Introductory Microeconomics (ES10001) Topic 2: Consumer Theory 1. Introduction We have seen how demand curves may be used to represent consumer behaviour. But we said very little about the nature of the demand curve; why it slopes down for example. Now we go ‘behind’ the demand curve i.e. we investigate how buyers reconcile what they want with what they can get 2 1. Introduction N.B. We can use this theory in many ways - not simply as household consumer buying goods. For example: Modelling decision of worker as regards his supply of labour (i.e. demand for leisure) Allocation of income across time (saving and investment) 3 2. Theory of Consumer Choice Four elements: (i) Consumer’s income (ii) Prices of goods (iii) Consumer’s tastes (iv) Rational Maximisation 4 3. The Budget Constraint The first two elements define the budget constraint The feasibility of the consumer’s desired consumption bundle depends upon two factors: (i) Income (ii) Prices Note: We assume, for the time being, that both are exogenous (i.e. beyond consumer's control) 5 3. The Budget Constraint Example (N.B two goods) Two goods - films and meals Student grant = £50 per week (p.w.) Price of meal = £5 Price of film = £10 6 3. The Budget Constraint Thus student can ‘consume’ maximum p.w. of 10 meals or 5 films by devoting all of his grant to the consumption of only one of these goods. Alternatively, he can consume some combination of the two goods For example, giving up one film a week (saving £10) enables student to buy two additional meals (costing £5 each) . 7 3. The Budget Constraint qm £5*qm qf £10*qf M 0 0 5 50 50 2 10 4 40 50 4 20 3 30 50 6 30 2 20 50 8 40 1 10 50 10 50 0 0 50 Table 1: Affordable Consumption Bundles 8 Figure 1: Budget Constraint Films 5 A 4 B 1 0 2 8 10 Meals 9 3. The Budget Constraint The budget constraint defines the maximum affordable quantity of one good available to the consumer given the quantity of the other good that is being consumed. N.B. Trade-off! Trade-off is represented slope of budget constraint. 10 3. The Budget Constraint Intercepts Determined by income divided by the appropriate price of the good Define maximum quantity of a particular good available to an individual Slope Independent of income Determined only by relative prices • . 11 3. The Budget Constraint If consumer is devoting all income to films (qf = £50/£10 = 5), then 1 meal can only be obtained by sacrificing consumption of some films. How many films must consumer give up? pm = £5; thus to obtain that £5, the consumer must give up 1/2 a film 12 3. The Budget Constraint The slope of the budget constraint in this example is thus: pm $5 1 ==pf $10 2 13 Figure 2: Slope of Budget Constraint Films qm = 1 5 Δqf = - 0.5 4.5 0 1 10 Meals 14 3. The Budget Constraint More generally: Two goods (x,y), prices (px, py) and money income (m) m = pxx + pyy Slope of budget constraint: - px/py 15 3. The Budget Constraint Proof: m = px x + p y y Þ p y y = m - px x Þ m px y= x py py 16 3. The Budget Constraint Thus: æ mö æ p ö y=ç ÷ -ç x÷ x è py ø è py ø a b Þ y = a - bx æp ö Such that Dy = -bDx = - ç x ÷ Dx è py ø 17 Figure 3: Budget Constraint y y = m/py - (px/py)x m/py Δx A Δy = -(px/py)Δx B 0 m/px x 18 3. The Budget Constraint Intuition: If additional units of x costs px Then their purchase requires a change in consumption of y of –(px/py) (i.e. a sacrifice of y) in order to maintain the budget constraint. 19 4. Preferences Consider now the consumer preferences Given what consumer can do, what would he like to do? Four assumptions: (i) Completeness (ii) Consistency (iii) Non-satiation (iv) Diminishing Marginal Rate of Substitution 20 4. Preferences Completeness Consumers can rank alternative bundles according to the satisfaction or utility they provide Thus given two bundles a and b, then a or a ∼ b b, a ∼ b Preferences assumed only to be ordinal, not cardinal; i.e. consumer simply has to be able to say he prefers a to b, not to say by how much. 21 IV. Preferences Consistency Preferences are also assumed to be consistent Thus if a a b and b c, then we would infer that c We assume consumer is logically consistent 22 4. Preferences Non-satiation Consumers assumed to always prefer more ‘goods’ to less. We can accommodate economics ‘bads’ (e.g. pollution) in this assumption by interpreting then as ‘negative’ goods We can illustrate the first three assumptions graphically as follows 23 Figure 4a: Preferences y a b c 0 x 24 Figure 4b: Preferences y d a g e b c f 0 x 25 Figure 4c: Preferences y d h a g e b c i f 0 x 26 Figure 4d: Preferences y d h a g e b c i f 0 Indifference Curve x 27 4. Preferences Marginal Rate of Substitution (MRS) The quantity of y (i.e. the ‘vertical’ good) the consumer must sacrifice to increase the quantity of x (i.e. ‘the horizontal’ good) by one unit without changing total utility. We generally assume (smooth) diminishing MRS To hold utility constant, diminishing quantities of one good must be sacrificed to obtain successive equal increases in the quantity of the other good. 28 4. Preferences Diminishing MRS derives from underlying assumption of diminishing marginal utility Marginal utility of a good is defined as the change in a consumer’s total utility from consuming the good divided by the change in his consumption of the good Diminishing MRS assumes that the increase in utility from consuming additional units of a good 29 is declining 4. Preferences Non-satiation implies downward sloping indifference curves; increases in one good require sacrifices in the other good to hold total utility constant. However, we can go further; diminishing MRS implies that indifference curves are convex to origin, becoming flatter as we move to the right. Indeed, the MRS of x for y is simply the slope of 30 the indifference curve Figure 5: Indifference Curves y I0 0 31 x Figure 5: Indifference Curves y A B I0 0 32 x Figure 5: Indifference Curves y A A´ B B´ 0 I0 33 x Figure 5: Indifference Curves y Δx = 1 A Δy A´ Δx = 1 Δy B B´ 0 I0 34 x 4. Preferences Diminishing MRS implies consumers prefer consumption bundles containing mixtures of goods rather than extremes i.e. Bundle C = (5, 5) preferred to both Bundle A = (2, 8) and Bundle B = (8, 2) Diminishing MRS (i.e. diminishing marginal utility) 35 Figure 6: Indifference Curves y A B I0 0 36 x Figure 6: Indifference Curves y A 8 B 2 0 I0 2 8 37 x Figure 6: Indifference Curves y A 8 C 5 B 2 0 I1 I0 2 5 8 38 x 4. Preferences Note: (i) Any point on the indifference map must lay on an indifference curve. (ii) indifference curves cannot cross Thus every point on the indifference map must lay on one and only one indifference curve. 39 Figure 7: Indifference Curves y I2 I1 I0 0 40 x Figure 8: Indifference Curves Cannot Cross y a b I1 c I0 0 41 x 5. Utility Maximisation Budget line shows the consumer’s affordable bundles given the market environment. The indifference map shows the consumer’s desired bundles To complete the model we assume rational maximisation - i.e. the consumer chooses the affordable bundle that maximises his utility. 42 5. Utility Maximisation This is a non-trivial point. We are implicitly assuming that the consumer only derives utility from the consumption of x and y. Moreover, rational maximisation implies consumer processes huge amount of information before choosing his most preferred bundle In reality, perhaps we ‘satisfice’ 43 5. Utility Maximisation The optimal choice bundle will be that point at which an indifference curve just touches the budget line That is, where an indifference curve is tangent to the budget line In words, where the consumer’s marginal rate of substitution (MRS) and economic rate of substitution (ERS) are in accord 44 5. Utility Maximisation Marginal Rate of Substitution (MRS) Amount of y consumer willing to sacrifice for one extra unit of x Slope of indifference curve Economic Rate of Substitution (ERS) Amount of y the consumer is obliged to sacrifice for one extra unit of x Slope of budget line 45 Figure 9: Equilibrium (MRS = ERS) y E1 y1 I2 I1 I0 0 x1 46 x Figure 10: Disequlibrium (MRS ≠ ERS) y Δx E0 ΔyERS ΔyMRS I0 0 47 x 5. Utility Maximisation Since preferences are unique, individuals will not choose identical bundles, even when confronted by same market environment But they will all move to point where MRS = ERS Even with different preferences, since ERS is the same for everyone (i.e. we all face same relative prices), it must be the case that in equilibrium: MRS1 = ERS = MRS2 48 6. Comparative Statics We now consider how the consumer responds to changes in his market environment That is, to changes in: (i) Endowment income; (ii) Prices. N.B, Comparative Statics / Dynamics 49 6. Comparative Statics Changes in Income An increase in endowment income causes a parallel shift out of the budget constraint A decrease in endowment income causes a parallel shift in of the budget constraint 50 Figure 11: Increase in Income m¢ > m y m¢ p y m py 0 m px m¢ px x 51 Figure 12: Increase in Income m¢ > m y A m¢ p y I1 x Normal y Normal B m py E1 E0 C I0 0 m px D m¢ px x 52 Figure 12: Increase in Income m¢ > m y A m¢ p y x Inferior y Normal E1 B I1 m py E0 C I0 0 m px D m¢ px x 53 Figure 12: Increase in Income m¢ > m y A m¢ p y B m py I1 E0 C E1 x Normal y Inferior D 0 m px m¢ px x 54 Figure 12: Increase in Income m¢ > m y A m¢ p y x Inferior y Normal B x Normal y Normal m py E0 C x Normal y Inferior I0 0 m px D m¢ px x 55 6. Comparative Statics Changes in Prices An increase in price causes a pivot inwards of the budget constraint An decrease price causes a pivot outwards of the budget constraint. 56 Figure 13: Fall in Price y px¢ < px m py 0 m px m px¢ x 57 7. Income & Substitution Effects Price changes affects the optimal choice bundle in two distinct ways: First, there is a change in relative prices as represented by a change in the slope of the budget constraint. Second, there is a change in purchasing power (i.e. real income). The same level of money income is now worth more to the consumer in 58 terms of its ability to purchase both goods. Figure 13: Fall in Price y px¢ < px m py 0 m px m px¢ x 59 Figure 14: Effects of Fall in Price y Fall in price of good x reduces slope of budget constraint (ERS) - i.e. fall in the relative price of good x m py Fall in price of good x increases consumer’s real income - i.e. expansion of the budget set 0 m px m px¢ x 60 Figure 15: Effects of a Fall in Price y px¢ < px m py E1 E0 0 m px m px¢ x 61 Figure 15: Effects of a Fall in Price y px¢ < px m py E0 E1 0 m px m px¢ x 62 Figure 15: Effects of a Fall in Price y px¢ < px m py E1 E0 0 m px m px¢ x 63 Figure 15: Effects of a Fall in Price y A m py px¢ < px Good x is Giffen B Good x is Non-Giffen E0 C 0 m px m px¢ x 64 Figure 15: Effects of a Fall in Price y p1x < px0 m py E1 E0 0 m px0 px px0 x E0 p1x 0 m p1x E1 x0 x1 pd ( x) x 65 Figure 15: Effects of a Fall in Price y p1x < px0 m py E1 E0 0 m px0 px px0 x E0 p1x 0 m p1x E1 x0 x1 pd ( x) x 66 Figure 15: Effects of a Fall in Price y p1x < px0 E1 m py E0 0 m px0 px p 0 x pd ( x) E0 px0 1 x m p1x E1 x1 x0 x 67 7. Income and Substitution Effects We decompose total effect of price change into: (i) Income Effect (ii) Substitution Effect The income effect is the adjustment of demand to the change in real income. The substitution effect is the adjustment of demand 68 to the change in relative prices. Figure 14: Income and Substitution Effects y (Fall in px) A E0 I0 0 A x 69 Figure 14: Income and Substitution Effects y (Fall in px) A E0 E1 I1 I0 0 A B x 70 7. Income and Substitution Effects We decompose the overall change in demand into income and substitution effects by (hypothetically) adjusting the consumer’s income to restore him to the level of real income he enjoyed before the price change Given the fall in px and the subsequent increase in real income, we therefore reduce the consumer’s real income; mechanically, we drag the new budget line back until it is just tangent to the original indifference curve. 71 Figure 14: Income and Substitution Effects y (Fall in px) A E0 E1 I1 I0 0 A B x 72 Figure 14: Income and Substitution Effects y (Fall in px) A C E0 E1 E2 I1 I0 0 A C B x 73 Figure 14: Income and Substitution Effects y (Fall in px) A C E0 E1 E2 I1 I0 0 A C B x 74 Figure 14: Income and Substitution Effects y (Fall in px) E0-E1: Total Effect (x0-x1) A E0-E2: Substitution Effect (x0-x2) E2-E1: Income Effect (x2-x1) E0 E1 E2 I1 I0 0 x0 x2 A x1 B x 75 8. Inferior and Giffen Goods In a two good model, a price change always induces a substitution effect in the opposite direction of the change in price i.e: a rise (fall) in px induces a substitution away (towards) good x ceteris paribus We usually say that ‘… the own price substitution effect is always negative.’ 76 8. Inferior and Giffen Goods The income effect, however, can be positive (i.e. normal good) or negative (i.e. inferior good) A rise in the price of a normal good induces a negative substitution effect and a negative income effect, both of which act to reduce the demand for good x A rise in the price of an inferior good, however, induces a negative substitution effect but a positive income effect, thus the overall effect is ambiguous77 8. Inferior and Giffen Goods If, when the price of an inferior good rises, the positive income effect dominates the negative substitution effect, we have the case of a Giffen Good That is, a good for which demand rises (falls) when price rises (falls) Giffen goods are very inferior good 78 Figure 15: Income and Substitution Effects y A Good x: Normal / Non-Giffen I0 C E1 E0 I1 E2 0 A C B 79 x Figure 15: Income and Substitution Effects y Good x: Inferior / Non-Giffen I1 A I0 E1 C E0 E2 0 A C B 80 x Figure 15: Income and Substitution Effects y Good x: Inferior / Giffen I1 A E1 C E0 E2 I0 0 A C B 81 x 9. Measuring Real Income When we decomposed the change in demand resulting from a change in price into an income and substitution effect, we did so by varying money income Specifically, when the price of good x fell, we ‘varied’ the consumer’s money income to hold his real income constant, where real income was defined as the consumer’s ability to enjoy a particular level of utility 82 9. Measuring Real Income Varying money income is this way is known as a Hicks Compensating Variation in money income (HCV) HCV allows consumer to enjoy original level of utility at the new relative price ratio We ‘compensate’ the consumer for the change in price Sounds odd in respect of a price fall. 83 Figure 16.1: Hicks Compensating Variation (Price Fall) y A C B I1 I0 0 x 84 Figure 16.2: Hicks Compensating Variation (Price Rise) y B C A I1 I0 0 x 85 9. Measuring Real Income An alternative definition of real income is the ability to consumer not a particular level of utility, but a particular bundle of goods i.e. we vary the consumer’s money income following a change in price to permit him to consumer his original bundle of goods at the new relative price ratio The is know as the Slutsky Compensating Variation (SCV) in money income. 86 Figure 16.3: Slutsky Compensating Variation (Price Fall) y A C I0 B I1 0 I2 x 87 Figure 16.4: Slutsky Compensating Variation (Price Rise) y B C I2 A I0 0 I1 x 88 9. Measuring Real Income Both Hicks and Slutsky compensating variations adjust the consumer’s new level of income (i.e. the level following the price change) such that he is able to enjoy either his original level of utility (Hicks) or his original consumption bundle (Slutsky) An alternative approach is to adjust the consumer’s original level of income in such a way that he is able to enjoy the level of utility (Hicks) or the consumption bundle (Slutsky) that he would have been able to enjoy were he to face the change in prices 89 9. Measuring Real Income That is, we vary the consumer’s money income at the original relative price ratio to enable him to enjoy the level of real income (i.e. utility or consumption bundle) that he would have been able to enjoy from the price change i.e. we provide the consumer with an Equivalent Variation in money income A variation in money income that will adjust the consumer’s real income in a manner analogous to the price change 90 Figure 16.5: Hicks Equivalent Variation (Price Fall) y B A C I1 I0 0 x 91 Figure 16.6: Hicks Equivalent Variation (Price Rise) y C A B I0 0 I1 x 92 Figure 16.7: Slutsky Equivalent Variation (Price Fall) y B A I2 C I0 0 I1 x 93 Figure 16.8: Slutsky Equivalent Variation (Price Rise) y C A I0 B I1 0 I2 x 94 9. Measuring Real Income To summarise, we have eight cases Hicks / Slutsky Compensating Variation / Equivalent Variation Price Rise / Price Fall 95 Figure 16.1: Hicks Compensating Variation (Price Fall) y A C B I1 I0 0 x 96 Figure 16.2: Hicks Compensating Variation (Price Rise) y B C A I1 I0 0 x 97 Figure 16.3: Slutsky Compensating Variation (Price Fall) y A C I0 B I1 0 I2 x 98 Figure 16.4: Slutsky Compensating Variation (Price Rise) y B C I2 A I0 0 I1 x 99 Figure 16.5: Hicks Equivalent Variation (Price Fall) y B A C I1 I0 0 x 100 Figure 16.6: Hicks Equivalent Variation (Price Rise) y C A B I0 0 I1 x 101 Figure 16.7: Slutsky Equivalent Variation (Price Fall) y B A I2 C I0 0 I1 x 102 Figure 16.8: Slutsky Equivalent Variation (Price Rise) y C A I0 B I1 0 I2 x 103 10. Applications Two key areas: (i) Labour Supply; (ii) Intertemporal Choice. 104 10.1 Labour Supply Consider individual’s role as a supplier of factor services Individuals sell their labour to firms in return for a wage. Individual makes a choice between income and leisure given the dual constraints of time and the wage 105 Figure 17: Budget Constraint Y Ymax Y0 0 w T 106 L Figure 18: Preferences Y I2 I1 I0 0 107 L Figure 21: Labour Market Equilibrium Y Ymax Y1 = Y0 + w(T – L1) Ymax = Y0 + wT Y1 E0 I1 w Y0 0 L1 A T 108 L Figure 22: Increase in Unearned Income Y E2 Y2 I2 Y1 E1 B I1 A Y0 0 L1 L2 T 109 L Figure 23: Increase in Wage Rate Y E2 E1 I2 I1 0 L2 L1 T 110 L Figure 23: Increase in Wage Rate Y E2 E3 E1 I2 I1 0 L3 L2 L1 T 111 L 10.1 Labour Supply Note that the income and substitution effects work against one another Because leisure is a normal good, the income effect from the increase in wage increases the demand for leisure But the wage rate is the opportunity cost, or price, of leisure. Thus, an increase in the wage rate / price of leisure induces a substitution away from leisure 112 Figure 23: Increase in Wage Rate Y E1-E2: Total Effect (L1-L2) E1-E3: Substitution Effect (L1-L3) E3-E2: Income Effect (L3-L2) E2 E3 E1 I2 I1 0 L3 L2 L1 T 113 L Figure 24: Labour Supply Curve w Ls E2 w2 w1 0 E1 (T-L1) (T-L2) T (T-L) 114 10.1 Labour Supply If the income effect dominates the substitution effect, then we have a situation in which an increase in the wage (i.e. the price of leisure) leads to an increase in the demand for leisure That is: Leisure is Giffen … … but Normal! 115 10.1 Labour Supply This is possible because there is also an Endowment Effect in operation … The Individual is entering the market with an endowment of leisure which he is selling to the firm The presence of endowment effects complicates the relationship between inferiority and Gifffeness 116 Figure 25: Increase in Wage Rate Y I2 E1-E2: Total Effect (L1-L2) E1-E3: Substitution Effect (L1-L3) E3-E2: Income Effect (L3-L2) I1 E3 E2 E1 0 L3 L1 L2 T 117 L Figure 26: Labour Supply Curve w Ls w2 E2 E1 w1 0 (T-L2) (T-L1) T (T-L) 118 10.1 Labour Supply Empirically, we tend to see labour supply curves bending backwards at high wage rates i.e. 119 Figure 27: Labour Supply Curve w 0 Ls H = (T-L) 120 10.1 Labour Supply Rather than at low wage rates i.e. 121 Figure 28: Labour Supply Curve w Ls 0 H = (T-L) 122 10.1 Labour Supply Moreover, backward bending labour supply curves are usually observed for males but nor females i.e. 123 Figure 29: Labour Supply Curve w 0 Lsm Lsf H = (T-L) 124 10.1 Labour Supply Implications of backward bending labour supply curve Multiple equilibria Unstable equilibria What happens to w if it is perturbed slightly above / below its equilibirum level, w*? Do forces of excess demand / excess supply force w back to w* 125 Figure 29: Labour Supply Curve w Ld Ls Unstable Equilibrium E1 Stable Equilibrium E 2 0 H = (T-L) 126 10.2 Intertemporal Choice Assume individual lives for two periods with a lifetime income endowment of y = (y1, y2) Consumption over time is c = (c1, c2) Now, £x saved today (i.e. period 1) will yield £(1+r)x tomorrow (i.e. period 2) The future value of £x today is thus £(1+r)x 127 10.2 Intertemporal Choice Conversely, the present value of £x received tomorrow (i.e. period 2) is: æ 1 ö $ç x ÷ è 1+ r ø Intuitively, if we receive £x tomorrow, can borrow £z today, where: æ 1 ö $z 1 + r = $x Þ $z = $ ç x ÷ è 1+ r ø ( ) 128 10.2 Intertemporal Choice Thus, given an income endowment of: y 0 = (y10 , y20 ) Then the maximum period 1 income is: æ 1 ö 0 yˆ = y + ç ÷ y2 è 1+ r ø 0 1 0 1 And the maximum period 2 income is: yˆ 20 = y20 + (1 + r ) y10 129 Figure 30: Intertemporal Budget Constraint y2 æ 1 ö 0 yˆ = y + ç ÷ y2 è 1+ r ø 0 1 yˆ 20 0 1 yˆ 20 = y20 + (1 + r ) y10 y 0 = (y10 , y20 ) y20 0 y 0 1 yˆ 0 1 y1 130 10.2 Intertemporal Choice Assume individual consumes in both periods If the value of consumption in period 1 is c10, then can save y10 - c10 in period 1 for period 2 consumption in excess of period 2 income, y20: )( ( c20 = y20 + 1 + r y10 - c10 Þ ( ) ) ( ) c20 = éë y20 + 1 + r y10 ùû - 1 + r c10 Intercept Slope 131 10.2 Intertemporal Choice ( ) ( ) c20 = éë y20 + 1+ r y10 ùû - 1+ r c10 Þ ( ) c20 = yˆ 20 - 1+ r c10 Þ ( ) ( ) Dc20 = - 1+ r Dc10 Þ Dc20 Dc 0 1 = - 1+ r 132 Figure 30: Intertemporal Budget Constraint c20 = éë y20 + (1 + r ) y10 ùû - (1 + r )c10 Þ c2 , y2 yˆ 20 c20 = yˆ 20 - (1 + r )c10 y 0 = (y10 , y20 ) y20 0 y 0 1 yˆ 0 1 c1 , y1 133 Figure 30: Intertemporal Budget Constraint ( c2 , y2 Dc10 yˆ 20 ) c20 = yˆ 20 - 1+ r c10 Þ ( ) Dc20 = - 1+ r Dc10 ( ) Dc20 = - 1+ r Dc10 slope = -(1+r) 0 yˆ 0 1 c1 , y1 134 Figure 30: Intertemporal Budget Constraint c2 , y2 (y 0 1 Þ yˆ 20 ( ) y20 - c20 < 0 c20 y 0 = (y10 , y20 ) y20 0 ) - c10 > 0 c 0 1 y 0 1 yˆ 0 1 c1 , y1 135 Figure 30: Intertemporal Budget Constraint c2 , y2 (y 0 1 Þ yˆ 20 ( ) - c10 < 0 ) y20 - c20 > 0 y 0 = (y10 , y20 ) y20 c20 0 y 0 1 c 0 1 yˆ 0 1 c1 , y1 136 10.2 Intertemporal Choice Note the effects of changes in income endowment or interest rate Change in income endowment shifts the intertemporal budget constraint parallel Changes in interest rate pivot the budget constraint around the initial income endowment 137 Figure 30: Intertemporal Budget Constraint c2 , y 2 æ 1 ö 0 yˆ = y + ç ÷ y2 è 1+ r ø 0 1 yˆ 12 0 1 yˆ 20 = y20 + (1 + r ) y10 yˆ 20 y0 y1 y y y20 0 0 1 1 1 yˆ 0 1 yˆ 1 1 y1 138 Figure 30: Intertemporal Budget Constraint c2 , y 2 æ 1 ö 0 0 0 0 ˆ yˆ = y + ç y Û y = y + 1+ r y 2 2 1 è 1+ r ÷ø 2 0 1 yˆ 21 yˆ10 y1 y21 y20 ( 0 1 ) æ 1 ö 1 1 1 0 ˆ yˆ = y + ç y Û y = y + 1+ r y 2 2 1 è 1+ r ÷ø 2 1 1 ( 0 1 ) y0 0 y 0 1 yˆ 0 1 yˆ 1 1 y1 139 Figure 30: Intertemporal Budget Constraint c2 , y2 yˆ 22 æ 1 ö 0 0 0 0 ˆ yˆ = y + ç y Û y = y + 1+ r y 2 2 1 è 1+ r ÷ø 2 yˆ10 æ 1 ö 2 2 2 2 ˆ yˆ = y + ç y Û y = y + 1+ r y 2 2 1 è 1+ r ÷ø 2 y2 0 1 2 1 y22 y20 ( 0 1 ) ( 2 1 ) y0 0 y 0 1 y 2 1 yˆ 0 1 yˆ 2 1 140 c1 , y1 Figure 30: Intertemporal Budget Constraint c2 , y2 Increase in Rate of Interest yˆ 20 yˆ æ 1 ö i yˆ = y + ç ÷ y2 è 1+ r ø i 1 i 1 yˆ 2i = y2i + (1 + r ) y1i 1 2 ( y 0 = y10 , y20 y20 0 y 0 1 ) yˆ 0 1 yˆ 1 1 c1 , y1 141 10.2 Intertemporal Choice Consider a (period 1) borrower That is: (c1 - y1) > 0 How does he react to changes in interest rate? 142 Figure 30: Intertemporal Budget Constraint c2 , y2 Period 1 Borrowing yˆ 20 y20 I0 y0 c20 0 E0 y 0 1 c 0 1 yˆ 0 1 c1 , y1 143 Figure 30: Intertemporal Budget Constraint c2 , y 2 Borrower (Fall in Interest Rate) yˆ 20 I1 y20 I0 y0 E1 c 0 2 0 E0 y 0 1 c 0 1 yˆ 0 1 c1 , y1 144 10.2 Intertemporal Choice Thus, if interest rate falls: (i) (Period 1) Borrower remains a (period 1) borrower; (ii) Is better-off; (iii) Increases (period 1) borrowing if c1 a normal good 145 Figure 30: Intertemporal Budget Constraint c2 , y 2 Borrower (Fall in Interest Rate): yˆ (i) Substitution Effect E0-E2; (ii) Income Effect E2-E1 0 2 I1 y20 I0 y0 E0 c 0 2 0 E1 E2 y 0 1 c 0 1 yˆ 0 1 c1 , y1 146 10.2 Intertemporal Choice If interest rate rises: (i) Borrower is definitely worse off; 147 Figure 30: Intertemporal Budget Constraint c2 , y 2 Borrower: Increase in Interest Rate: yˆ 20 I1 y20 I0 y0 E1 c 0 2 0 y 0 1 E0 c 0 1 yˆ 0 1 c1 , y1 148 10.2 Intertemporal Choice Conversely, for savers (c1 - y1) <0: Rise in interest rates: (i) Remain savers; (ii) Better off; (iii) Increase saving if c1 is an inferior good Fall in interest rate: (i) Definitely worse off 149 Figure 30: Intertemporal Budget Constraint c2 , y 2 Saver (Rise in Interest Rate) yˆ 20 E1 c20 y20 0 I1 E0 I0 y0 c 0 1 y 0 1 yˆ 0 1 c1 , y1 150 Figure 30: Intertemporal Budget Constraint c2 , y 2 Saver (Rise in Interest Rate) yˆ 20 E2 c20 y20 0 E1 I1 E0 I0 y0 c 0 1 y 0 1 yˆ 0 1 c1 , y1 151

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# Consumer Theory