These are cardinal and ordinal approaches. The cardinalist school postulated that utility can be measured objectively. However, the assumption of cardinal utility is doubtful because utility may not be quantified. Unlike the cardinal theory, the ordinal utility theory says that utility cannot be measured in absolute terms but the consumer can rank or order the utility he derives from different goods and goods. The ordinal/indifference curve approach is based on the consumer‘s budget line and indifference curves. An indifference curve shows all combinations of two goods which yield the same total utility to a consumer and the budget line represents all combinations of two products that the consumer can purchase, given product prices and his or her money income. The consumer is in equilibrium (utility is maximized) at the point where the budget line is tangent to the highest attainable indifference curve. 57  Review questions Part I: Discussion questions 1. Explain briefly the following concepts. A) Utility B) Indifference curve C) Law of diminishing marginal utility D) Budget line E) Consumer preference F) Marginal rate of substitution 2. What is the basic difference between cardinal and ordinal approaches of utility? 3. Elaborate the justifications for the negative slope and convexity of indifference curve. 4. Standard indifference curves cannot intersect each other. Why? 5. Does the change in income affect the slope of the budget line? Explain. Part III: Workout 1. A person has $ 100 to spend on two goods X and Y whose respective prices are $3 and $5. A. Draw the budget line. B. What happens to the original budget line if the budget falls by 25%? C. What happens to the original budget line if the price of X doubles? D. What happens to the original budget line if the price of Y falls to $4? 2. A rational consumer spends all of her income on two goods: Apple and Banana. Suppose the last dollar spent on Apple increased her total utility from 60 utils to 68 utils and the last dollar spent on Banana increased her total utility from 25 utils to 29 utils. If the price of a unit of Apple is 2 Birr, what is the price of a unit of Banana at equilibrium? 3. Given utility function U= where PX = 12 Birr, Birr, PY = 4 Birr and the income of the consumer is, M= 240 Birr. A. Find the utility maximizing combinations of X and Y. B. Calculate marginal rate of substitution of X for Y (MRSX,Y) at equilibrium and interpret your result. 58 4. Suppose a particular consumer has 8 birr to be spent on two goods, A and B. The unit price of good A is 2 birr and the unit price of B is 1 birr. The marginal utility (MU) she gets from consumption of the goods is given below. Quantity 1 36 30 2 24 22 3 20 16 4 18 12 5 16 10 6 10 4 A) Based on the cardinal analysis, what is the combination of the two goods that gives maximum utility to the consumer? B) What is the total utility at the utility maximization level? Suggested reading materials  A. Koutsoyiannis, Modern Microeconomics, 2nd edition, 1979  D.N.Dwivedi, 1997, Micro Economic Theory, 3rd edition., Vikas Publishing  R. S. Pindyck and D. L. Rubinfeld, Microeconomics, 2nd edition,1992  Varian, 2010, Intermediate Microeconomics: A Modern Approach, 8th edition  C.L.Cole, Micro Economics: A Contemporary Approach.  Ferguson & Gould‘s, 1989, Microeconomic Theory, 6th edition.  E. Mansfield, 1988, Microeconomics: Theory and Applications  Arnold, 2008, Microeconomics, 8th edition, International student edition 59  Chapter Four The Theory of Production and Cost Introduction This chapter has two major sections. The first part will introduce you to the basic concepts of production and production function, classification of inputs, essential features of short run production functions and the stages of short run production. The second part mainly deals with the difference between economic cost and accounting cost, the characteristics of short run cost functions, and the relationship between short run production functions and short run cost functions. Chapter objectives After successful completion of this chapter, you will be able to:  define production and production function  differentiate between fixed and variable inputs  describe short run total product, average product and marginal product  compare and contrast the three stages of production in the short run  explain the difference between accounting cost and economic cost  describe total cost, average cost and marginal cost functions  explain the relationship between short run production functions and short run cost functions 4.1 Theory of production in the short run 4.1.1 Definition of production Raw materials yield less satisfaction to the consumer by themselves. In order to get better utility from raw materials, they must be transformed into outputs. However, transforming raw materials into outputs requires inputs such as land, labour, capital and entrepreneurial ability. Production is the process of transforming inputs into outputs. It can also be defined as an act of creating value or utility. The end products of the production process are outputs which could be tangible (goods) or intangible (services). 4.1.2 Production function Production function is a technical relationship between inputs and outputs. It shows the maximum output that can be produced with fixed amount of inputs and the existing technology. A production function may take the form of an algebraic equation, table or graph. A general equation for production function can, for instance, be described as: 60  Q = f(X 1 , X 2 , X 3 ,..., X n ) where, Q is output and X1, X2, X3,…, Xn are different types of inputs. Inputs are commonly classified as fixed inputs or variable inputs. Fixed inputs are those inputs whose quantity cannot readily be changed when market conditions indicate that an immediate adjustment in output is required. In fact, no input is ever absolutely fixed but may be fixed during an immediate requirement. For example, if the demand for Beer rises suddenly in a week, the brewery factories cannot plant additional machinery overnight and respond to the increased demand. Buildings, land and machineries are examples of fixed inputs because their quantity cannot be manipulated easily in a short period of time. Variable inputs are those inputs whose quantity can be altered almost instantaneously in response to desired changes in output. That is, their quantities can easily be diminished when the market demand for the product decreases and vice versa. The best example of variable input is unskilled labour. Does a short run refer to specific period of time that is applicable to every firm or industry? If this condition is rather unique to the firm, industry or economic variable being studied, what is our basis to classify production as a short run? In economics, short run refers to a period of time in which the quantity of at least one input is fixed. In other words, short run is a time period which is not sufficient to change the quantities of all inputs so that at least one input remains fixed. Here it should be noted that short run periods of different firms have different durations. Some firms can change the quantity of all their inputs within a month while it takes more than a year for other types of firms. This sub-section is confined to production with one variable input and one fixed input. Consider a firm that uses two inputs: capital (fixed input) and labour (variable input). Given the assumptions of short run production, the firm can increase output only by increasing the amount of labour it uses. Hence, its production function can be given by: Q = f (L) where, Q is output and L is the quantity of labour. The production function shows different levels of output that the firm can produce by efficiently utilizing different units of labour and the fixed capital. In the above short run production function, the quantity of capital is fixed. Thus, output can change only when the amount of labour changes. 61  4.1.3 Total, average, and marginal product In production, the contribution of a variable input can be described in terms of total, average and marginal product. Total product (TP): it is the total amount of output that can be produced by efficiently utilizing specific combinations of the variable input and fixed input. Increasing the variable input (while some other inputs are fixed) can increase the total product only up to a certain point. Initially, as we combine more and more units of the variable input with the fixed input, output continues to increase, but eventually if we employ more and more unit of the variable input beyond the carrying capacity of the fixed input, output tends to decline. In general, the TP function in the short-run follows a certain trend: it initially increases at an increasing rate, then increases at a decreasing rate, reaches a maximum point and eventually falls as the quantity of the variable input rises. This tells us what shape a total product curve assumes. Marginal Product (MP): it is the change in output attributed to the addition of one unit of the variable input to the production process, other inputs being constant. For instance, the change in total output resulting from employing additional worker (holding other inputs constant) is the marginal product of labour (MPL). In other words, MPL measures the slope of the total product curve at a given point. dTP Q MPL   dL L In the short run, the marginal product of the variable input first increases, reaches its maximum and then decreases to the extent of being negative. That is, as we continue to combine more and more of the variable input with the fixed input, the marginal product of the variable input increases initially and then declines. Average Product (AP): Average product of an input is the level of output that each unit of input produces, on the average. It tells us the mean contribution of each variable input to the total product. Mathematically, it is the ratio of total output to the number of the variable input. The average product of labour (APL), for instance, is given by: TP APL  L Average product of labour first increases, reaches its maximum value and eventually declines. The AP curve can be measured by the slope of rays originating from the origin to a point on the TP curve (see figure 4.1). For example, the APL at L2 is the ratio of TP2 to L2. This is identical to the slope of ray a. 62 Output a TP3 TP2 TP TP1 Units of labour (variable input) L1 L2 L3 APL MPL APL Units of labour (variable input) L1 L2 L3 MPL Figure 4.1: Total product, average product and marginal product curves The relationship between MPL and APL can be stated as follows.  When APL is increasing, MPL > APL.  When APL is at its maximum, MPL = APL.  When APL is decreasing, MPL < APL. Example: Suppose that the short-run production function of certain cut-flower firm is given by: Q = 4KL - 0.6K 2 - 0.1L2 where Q is quantity of cut-flower produced, L is labour input and K is fixed capital input (K=5). a) Determine the average product of labour (APL) function. b) At what level of labour does the total output of cut-flower reach the maximum? c) What will be the maximum achievable amount of cut-flower production? 63 Solution: Q 4KL - 0.6K 2 - 0.1L2 0.6K 2 15 20L - 15 - 0.1L2 a) APL = = = 4K - - 0.1L = 20 - - 0.1L = L L L L L b) When total product (Q) is maximum, MP will be zero. Q (4KL - 0.6K 2 - 0.1L2 ) MPL = = = 4K - 0.2L = 0 L L 20  20 - 0.2L = 0  L = = 100 0.2 Hence, total output will be the maximum when 100 workers are employed. c) Substituting the optimal values of labor (L=100) and capital (K=5) into the original production function (Q): Qmax = 4KL - 0.6K 2 - 0.1L2 = 4* 5* 100 - 0.6* 52 - 0.1* 100 2 = 985 4.1.4 The law of variable proportions The law of variable proportions states that as successive units of a variable input(say, labour) are added to a fixed input (say, capital or land), beyond some point the extra, or marginal, product that can be attributed to each additional unit of the variable resource will decline. For example, if additional workers are hired to work with a constant amount of capital equipment, output will eventually rise by smaller and smaller amounts as more workers are hired. This law assumes that technology is fixed and thus the techniques of production do not change. Moreover, all units of labour are assumed to be of equal quality. Each successive worker is presumed to have the same innate ability, education, training, and work experience. Marginal product ultimately diminishes not because successive workers are less skilled or less energetic rather it is because more workers are being used relative to the amount of plant and equipment available. The law starts to operate after the marginal product curve reaches its maximum (this happens when the number of workers exceeds L1 in figure 4.1). This law is also called the law of diminishing returns. 4.1.5 Stages of production We are not in a position to determine the specific number of the variable input (labour) that the firm should employ because this depends on several other factors than the productivity of labour. However, it is possible to determine the ranges over which the variable input (labour) be employed. To this end, economists have defined three stages of short run production. 64 Stage I: This stage of production covers the range of variable input levels over which the average product (APL) continues to increase. It goes from the origin to the point where the AP L is maximum, which is the equality of MPL and APL (up to L2 level of labour employment in figure 4.1). This stage is not an efficient region of production though the MP of variable input is positive. The reason is that the variable input (the number of workers) is too small to efficiently run the fixed input so that the fixed input is under-utilized (not efficiently utilized). Stage II: It ranges from the point where APL is at its maximum (MPL=APL) to the point where MPL is zero (from L2 to L3 in figure 4.1). Here, as the labour input increases by one unit, output still increases but at a decreasing rate. Due to this, the second stage of production is termed as the stage of diminishing marginal returns. The reason for decreasing average and marginal products is due to the scarcity of the fixed factor. That is, once the optimum capital-labour combination is achieved, employment of additional unit of the variable input will cause the output to increase at a slower rate. As a result, the marginal product diminishes. This stage is the efficient region of production. Additional inputs are contributing positively to the total product and MP of successive units of variable input is declining (indicating that the fixed input is being optimally used). Hence, the efficient region of production is where the marginal product of the variable input is declining but positive. Stage III: In this stage, an increase in the variable input is accompanied by decline in the total product. Thus, the total product curve slopes downwards, and the marginal product of labour becomes negative. This stage is also known as the stage of negative marginal returns to the variable input. The cause of negative marginal returns is the fact that the volume of the variable inputs is quite excessive relative to the fixed input; the fixed input is over-utilized. Obviously, a rational firm should not operate in stage III because additional units of variable input are contributing negatively to the total product (MP of the variable input is negative). In figure 4.1, this stage is indicated by the employment of labour beyond L3. 4.2 Theory of costs in the short run 4.2.1 Definition and types of costs To produce goods and services, firms need factors of production or simply inputs. To acquire these inputs, they have to buy them from resource suppliers. Cost is, therefore, the monetary value of inputs used in the production of an item. Economists use the term ―profit‖ differently from the way accountants use it. To the accountant, profit is the firm‘s total revenue less its explicit costs (accounting costs). To the economist, economic profit is total revenue less economic costs (explicit and implicit costs). 65