Theory of Consumer Behavior PDF

Chapter One 2. The theory of consumer behavior Defn: The theory of consumer behavior deals with the way in which scarcities encroach upon the individual consumer & hence the way such individual makes a choice. The theory states the way consumers take decision on such goods and services. Consumers b...

Chapter One 2. The theory of consumer behavior Defn: The theory of consumer behavior deals with the way in which scarcities encroach upon the individual consumer & hence the way such individual makes a choice. The theory states the way consumers take decision on such goods and services. Consumers buy goods /services to obtain satisfaction from possession of goods /services. 2.1. Consumer preference, utility and consumer choice Given vast number of goods and services that the economy provides and given wide diversity of personal tastes, the consumer make preference among the market basket—collection of one or more commodities. The economic theory f consumer is understood in terms of concepts like; Budget constraint, Consumer preference & Consumer choice Budget constraint Budget is the level of income an individual consumer has acting as a constraint to the quantities of goods the consumer can buy. E.g. suppose a consumer with the money income “M” buys only two goods, say good X and good X, then the budget constraint is written as follow; PX.X+PY.Y < M where PX-Price of good X Y- Quantity of good Y PY- Price of good Y M- Money income of the consume X- Quantity of good X It can also be illustrated using Budget line which shows a combination of the two goods (X & Y) for which total expenditure equals income, i.e. PX.X+PY.Y =M Good Y Budget line – tell us what choices are available D to the consumer.C Budget line 0 M Good X PX Note: Point “D” shows the non-feasibility area (unattainable) i.e. the consumer is unable to buy the corresponding quantities because his /her income is fixed. Point “C” shows the feasibility area (attainable) i.e. the consumer is able to buy the corresponding quantities / or the consumer doesn’t spend his/ her income totally on the consumption of these two goods. Consumer preference In addition to budget line, the information we need about consumer to analyze his/her choice is his/her ranking of the alternative combination of goods /services available. But all combination of 1 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith goods /services has no equal importance for an individual consumer. That is why a consumer ranks his/her desire and builds up a scale of preference. E.g. See the following graph Coffee Mr. A. prefers coffee to tea Mr. B. prefers coffee & tea equally Mr. C. prefers tea to coffee 6 A 4 B 2 C 0 2 4 6 Tea Preference ordering: - is the scheme that enables the consumer to rank different bundles of goods in terms of their desirability or order of preference. It depends on the following assumptions: a. Completeness: - i.e. a consumer able to compare and rank all possible combination or has a complete information about the good he /she can buy. b. Consistency and Transitivity:- Consistency in a sense if at one time regards combination X is better than of Y he/she will not consider combination Y is better than of X at another time. Where as when we say transitivity, if consumer prefers combination X to combination Y and combination Y to Z, then he /she prefers combination X to Z. c. No satiation: - i.e. a consumer is never satisfied and always prefers more of a good to less. Utility Utility is the level of satisfaction that a person gets from consuming a good or undertaking an activity. For example if you purchase, say an apple, and consume this apple, then the satisfaction that you obtained by doing so, is said to be utility.. It varies from person to person and from time to time. Whether good is useful or not, it has utility for the consumer consuming it. E.g. -Drug -Alcoholism, etc, though they are socially immoral, they give a satisfaction for the consumer consuming these items. 2.2. Approaches to Analyze consumer behavior/Measurement of utility In order to analyze consumer behavior economists agreed on the axiom that consumers ate utility maximizing entity. But they are not agreed on the measurability of utility. There are two approaches which can be used to measure utility. These are the cardinal utility approach and the ordinal utility approach. The first says that utility is measurable (quantifiable) using total utility and marginal utility, the classical and Neo-classical economists. The second approach, on the other hand says that, utility can be ranked using indifference curve, rather than being measured, the modern economists. A. Cardinal Utility Analysis Assumptions The cardinal utility approach builds on certain assumptions: 1. Utility is additive: 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 X1, X2, …, Xn the total utility is 2 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith  U= f (X1, X2 ,… Xn). 2. Rationality: the consumer is rational. He/she aims at the maximization of his/her utility subject to the constraint imposed by his /her given income. 3. Utility is cardinal: the utility derived from each commodity is measurable. 4. Constant marginal utility of money: this assumption is necessary if monetary units are to be used as the measure of utility. 5. Diminishing marginal utility: the extra satisfaction gained from successive units of a commodity diminishes. 2.2.1. Relation between Total and marginal utility n Def : - Total utility is the total amount of utility that consumers receive from consumption of commodities. Utility being measurable, it is given as the sum of the utilities obtained from consumption of each unit of the commodity consumed. If for example a consumer consumes 5 units of a commodity the total utility he derives would be: TU = U1+U2+U3+U4+U5 Where TU is total utility, U1, U2, U3, U4 and U5 are utils from the successive units consumed. -Marginal utility is the amount of satisfaction added by an additional unit of consumption. Marginal utility is calculated as MU = = where Un is the total utility from consumption of n units of a good, while Un-1 units of a good. Un-Un-1, therefore, measures the extra satisfaction from consuming the nth unit. 2.2.2. Principle of diminishing marginal utility The principle of diminishing marginal utility holds that for a given time period, the greater the level of consumption of a particular commodity, the lower the marginal utility. Total Utility Total Utility Quantity Marginal Utility X* MU Quantity of X Fig.2.12 Total and marginal utility The total utility increases at decreasing rate up to quantity X*, and starts declining. Graphically, MU is the slope of the Total utility curve. The slope of the total utility curve decreases until TU reaches its maximum at X*. At the maximum point of the TU curve slope is zero, and hence MU will be zero. Beyond X*, however, since TU curve is falling MU is negative. Mathematically, MU is given as 3 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith  = , where dU is change in TU and dQ is change in quantity of the commodity. 2.2.3. Equilibrium of the consumer: Cardinal utility approach A consumer is said to be at equilibrium when he/she maximizes his/her utility from the consumption of commodities for a given price and income. In the simplest case, where the consumer buys just a single commodity X, he/she is faced with the choice of either spending his income on the purchase of good X or retaining his/her income. The decision of the consumer depends on the satisfaction he/she derives from consuming additional units of the commodity and the satisfaction he/she derives from keeping his/her income. If consumption gives him /her more satisfaction than saving, he/she would buy the commodity. If consumption yields relatively lower satisfaction to the consumer compared to the satisfaction from saving, then the consumer would keep his/her income. The equilibrium quantity of the commodity is, then, defined at the equality of the additional utility (Marginal Utility) of the commodity and the marginal utility of money (which is assumed to be constant). Mathematically, the equilibrium condition of the consumer that consumes a single good X occurs when the marginal utility of X (MUX) is equal to its market price (PX). MUX= PX Proof The utility function is given as U=f(X) If utility is measured in monetary terms and the consumer buys Qx units of the commodity, his expenditure is PX.QX. The consumer wishes to maximize his utility for any birr spent. Therefore, the consumer wishes to maximize the difference between his utility and his expenditure: Max (U - QX.PX) The necessary condition for maximization is that the partial derivative with respect to QX be zero. This is because, at the maximum point, the slope of the total utility function (MU) is equal to zero. $!% &% ' − =0 !" !" Rearranging we obtain = &% * = &% ) If MUx is greater than Px, the consumer can increase his welfare by purchasing more units of X. If, on the other hand, MUx is less than Px, the consumer can increase its welfare by reducing the quantity of X he purchases. Utility is maximized when the condition MUx=Px is satisfied. The consumption decision involving n commodities, the consumer’s equilibrium is defined by the equality of the ratios of marginal utilities of individual commodities to their prices. " + = =⋯= &" &+ & 4 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith Derivation of the Demand Curve of the Consumer The derivation of demand curve is based on the axiom of diminishing marginal utility. The MU of the commodity X may be depicted by a line with a negative slope. Geometrically, MU is the slope of the TU function U=f (QX). MUX declines continuously, and become negative beyond quantity X*. If MU is measured in monetary units, the demand curve for X is identical to the positive segment of the marginal utility curve. MUX PX P1 MU1 Demand curve P2 MU2 P3 MU3 QX QX X1 X2 X3 X* X1 X2 X3 X* MUx At X1 the marginal utility is MU1, which at equilibrium is equal to P1 and at X2 marginal utility is MU2, which in turn is equal to P2 at equilibrium. The negative section of the MU curve does not form part of the demand curve, since negative quantities and price do not make sense in economics. Weaknesses of cardinal utility approach: The assumption of cardinal (measurable) utility is doubtful. The satisfaction derived from the consumption of various commodities cannot be objectively measured. The assumption of constant marginal utility of money is also unrealistic. The utility derived from a unit of money varies with the level of income of the consumer. MU of a unit of money for a poor person is by far higher than the MU of a rich person. Thus, money cannot be used as a measuring rod since its own utility changes. B. Ordinal Utility Approach Ordinal theorists say utility is not measurable cardinally (quantitatively) but can be ranked as 1st ,2nd,3rd,…. Assumptions Consumer have limited income that maximize his/ her satisfaction Consumer can rank bundles of good as their desirability. Having these assumptions in mind, consumer’s preference which is discussed in the above section can be shown graphically in terms of Indifference curve. 2.3.1. Indifference curve analysis Indifference curve (IC) – is a curve or a locus of points which represent various combinations of two goods which give the same level of satisfaction so the consumer is indifferent between any two bundles on the curve. 5 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith Indifference schedule Y Bundle com com utility X Y 30 E A 25 5 U B 15 7 U C 10 12 U D 6 20 U 5 A U E 4 30 U 4 25 x Indifference Map A consumer similarly make many other combination of goods X &Y with less one or both the good or many other combination with more of one or both of the goods yielding equal level of satisfaction but less than & greater than the curve drawn above respectively. These ICs create a family of ICs corresponding to different levels of satisfaction called Indifference map. Y I3 I2 I1 X N.B: movement from one IC to the other to Northeast wards leads to higher level of satisfaction. Higher ICs correspond to higher level of utility 2.3.1.1. Characteristics of indifference curves i) ICs slope downward from left to right If both X&Y are goods and if the consumer is rational, then we must conclude that if consumers give up some of X, they will want more of Y to remain at the same level of utility. Y P YO A Y1 B XO X1 X X Figure a figure b 6 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith Consider figure a moving from A to B , as units of Y are given up ,more units of X are obtained and the utility derived is unchanged.for this to be true , ICs must slope downward from left to right. ii) ICs are convex to the origin As more and more units of one good, say Y, are given up, it is reasonable to suppose that successively bigger quantities of X must be obtained to compensate the consumer for his loss and leave him the same level of utility. In the above figure b this proposition is considered. Since the slope of an IC is called the Marginal Rate of Substitution (MRS), the proposition is sometimes summed as the Diminishing MRS. The slope of IC measures MRS between two goods. dMRS ⇒ 0, d>0. 2.3.3 2.3. 3. Consumer equilibrium: O rdinal utility approach A consumer attains his equilibrium position when he maximizes his total utility given is income and price of the commodities. 8 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith  Technically, the conditions that make the consumer in equilibrium are: i) First order condition (Necessary condition) MRSxy should be equal with price ratio. i.e. MRSxy=-./-0 ii) Second order condition ( Sufficient condition) MRSxy= -./-0 at higher IC Graphically, Com y I3 E. ← equilibriu m po int I2 I1 ← budgetline Com x At point of equilibrium E, Slope of the budget line = slope of I2 Px ⇒ = MRSxy Py Mathematical derivation of equilibrium point To determine the consumer’s optimum point, we will maximize U=f (Qx, Qy) subject to the budget constraint Qx.Px +Qy.Py=Y To do so, we will follow the following steps: i) Rewrite the budget equation as Qx.Px+Qy.Py-Y=0 ii) then multiply left hand side of the above equation by the lagrangian multiplier ( λ ), in doing so, we get λ (Qx.Px + Qy.Py − Y ) = 0 iii) subtract the above rewritten constraint from the utility function and construct the composite function as φ = U − λ (Qx.Px + Qy.Py − Y ) iv) Then maximize the composite function and find the optimal values of Qx, Qy and λ ∂φ ∂U ∂λ (Qx.Px + Qy.Py − Y ) ⇒ = − = 0...............................................................(1) ∂Qx ∂Qx ∂Qx ∂φ ∂U ∂λ (Qx.Px + Qy.Py − Y ) ⇒ = − = 0...............................................................( 2) ∂Qy ∂Qy ∂Qy ∂φ ∂U ∂λ (Qx.Px + Qy.Py − Y ) ⇒ = − = 0...................................................................( 3) Then, ∂λ ∂λ ∂λ ∂φ ∂U = − λPx = 0............................ from(1) ∂Qx ∂Qx ∂U MUx ⇒ = λPx = MUx ⇒ λ = ∂Qx Px 9 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith  ∂φ ∂U = − λPy = 0............................ from(2) ∂Qy ∂Qy ∂U MUy ⇒ = λPy = MUy ⇒ λ = ∂Qy Py ∂φ = −(Qx.Px + Qy.Py − Y ) = 0............................ from (3) ∂λ ⇒ Qx.Px + Qy.Py − Y = 0 Solving the above simultaneous equations we will get λ =λ MUx MUY ⇒ = Px Py Rearranging the above expression ,we will arrive at the consumer’s equilibrium point MUx Px = = MRSxy MUy Py Interpretation of λ : λ is interpreted as the marginal utility of income (MU I ), because ∂U ∂U ∂X ∂U ∂Y ∂X ∂Y MUI = =. +. ⇒ MUx. + MUy. ∂I ∂X ∂I ∂Y ∂I ∂I ∂I ∂X ∂Y = λPx. + λPy. ∂I ∂I λ ( Px.∂X + Py∂Y ) = , here Px.∂X + Py.∂Y = ∂I ∂I λ (∂I ) = ∴ MUI = λ Thus, MUI is interpreted as the extra satisfaction derived from having one ∂I more birr and it is amounted to λ. Illustration Consider Cobb-Douglas utility function of the consumer having a given income of 120 birr and consuming only two commodities X&Y is given as 3 5 $*, 2' = * 2 ,assuming further that prices of X&Y are 3 birr and 5 birr respectively, 4 4 determine: a) the consumer’s optimal bundles b) his marginal utility of income and its interpretation c) the portion of income that he spends on the consumption of the optimal bundles X&Y respectively. Solution i) Technique 1 (using lagrangian) The budget equation: 3x+5y=120 3 5 ∅ = * 4 7 4 − 8$3* + 57 − 120' >? 1 A C D = * B 7 B − 38 = 0 … … … … … … … … … ….. $1' >* 4 >? 3 D A C = * B7 B − 58 = 0 … … … …. … … … … … …. $2' >7 4 10 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith  GH GI = −$3* + 57 − 120' … … … … ….. … … … …. ….. $3' 1 D D ⟹ * B 7 B = 38 … … … … … … …. KLMN $1' 4 3 ⟹ * B 7 B = 58 … … … … ….. KLMN $2' 4 D D * B 7B 3* B 7 B ⟹ =8= … … … … … … … … … ….. KLMN $1'&$2' 4∗3 4∗5 D D * B 7B 3* B 7 B ⟹ D = D 12* B 7 B 20* B 7 B D D 7 $B B' 3* $B B' ⟹ 12 ∗ = ∗ 12 12 20 18 7= * 10 Now, let’s substitute this proportion in to equation (3) 18 ⟹ 3* + 5 R *S = 120 ⟹ 3* + 9* = 120 ⟹ 12* = 120 10 ⟹ * = 10UVWXY Z ⟹ 7 = [*10⟹ 7 = 18UVWXY ∴ Xℎ^ _MVYUN^L ` Y aXWNbc dUV c^Y eWcc d^ 10 UVWXY MK * bV 18 UVWXY MK 7. 5 3 f5 5 Z 4 hZDg 4 C = i √5.832k 4 b)MUI=8 = A10 C A18 C = A 4 = 4 C A ≈ 0.129 UVWXY D∗B g [ g [[[ g and it is interpreted as the extra satisfaction that the consumer derives from consuming one more birr is approximately 0.129 units. c) the portion of income that the consumer spends on the consumption of X 3 n o = = 3 4 5 = MKXℎ^ 120 dWLL = 30 dWLL m nA CmA Co B 4 4 The portion of income that the consumer spends on the consumption of Y 5 n o D = = 3 4 5 = MK Xℎ^ 120 dWLL = 90 dWLL m nA CmA Co B 4 4 ii) Technique 2: the short cut (marginal analysis) > 1 A C D *= = * B 7B >* 4 > 3 D A C 7= = * B7 B >* 4 * 7 = … … … … Xℎ^ _MVYUN^L ` Y ^pUcWdLWUN aMWVX &* &7 1 D D 3 1 D D 3 q R* B S R7 B Sr q R* B S R7 B Sr q R* B S R7 B Sr q R* B S R7 B Sr 4 4 4 4 ⟹ = ⟹ = 3 5 D D q3 R* B S R7 B Sr q5 R* B S R7 B Sr 11 “It is not due to the benevolent of the waiter that we get our dinner, rather from their interest of maximizing their utility” A. Smith  f5 f5 5 f3 3 f5 f3 f3 A C A C D ⟹ R* 4 4 S R7 4 4 S= A* 4 4 C A7 4 4 C B∗D B∗h 1 3 18 ⟹ 7= *⟹7= * 12 20 10 Then substitute this proportion to equation (3) 18 3* + 5 R S * = 120 ⟹ 12* = 120 ⟹ MaXWNbc * = 10 UVWXY 10 18 ⟹7= ∗ 10 ⟹ MaXWNbc 7 = 18 UVWXY 10 ∴ the consumer’s optimal bundles are 10 units of X and 18 units of Y. Then after, similar procedures to the 1st technique will be employed to determine the rest requirements. 2.4 Effects of change in Income and price on consumer optimum point 2.4.1 E ffects of change in I ncome on C onsumption a) Income effect on Normal good (eI>0) Good y ICC- Income Consumption Curve (Income Offer Curve) Or Income Expansion Path I4 I3 I2 I1 Good X ICC- is a curve which is a locus of various consumer equilibrium points resulting from changes in income, citrus paribus. b) Income effect on Inferior good (eI1, elastic , 2. |Ed|0 , Normal good 3. 0