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11/6/2013 Keynes’s conjectures Chapter 17: Consumption 1. 0 < MPC < 1 2. Average propensity to consume (APC) falls as income rises. (APC = C/Y ) 3. Income is the main determinant of consumption. CHAPTER 17 Consumption 0 CHAPTER 17 Consumption 1 The Keynesian consumption function The Keynesian consumption function As income rises, consumers save a bigger C C fraction of their income, so APC falls. CCcY CCcY c c = MPC = slope of the 1 CC consumption APC c C function YY slope = APC Y Y CHAPTER 17 Consumption 2 CHAPTER 17 Consumption 3 Early empirical successes: Problems for the Results from early studies Keynesian consumption function . Households with higher incomes: . Based on the Keynesian consumption function, . consume more, MPC > 0 economists predicted that C would grow more . save more, MPC < 1 slowly than Y over time. save a larger fraction of their income, . This prediction did not come true: APC as Y . As incomes grew, APC did not fall, . Very strong correlation between income and and C grew at the same rate as income. consumption: . Simon Kuznets showed that C/Y was income seemed to be the main very stable in long time series data. determinant of consumption CHAPTER 17 Consumption 4 CHAPTER 17 Consumption 5 1 11/6/2013 The Consumption Puzzle Irving Fisher and Intertemporal Choice . The basis for much subsequent work on Consumption function consumption. C from long time series data (constant APC ) . Assumes consumer is forward-looking and chooses consumption for the present and future to maximize lifetime satisfaction. Consumption function . Consumer’s choices are subject to an from cross-sectional intertemporal budget constraint, household data a measure of the total resources available for (falling APC ) present and future consumption. Y CHAPTER 17 Consumption 6 CHAPTER 17 Consumption 7 The basic two-period model Deriving the intertemporal budget constraint . Period 1: the present . Period 2 budget constraint: . Period 2: the future CY (1 rS ) . Notation 22 Y211(1rY ) ( C ) Y1, Y2 = iiid12income in period 1, 2 . Rearrange terms: C1, C2 = consumption in period 1, 2 S = Y1 C1 = saving in period 1 (1 rC )122 C Y (1 rY ) 1 (S < 0 if the consumer borrows in period 1) . Divide through by (1+r ) to get… CHAPTER 17 Consumption 8 CHAPTER 17 Consumption 9 The intertemporal budget constraint The intertemporal budget constraint CY22 C2 CY CY 1111rr CY22 1111rr (1 rY ) Y 12 Consump = Saving income in present valflue of present valflue of The budget both periods lifetime consumption lifetime income constraint shows all combinations Y2 Borrowing of C1 and C2 that just exhaust the consumer’s C Y 1 resources. 1 Y12Yr(1 ) CHAPTER 17 Consumption 10 CHAPTER 17 Consumption 11 2 11/6/2013 The intertemporal budget constraint Consumer preferences Higher CY22 C2 CY C2 1111rr An indifference indifference The slope of curve shows curves the budget all combinations represent line equals higher levels 1 of C1 and C2 (1+r ) (1+r ) that make the ofhf happ iness. consumer Y 2 equally happy. IC2 IC1 C1 C1 Y1 CHAPTER 17 Consumption 12 CHAPTER 17 Consumption 13 Consumer preferences Optimization The slope of C2 C2 Marginal rate of The optimal (C ,C ) an indifference 1 2 At the optimal point, substitution (MRS ): curve at any is where the MRS = 1+r the amount of C2 point equals budget line the consumer the MRS just touches would be willing to 1 at that point. the highest MRS substitute for indifference curve. O one unit of C1. IC1 C1 C1 CHAPTER 17 Consumption 14 CHAPTER 17 Consumption 15 How C responds to changes in Y Keynes vs. Fisher . Keynes: C Results: 2 An increase in Y or Y Current consumption depends only on Provided they are 1 2 shifts the current income. both normal goods, budget line C and C both . Fisher: 1 2 outward. increase, Current consumption depends only on …regardless of the present value of lifetime income. whether the The timing of income is irrelevant income increase because the consumer can borrow or lend occurs in period 1 between periods. or period 2. C1 CHAPTER 17 Consumption 16 CHAPTER 17 Consumption 17 3 11/6/2013 How C responds to changes in r How C responds to changes in r C2 . income effect: If consumer is a saver, As depicted here, An increase in r the rise in r makes him better off, which tends to pivots the budget C falls and C rises. increase consumption in both periods. 1 2 line around the However, it could point (Y1,Y2 ). substitution effect: The rise in r increases turn out differently… B the opportunity cost of current consumption, which tends to reduce C1 and increase C2. A . Both effects C2. Y 2 Whether C1 rises or falls depends on the relative size of the income & substitution effects. C1 Y1 CHAPTER 17 Consumption 18 CHAPTER 17 Consumption 19 Constraints on borrowing Constraints on borrowing . In Fisher’s theory, the timing of income is irrelevant: C Consumer can borrow and lend across periods. 2 The budget . Example: If consumer learns that her future income line with no will increase, she can spread the extra consumption borrowing over both ppyeriods by borrowing in the current p eriod. constraints . However, if consumer faces borrowing constraints Y (aka “liquidity constraints”), then she may not be 2 able to increase current consumption …and her consumption may behave as in the C Keynesian theory even though she is rational & Y 1 forward-looking. 1 CHAPTER 17 Consumption 20 CHAPTER 17 Consumption 21 Consumer optimization when the Constraints on borrowing borrowing constraint is not binding C2 C2 The borrowing The borrowing constraint takes constraint is not the form: The budget binding if the line with a C Y consumer’ s 1 1 borrowing optimal C1 Y constraint 2 is less than Y1. C1 C1 Y1 Y1 CHAPTER 17 Consumption 22 CHAPTER 17 Consumption 23 4 11/6/2013 Consumer optimization when the The Life-Cycle Hypothesis borrowing constraint is binding . due to Franco Modigliani (1950s) C The optimal 2 Fisher’s model says that consumption depends choice is at . point D. on lifetime income, and people try to achieve smooth consumption. But since the consumer . The LCH says that income varies systematically cannot borrow, E over the phases of the consumer’s “life cycle,” the best he can D and saving allows the consumer to achieve do is point E. smooth consumption. C1 Y1 CHAPTER 17 Consumption 24 CHAPTER 17 Consumption 25 The Life-Cycle Hypothesis The Life-Cycle Hypothesis . The basic model: . Lifetime resources = W + RY W = initial wealth . To achieve smooth consumption, Y = annual income until retirement consumer divides her resources equally over time: (assumed constant) C = (W + RY )/T , or R = number of years until retirement C = W + Y T = lifetime in years where . Assumptions: = (1/T ) is the marginal propensity to . zero real interest rate (for simplicity) consume out of wealth . consumption-smoothing is optimal = (R/T ) is the marginal propensity to consume out of income CHAPTER 17 Consumption 26 CHAPTER 17 Consumption 27 Implications of the Life-Cycle Hypothesis Implications of the Life-Cycle Hypothesis The LCH can solve the consumption puzzle: $ The life-cycle consumption function implies . The LCH Wealth APC = C/Y = (W/Y ) + implies that . Across households, income varies more than saving varies wealth, so high-income households should have systematically Income a lower APC than low-income households. over a person’s Saving . Over time, aggregate wealth and income grow lifetime. Consumption together, causing APC to remain stable. Dissaving Retirement End begins of life CHAPTER 17 Consumption 28 CHAPTER 17 Consumption 29 5 11/6/2013 The Permanent Income Hypothesis The Permanent Income Hypothesis . due to Milton Friedman (1957) . Consumers use saving & borrowing to smooth consumption in response to transitory changes . Y = Y P + Y T in income. where The PIH consumption function: Y = current income . P Y P = permanent income C = Y average income, which people expect to where is the fraction of permanent income persist into the future that people consume per year. Y T = transitory income temporary deviations from average income CHAPTER 17 Consumption 30 CHAPTER 17 Consumption 31 The Permanent Income Hypothesis PIH vs. LCH The PIH can solve the consumption puzzle: . Both: people try to smooth their consumption . The PIH implies in the face of changing current income. P APC = C/Y = Y /Y . LCH: current income changes systematically . If high-income households have higgyher transitory as pppeople move throug h their life cy cle. income than low-income households, APC is lower in high-income households. PIH: current income is subject to random, transitory fluctuations. Over the long run, income variation is due mainly (if not solely) to variation in permanent income, . Both can explain the consumption puzzle. which implies a stable APC. CHAPTER 17 Consumption 32 CHAPTER 17 Consumption 33 The Random-Walk Hypothesis The Random-Walk Hypothesis . due to Robert Hall (1978) . If PIH is correct and consumers have rational . based on Fisher’s model & PIH, expectations, then consumption should follow a random walk: changes in consumption should in which forward-looking consumers base be unpredictable. consumption on expected future income . A change in income or wealth that was . Hall adds the assumption of anticipated has already been factored into rational expectations, expected permanent income, that people use all available information so it will not change consumption. to forecast future variables like income. Only unanticipated changes in income or wealth that alter expected permanent income will change consumption. CHAPTER 17 Consumption 34 CHAPTER 17 Consumption 35 6 11/6/2013 Implication of the R-W Hypothesis The Psychology of Instant Gratification .
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