III. ECON110B Expectations and Consumption Household decision: how much of their income to consume today and how much to save for the future To show how consumption decisions depend not only on a persons current income but also on his or her expected future income and on financial wealth To look at the movements in consumption over time 1. Consumption behavior The theory of consumption was developed by Milton Friedman in the 1950s, who called it the permanent income theory of consumption, and by Franco Modigliani, who called it the life cycle theory of consumption How much to consume and how much to save? To explore how expectations affect the consumption decision 1) The very foresighted consumer a. The consumption decision of a very foresighted consumer i) The value of his nonhuman wealth, or the sum of financial wealth and housing wealth
ii) Human wealth: The present value of expected aftertax labor income over his working life iii) The value of his human wealth and nonhuman wealth together gives an estimate of his total wealth - Reasonable assumption: one would decide to spend a proportion of ones total wealth such as to maintain roughly the same level of consumption each year throughout his life b. Ct = C(total wealtht) - Total wealtht: the sum of nonhuman wealth (financial plus housing wealth) and human wealth at time t (the expected present value of current and future after-tax labor income) c. Example - Three more years of college student, 19 years old, - Assumption: nonhuman wealth is equal to zero. - Starting annual salary: $40,000 (base-year dollar) and increase by an average of 3% a year in real terms, 25% of income tax, 39 years to retire,
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e e - V (YLt Tt ) : Present value of your labor income = the value of real expected after-tax labor income, discounted using real interest rates = human wealth - YeLt: real labor income in year t - Tet: real tax in year t
- To be quite happy to defer higher consumption until later rather than constant consumption over your lifetime - Less forward-looking fashion: never thought how much income and how many years - Forecasts might not be correct - Hard time finding a bank willing to lend it to you. b. Modified consumption - Consumption depends not only on total wealth but also on current income - Ct = C(Total wealtht, YLt Tt) - Consumption is an increasing function of total wealth, and also an increasing function after-tax labor income. Total wealth is the sum of nonhuman wealth financial wealth plus housing wealth and human wealth the present value of expected after-tax income 3) Putting things together: current income, expectations and consumption a. Expectations: two ways to affect consumption i) Directly through human wealth, or expectations of future labor income, real interest rates, and taxes
- Under assumption that the real interest rate equals zero e - V (YLt Tt e ) = ($40000)(0.75)[1 + (1.03) + (1.03) 2 + + (1.03) 38 ] - V (YLt Tt ) = $2,166,000 - To expect to live about 16 years after you retire Expected remaining life today is 58 years
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- To consume the same amount every year (consumption smoothing) $2,166,000/58 = $37,344 a year - Given that your income until you get your first job is equal to zero You will have to borrow $37,344 a year for the next three years, and begin to save when you get your first job 2) More realistic description a. Other situations against to above example
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- Expected future output Expected future labor income Human wealth Consumption ii) Indirectly through nonhuman wealth - stocks, bonds, and housing. Expectations of the value of nonhuman wealth is computed by financial markets - Expected future output Expected future dividends Stock prices Nonhuman wealth Consumption b. This dependence of consumption on expectations has two main implications for the relation between consumption and income i) Consumption is likely to respond less than one for one to fluctuations in current income ii) Consumption may move even if current income does not change.
2. Irving Fisher & intertemporal choice Both present and future Intertemporal choices: choices involving different periods of time Constraints & preferences Determinants of their choices about consumption & saving 1) The intertemporal budget constraint a. Intertemporal budget constraint - How much to consume today versus how much to save for the future Depends on the total resources available for consumption today and in the future b. A consumer with two periods (young and old) - Period 1: youth, period 2: old age - Y1: income in period one (young) - C1: consumption in period one - Y2: income in period two - C2: consumption in period 2 c. Opportunity to borrow & save - Borrowing: current consumption > current income - Saving: current consumption < current income
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d. Consumers constraint in each period - First period: S (saving) = Y1 C1 - Second period: C2 = (1 + r)S + Y2 - r: real interest rate - No saving in the second period e. S represents either saving or borrowing - C1 < Y1 S > 0 - C1 > Y1 S < 0: borrowing f. Consumers budget Graph constraint III 1: The consumers budget constraint
- Combining each period consumer constraint - C2 = (1 + r)(Y1 C1) + Y2 - (1 + r)C1 + C2 = (1 + r)Y1 + Y2
2 2 - C1 + 1 + r = Y1 + 1 + r
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- The present value of consumption = the present value of income g. Discounting - C2 & Y2 are discounted by a factor 1 + r. - Interest earned on savings Future income is worth less than current income & future consumption costs less than current consumption h. 1/(1 + r) - The price of second period consumption measured in terms of first-period consumption - The amount of first-period consumption that the consumer must forgo to obtain 1 unit of second-period consumption 2) Consumer preferences a. Indifference curve - Combinations of first-period & second-period consumption that make the consumer equally happy.
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Graph III 2: The consumers preferences
- The rate at which the consumer is willing to substitute second period consumption for first-period consumption - MRS depends on the levels of consumption in the two periods c. Prefers higher indifference curves to lower ones d. A complete ranking of the consumers preferences 3) Optimization a. Decision about how much to consume Graph III 3: The consumers optimum
b. Slope of indifference curve - Marginal rate of substitution (MRS) between firstperiod consumption & second-period consumption - Implication: how much second-period consumption the consumer requires in order to be compensated for a 1unit reduction in first-period consumption
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- To end up with the best possible combination of consumption in the two periods - On the highest possible indifference curve - Budget constraint: end up on or below the budget line b. Consumers optimum - The point at which the indifference curve & budget line touch (tangent line) - Slope of indifference curve (MRS) = slope of budget line - MRS = 1 + r 4) The effect of income change on consumption a. An increase in either Y1 or Y2 Graph III 4: An increase in income
- The budget constraint is outward - Reach higher indifference curve - If C1 & C2 are normal goods When income, C1 & C2: most usual case b. Consumption smoothing - Regardless of whether Y1 or Y2, the consumer spreads it over consumption in both periods. - The timing of the income is irrelevant to how much is consumed today because of borrowing or lending between periods c. Key conclusion - Consumption depends on the present value of current and future income - Keynes: Current consumption depends largely on his current income - Fisher: Consumption is based on the resources the consumer expects over his lifetime. 5) The effect of change in the real interest rate on consumption a. Two cases - Case 1: consumer is initially saving - Case 2: consumer is initially borrowing
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b. Case 1 & increase in the real interest rate - Rotates the consumers budget line around the point (Y1, Y2) - Alter the amount of consumption he chooses in both periods c. Decomposition of the impact of an increase in the real interest rate on consumption into two effects Graph III 5: An increase in the interest rate
i) Income effect - The change in consumption that results from the movement to a higher indifference curve - Saver: r Better off Under assumption that both consumptions are normal goods, the consumer will want to spread this improvement in his welfare over both periods Tends to make more consumption in both periods ii) Substitution effect - The change in consumption that results from the change in the relative price of consumption in the two periods -r Earnings on saving Give up less C1 to obtain an extra unit of C2 C2 becomes less expensive relative to C1 Make more C2 & less C1 d. Consumers choice: depends on both effects - Both effects C2 - Opposite effects of two effects on C1 e. Depending on the relative size of the income & substitution effects, an increase in the interest rate could either stimulate or depress saving
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6) Constraints on borrowing a. Borrowing constraint (liquidity constraint) - Inability of borrowing - Current consumption does not exceed current income - C1 Y1 Graph III 6: A borrowing constraint
- Less consumer choices c. The impact of borrowing constraint on consumption decision - Two possibilities i) The borrowing constraint is not binding - C1 < Y1 Borrowing constraint does not matter ii) The borrowing constraint is binding - Desire: C1 > Y1 Borrowing constraint: prevents this outcome Second best: to consume his first-period income (Y1) Graph III 7: The consumers optimum with a borrowing constraint
b. Restrictions of consumers set of choices - To satisfy both the intertemporal budget constraint & the borrowing constraint
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d. Conclusion: two consumption functions i) Consumer with non-binding borrowing constraint Both consumptions depends on the present value of lifetime income ii) Consumer with binding borrowing constraint C1 = Y1, C2 = Y2 - For those consumers who would like to borrow but cannot, consumption depends only on current income.
References Blanchard Ch. 16.1 Mankiw Ch. 16.2
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