2 IntroductionEach consumer has to face the problem of multiplicity of wants and limited income.In such state of affairs it is the desire of each consumer to maximize his satisfaction in the presence of income constraint.Whenever a consumer maximizes his satisfaction, he is satisfied with his spending pattern, does not have any tendency to change his style of expenditure, he is said to be in equilibrium in economics.
3 Assumption of Model(1) The satisfaction or utility can be measured into numbers. E.g. If a consumer drinks a glass of milk, the satisfaction he derives from that glass of milk can be represented into number like 1,2,4,5 etc.It is the view of the economist that the satisfaction or utility is a cardinally measureable quantity as length, weight and volume.Therefore they accepted the existence of unit of measurement of utility called “util”.They believed that each consumer has a utilometer to measure the utility into numbers when a consumer uses that units of a good.
4 Assumption of Model(2) Utility depends upon the units of one good which a consumer is consuming. In other words utilities are independently determined as U=f(Q).Where “U” stands for utility, while “Q” represents the units of the particular good which a consumer is consuming.Moreover, the utilities from different goods can be added. It shows by additive utility function. U = U1(Q1) + U2(Q2)+....+Un(Qn)Where U1, U2 are the utilities of commodity no. 1,2 etc, which are included in the bundle or basket of goods which a consumer is purchasing. While Q1, Q2 are the number of commodities.
5 Assumption of Model(3) The behaviour of all consumers remain a like. This means that what is the behaviour of a representative consumer, the same is the behaviour of rest of consumers during the consumption.(4) Consumer is rational i.e. He is well aware of with his income and prices of the good in the market.(5) The money is a measure which is employed to measure the utility of the goods and service. And there is no change in the marginal (extra) utility of the money, it means that marginal utility of the goods may change while the marginal utility of money remain the same.
6 Law of Diminishing Marginal Utility (DMU) Before we explain this law, we clarify the meanings of utility and marginal utility.By utility we mean, the power of a good to satisfy human want. i.e. The water has a power to quench one’s thirst. For our discussion, by utility we mean “The satisfaction”.As we discussed above that utility or satisfaction depends upon the units of a particular good. It is as: U= f(Q) or TU=f(Q). This is called utility or total utility function.By “Marginal utility” we mean the net change in total utility by having consumed an additional unit of a commodity.
7 Law of Diminishing Marginal Utility (DMU) For example a consumer is using the units of apple, if the total utility of 1st apple is 10 units while the total utility goes to 18 units if he uses the two apples, then the net change in total utility or marginal utility is 8.MU is the derivative of total utility function or it is the slope of TU curve, it is as: U = f(Q).Then its derivative will be MU = dU/dQ.Now we introduce “Law of DMU”. This law is based upon a common reality of life, “The more we have of any commodity, the desire to get any more of it decreases”.
8 Law of Diminishing Marginal Utility (DMU) “When a consumer goes on to use the units of good, the total utility derived from the units of good increases at a decreasing rate.In other words “along with successive and continuous use of any commodity the marginal utility derived from the units of the commodity goes on to fall”.From the definition we deduce the following:Along with increase in use of any commodity, TU increases at a decreasing rate, hence MU decreases.When the total utility reaches maximum , MU becomes zero. This situation is called point of saturation.When total utility itself falls, MU becomes negative.
9 Law of Diminishing Marginal Utility (DMU) In this context, we get the assistance of a specific quadratic utility function which encompasses all of above relationships.On such lines a specific utility function is as: U = 11Q – Q2.By assuming different values of “Q” we can find the values of “U” and then values of MU will be attained.Reference pg no.322 and 323.
10 Assumption of Law of DMU There should be a continuous use of the commodity which a consumer is consuming.All the units of the commodity in use must be similar.The units of good must be a of a suitable amount.The taste of consumer should remain the same.The income of the consumer should not change.
11 Consumer EquilibriumAccording to law of equi. Marginal utility; “ A consumer is in equilibrium when he spends his money income on different goods in such a way that MU of the last units of money spent on each good is equal”.This is explained with the help of a schedule and diagram. We assume that a consumer has 5 rupees which he has to spend on two goods like “X” and “Y”. The MU of different units of money are assumed as:Units of MoneyMuxMuy116142121036485
12 Consumer EquilibriumWhen a consumer decided to spend his 1st unit of money whether this will go for good x or for good y. Obviously it will go for good x because here he gets 16 utils.While he get 14 utils if he spends it on good y. Then 2nd rupee will be spend on good y because spending it on y yields 14 utils while spending it on x yields 12 utils.The 3rd rupee will be spent on x, because 12>10. The 4th rupee will be spent on y and 5th will be spent on x yielding the 10 utils each.In this way out of 5 rupee, 3 rupee will be spend on good x and the remaining 2 rupee will be spend on good y. By such arrangements the MU of the last rupee spent on each good has equalized as 10=10.
13 Consumer EquilibriumNow we prove here that how this situation leads to maximization of satisfaction.Total satisfaction or total marginal utility when 3 rupee are spent on good x: = 38.Total satisfaction or total marginal utility when the remaining 2 rupees are spent on good y: = 24.Total satisfaction or total marginal utility of 5 rupees: 38+24=62.We assume that if the consumer plans to spend 4 rupee on x and remaining 1 rupee on y. This situation will not equate MU of the last unit of money spent on each good.
14 Consumer EquilibriumMoreover the total satisfaction will be less than earlier, it is as: if 4th rupee is last on x, its MU = 8. if remaining one rupee is spent on y, its MU = 14. thus 8 not equal to 14.Total satisfaction of 4 rupee on x: = 46. Total satisfaction of 1 rupee on y = 14. Total satisfaction of 5 rupees: = 60.Reference page no. 325.
15 Indifference Curve“An indifference curve is a curve which shows difference combinations of two commodities like x and y which give a consumer an equal satisfaction”.“An IC shows different bundles of two goods like x and y amongst which consumer remains indifferent because of all such bundles yield a specific level of utility”.“An indifference curve is the locus of all points in the commodity space that are equally attractive to the consumer”. That is the consumer is indifferent between any two commodity bundles (points) that lie on the same IC curve. U = f(x,y) = k
16 Indifference Curve Reference page no. 335. In fig we have IC which has been constructed with the help of bundles of two goods x and y represented in the schedule.As the concept of IC is concerned with the pairs providing equal satisfaction. While the pair giving more satisfaction to consumer will lie above these combination or above this IC.BundlesCommodity xCommodity yMRSxy = dy/dxA111B283/1 = 3C362/1 = 2D451/1 = 1E4.50.5/1 = 1/2
17 Indifference CurveWhile the pairs giving less satisfaction to the consumer will lie below these combinations or below this IC – all such is shown with the help of indifference map. (reference fig 336).Marginal rate of substitution MRSxy = dY/dxSimply the rate of exchange between two commodities x and y is called MRS. In proper words by “MRSxy we mean how many units of commodity y the consumer has to forego to get an additional unit of commodity x while the new combination of commodity x and y yields the same level of satisfaction”.Reference our previous schedule we see that as consumer moves from pair A to pair B, he losses 3 units of y for an additional unit of x. Accordingly, marginal rate of substitution of x for y is 3.
18 Indifference CurveMRS is also known as slope of an IC. It is shown with the help of fig-6. (ref page no. 337)If we observe the indifference schedule and indifference curve, we find that MRS goes on to fall. Such tendency of falling MRS is known as “Principle of DMRS” between x and y.It is well evident fact that as a consumer has more and more of any commodity his desire to get any more of it decreases because of an application of law of diminishing marginal utility.
19 Budget LineAn IC shows different combinations of two goods x and y which yield and equal level of satisfaction. Now the question is this which combinations of two goods a consumer can afford to purchase.This is concerned with the budget constraint line, price line or budget line of the consumer. It is defined as:“Budget line is a curve which shows different combinations of two goods like x and y which a consumer can purchase, while the consumer’s income, price of x and price of y are given”.It is as: xPx + yPy = IWhere x represents x commodity, Px is price of x, y represents y commodity and Py is the price of y while I is the income of the consumer.
20 Budget Line Y = I/Py – Px/Py (x). Now by assuming different values of x, we can find the values of y and then putting such values of x and y in the budget constraint equation, the expenditure of the consumer will become equal to the fixed given income of the consumer.We suppose I = 10, Px = 2 and Py = 1. If x = 0,1,2,3,4,5. plotting values.PairsXYxPx + yPy = IA100(2) + 10(1) = 10B181(2) + 8(1) = 10C262(2) + 6(1) = 10D343(2) + 4(1) = 10E4(2) + 2(1) = 10F55(2) + 0(1) = 10
21 Budget Line Figure (ref pg no. 339). The OF is x intercept of BL which has been attained as I/Px=10/2 = 5. While OA is y intercept of BL which has been found as I/Py = 10/1 = 10.Thus BL shows different pairs of x and y where a consumer is fully spent as the pairs A, B, C, D, E and F. Now we explain certain properties of BL.Mathematically, the BL is the locus of all combinations of x and y that satisfy the equation: x Px+yPy=I. Thus BL represents all those points which enables to exhaust the consumer’s fixed income.The BL divides the entire commodity space into attainable and unattainable pairs. As BL divides the commodity space into the triangular area OAF and rest of space (unattainable pairs). Given his fixed income and commodity
22 Budget Lineprices, the consumer can choose only among those bundles that lie in the triangular area OAF, including its boundaries. The existence of the unattainable set reflects the influence of the law of scarcity.The BL depends upon only two elements: the consumer’s money income (I) and commodity prices (Px and Py). When either of these two elements changes, the BL shifts to a new position. However the BL remains totally unaffacted by a particular change: a proportional increase or decrease in money income and all commodity prices. Such a change leaves horizontal and vertical axis intercepts of the BL same.
23 Production FunctionTheory of production function establishes a relationship between inputs and output. In other words production function shows a physical relationship between inputs and output.The firms production function is merely a statement of maximum quantity of output that it can produce with any specified quantities of labor, capital and land etc.“Production function (P.F) is a schedule or mathematical equation that gives a maximum quantity of output that can be produced from specified sets of inputs while techniques of production are given”.The classical production function is concerned with short run period. Short run represents that particular period where some or at least one factor of production is kept constant.
24 Production FunctionE.g. If any firm keeps the plant or machinery fixed (which is not possible to change in short run) and go on employing the units of labour such situation will represent short run.Accordingly the classical or short run production function is stated as: Q = f(L)K where Q represents total output, L represents units of labour and K represents capital which is constant here.Classical are of the view that keeping the other factor constant if we go on employing the units of labour, the total production will increase at different rates.In other words the rate of change in total product which is called marginal product may increase, may remain constant and may decrease.
25 Production FunctionBy employing more labour if marginal product (MP) increases such will demonstrate the operation of “law of increasing returns”. If MP remains constant such depicts the situation of “law of constant returns””. And if MP falls the it means “law of decreasing returns”.Total product (TP=Q): by having employed a certain number of labour whatsoever is produced by a firm represents total output of the firm. E.g. If firm produces 50 motorcycles by employing 10 labour, such will represent total output or total product of the firm.Average product (AP): if we divide total product by the units of the labour, we will get AP. It is as: AP=TP/L=Q/L=50/10 = 5.
26 Production FunctionMarginal product (MP): it represents addition to total output that results from a unit increase in the employment of labour, assuming that the fixed input remains unchanged.E.g. As 10 labour produce 50 motorcycles and by employing 11th labour if the production of motorcycle goes to 54 motorcycles, then the marginal product of 11th labour is 4 motorcycles. MP also denotes the derivative of production function or slope of the TP curve. MP = dQ/dLBy keeping the capital fixed, if we go on to employ the units of labour, the following phenomena is observed.In the beginning TP will increase at an increasing rate, hence both AP and MP increase but MP will increase more than AP (MP>AP)
27 Production FunctionLater on TP will increase at a constant rate, hence both AP and MP will remain constant. (MP=AP).Finally TP will increase at a decreasing rate hence both AP and MP decrease but MP will decrease more than AP (MP<AP).Afterwards by employing more units of labour TP will reach maximum . Consequently MP will be zero. Still employing more units of labour means the falling of TP itself and making the MP negative.
28 Production Function L Q APL=Q/L MPL=dQ/dL Stages 1 10 MP>AP 2 25 12.51534520460MP=AP57014MP<AP675710.7MP=08729-3MP=-ve63-9Reference diagram (pg 405)
29 Producer EquilibriumThe basic objective of the firm is to maximize its output or minimize its cost of production. Therefore if the budget (cost) constraint is given, then the problem before the firm is to employ different units of labour and capital in such a way that its output be maximized. And such combination of labour and capital is known as optimum factor combination. Such represents a firms equilibrium.“A firm will be in equilibrium or attains optimal factor combination when it spends its budget on different factors of production in such away that the ratio of marginal productivities of different factors and their prices be equalized”It is as: LPL + KPK + NPN = CMPL/PL = MPK/PK = MPN/PN
30 Producer EquilibriumWhere L, K and N represents units of labour, capital and land. While PL, PK and PN are the prices of labour, capital and land. Whereas MPL, MPK and MPN represents marginal productivities of labour, capital and land. While ‘C’ represents budget of the firm.With the help of above schedule we have constructed the fig. 1 which has two parts. In the upper part we have total product curve shown by Q=f(L). The total output is increasing at different rates.In the lower part of the diagram we have AP and Mp curves. In the beginning from 1st labour to 3rd labour TP is increasing at an increasing rate. Here both AP and MP are increasing but MP is increases more than AP.The situation corresponds to ‘’Law of increasing return”. The point ‘C’ represents point of ‘point of inflexion’ because here the slope of TP curve changes.
31 Producer EquilibriumWhen the firm employs 4th labour, AP has reached its maximum and both AP and MP are equal here. The production stage which starts from origin and lasts till AP is maximised is known as production stage 1.By employing 5th and 5th labour the TP of the firm increases at a decreasing rate. As a result both AP and MP fall but MP falls more than AP. This situation represents the operation of ‘law of diminishing returns’.When the firm employs the 7th labour, there is no change in TP. Consequently MP is zero. The production stage which starts from AP being maximum and lasts for MP being equal to zero in known as production stage II.There is an important property of this stage that here both AP and MP fall but still they are positive.
32 Producer EquilibriumBy employing 8th and 9th labour, the TP of the firm itself falls. Here MP becomes negative while AP is still falling. This situation represents the operation of ‘law of negative returns’.The production stage which starts from MP being equal to zero to MP being equal to negative is said to be production stage III.Importance of production stageThe purpose of each rational producer is to maximize its output or minimize its costs of production therefore, the firm which is to produce with the help of labour will not employ those units of labour having negative MP.Accordingly stage III will be an uneconomic stage for producer. Therefore the producer will not employ any unit of labour corresponding to stage III.
33 Producer EquilibriumAgain the stage I is not also an economically efficient stage. Although here both AP and MP are rising, yet this stage indicates that the fixed factor (capital) is enough big and has not been fully utilized.Accordingly the MP of labour is increasing. If the employment of labour is stopped here it would mean the losing of the gains which could be reaped through rising of MP.All this concludes that it is stage II ( in connection with the employment of labour) which is accorded as most beneficial from economic point of view. Although here both MP and AP are decreasing, yet they are positive.In this stage how many units of labour firm will employ – this is concerned with the behaviour of the firm which will be explained in the presence of firm’s budget and prices of factors of production.
34 Producer EquilibriumTo explain it we take the following examples. We assume that C=8, PL = 2 and Pk=1. we also assume the MPL and MPK corresponding to different units of labour and capital.In the light of this table we assume a pair which consists of 2 units of labour and 4 units of K is selected by the firm. Putting the number of such units and their prices in the budget constraint.Units of labourMPLUnits of capital KMPK12072166312548
35 Producer Equilibrium LPL + KPK = C; 2(2) + 4(1) = 8; 4+4 = 8 As the MP of 2nd labour is 16 and PL = 2, the MP of the 4th capital is 4, and Pk=4. now putting such information in the proportionally equation.MPL/PL = MPK/P; 16/2 not equal to 4/1This shows that if firms employs 2 of L and 4 of K his budget is fully spent but the ratios of MP’s and the prices of factors are not equalized. Hence this does not represent the optimality and the firm will have to change the pair of L and K.Accordingly, if the firm decides to purchase 3 of L and 2 of K. Putting them in budget constraint.
36 Producer Equilibrium MPL/PL = MPK/PK; 12/2 = 6/; 6 = 6. All this shows that in this situation not only the entire budget of the firm is spent but the ratio of MP and prices of factors have also been equalized. Thus if the firm purchases 3 of L and 2 of K, the firm will attain equilibrium. Or such combination represents an optimum factor combination.From above discussion it is concluded that it is necessary for the firm that it should compare MP of the factor with the prices of the factor and they should be equal.If they are not equal, the firm will go on substituting the factors until they are equalized. This is the reason that such approach to firm’s equilibrium is also known as law of substitution in production.
37 ISO COST APPROACHEarlier we presented optimum factor combination with the help of MP theory. Now we present the same situation with the help of “ISO quant approach”.Optimum factor combination represents such combination of labour and capital where either (1) the production of the firm be maximized or (2) the cost of the firm be minimized.Simply an “an Isoquant is a curve which shows those combinations of labour and capital which can produce a specific level of output”. Or“equal product curve is a curve which represents those pairs of two factors like labour and capital which produce an equal level of output”.An isoquant represents different input factor combinations of input ratios that may be used to produce a specific level of output. For a movement along an isoquant the level of output remains constant but the input ratio changes.
38 ISO COST APPROACHAs here the production depends upon labour and capital. Accordingly the production function will be as: Q = f(L, K). To construct an isoquant, we first present an schedule.With the help of above schedule we can construct isoquant (IQ) in fig:2 (reference pg.410)OutputPairsLKMRTSlk= dK/dL1000 yardsI1161000 “II2124/1=4III393/1=3IV472/1=2V561/1=1
39 ISO COST APPROACHThe isoquant consists of pair of L and K which yield a specific level of output which we named 1000 yd. The lines drawn from the origin to the points I, II, III, IV and V show the capital labour ratios.As the pair I shows that 16 units of K has been employed with 1 unit of L. Accordingly, the K/L =16/1 =16. while pair V shows that 6 of K has been emloyed with 5 of L.Thus K/L =6/5 =1.2. In between 1 and , we have other pairs like II, III and IV, they also show certain K/L.The important property of an isoquant is this that it shows a specific level of output. Hence the level of output remains fixed along an isoquant while the ratio of K to L goes of changing along an isoquant.
40 ISO COST LINEAs we are dealing with the issue of firms optimal factor combination. Accordingly earlier we presented the concept of isoquant which is concerned with the different factor combinations which yield equal level of output.This was technical phenomenon but now the question to be confronted is this which combination of two factors like labour and capital a firm can afford to purchase.This is concerned with the iso cost line. It is defined as:‘ISO cost line is a curve which shows different combinations of two factors like labour and capital which a firm can purchase while the firm’s budget (cost), price of labour (PL) and price of capital (PK) are given”.
41 ISO COST LINEIt is as: LPL + KPK = C; solving it for K: KPK = C-LPL; K = C/PK – PL/PK (L).Now by assuming different values of L, we can find the values of K and putting such values of L and K in isocost equation, the expenditure of the firm will become equal to the fixed given cost of the firm.We suppose C=10, PL =2 and PK =1, if L=0,1,2,3,4,5 and putting them in cost constraint equation. K= C/PK – PL/PK (L) (reference pg 413).PairsLKLPL+KPK=CA100(2) + 10(1) = 10B181(2) + 8(1) = 10C262(2) + 6(1) = 10D343(2) + 4(1) = 10E4(2) + 2(1) = 10F55(2) + 0(1) = 10
42 ISO COST LINEPutting these pairs in the fig 5 (ref pg 414) we get the iso cost line AF.The OF is L intercept of iso cost line which has been attained as C/PL = 10/2 = 5. while OA is k intercept of isocost line which has been attained as C/PK = 10/1 = 10/
43 EXPANSION PATH Reference pg no. 418. Earlier we presented firm’s equilibrium in two cases. Now we will see what will be the effect on firms equilibrium if the firm changes its budget.Such analysis will be similar to that of income effect presented in case of consumer equilibrium. The effect in change of costs(budget) will result in expansion path.Thus expansion path shows ‘what will be the effect on firm’s equilibrium if firm changes its cost (budget) while the prices of both factor like labour and capital remain the same’.In this figure the basic equilibrium of the firm take place at E1 where IQ1 is tangent to AA.
44 EXPANSION PATHAccordingly the firm purchases OL1 of labour and OK1 of capital. We suppose that the budget of the firm increases. Accordingly its iso cost line shits upward as BB.Now the firm is in a position to increase it output. In this way it is an equilibrium at E2. where IQ2 is tangent to BB. Hence the firm is employing OL2 of labour and OK2 of capital.By joining E1 and E2 we get expansion path which shows that along with increase in budget , the firm has increased the employment of both the factors which have led to increase firms output.