CH04 Consumption and Saving
CH04 Consumption and Saving
CH04 Consumption and Saving
Goals of Chapter 4
Examine the factors that underlie economywide demand for goods and services Assumes closed economy (for now) Focuses on consumption and investment Equivalent to studying saving and capital formation Examines trade-off of present vs. future Goods market equilibrium when desired saving equals desired investment Real interest rate plays key role in bringing goods market to equilibrium
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-2
4-3
4-4
4-5
4-6
4-7
Empirical studies have mixed results; probably a slight increase in aggregate saving
4-8
ra-t = (1 - t)i - e
(4.2)
ra-t
4-9
4-10
4-11
4-12
4-13
4-14
4-15
4.2 Investment
Why is investment important?
Investment fluctuates sharply over the business cycle, so we need to understand investment to understand the business cycle Investment plays a crucial role in economic growth
4-16
4.2 Investment
The user cost of capital
Example of Kyle's Bakery: cost of capital, depreciation rate, and expected real interest rate User cost of capital = real cost of using a unit of capital for a specified period of time uc = rpK + dpK = (r + d)pK (4.3)
4-17
Figure 4.2
4-18
4.2 Investment
Changes in the desired capital stock
Factors that shift the MPKf curve or change the user cost of capital cause the desired capital stock to change These factors are changes in the real interest rate, depreciation rate, price of capital, or technological changes that affect the MPKf (Fig. 4.3 shows effect of change in uc) Taxes and the desired capital stock
With taxes, the return to capital is only (1 - )MPKf Setting the return equal to the user cost gives MPKf = uc/(1 - ) = (r + d)pK/(1 - ) Tax-adjusted user cost of capital is uc/(1 - ) An increase in raises the tax-adjusted user cost and reduces the desired capital stock
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-19
Figure 4.3 A decline in the real interest rate raises the desired capital stock
4-20
4.2 Investment
In reality, there are complications to the tax-adjusted user cost
We assumed that firm revenues were taxed In reality, profits, not revenues, are taxed So depreciation allowances reduce the tax paid by firms, because they reduce profits Investment tax credits reduce taxes when firms make new investments Summary measure: the effective tax ratethe tax rate on firm revenue that would have the same effect on the desired capital stock as do the actual provisions of the tax code Table 4.2 shows effective tax rates for nine different countries; some are negative, implying a subsidy to capital
4-21
4-22
4-23
4.2 Investment
Stock price times number of shares equals firms market value, which equals value of firms capital
Formula: q = V / (pKK), where V is stock market value of firm, K is firms capital, pK is price of new capital So pKK is the replacement cost of firms capital stock Stock market boom raises V, causing q to rise, increasing investment
Data show general tendency of investment to rise when stock market rises; but relationship isnt strong because many other things change at same time This theory is similar to text discussion
Higher MPKf increases future earnings of firm, so V rises A falling real interest rate also raises V as people buy stocks instead of bonds A decrease in the cost of capital, pK, raises q
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-24
Figure 4.4 An increase in the expected future MPK raises the desired capital stock
4-25
4.2 Investment
From the desired capital stock to investment
The capital stock changes from two opposing channels
New capital increases the capital stock; this is gross investment The capital stock depreciates, which reduces the capital stock Net investment = gross investment (I) minus depreciation: Kt+1 - Kt = It - dKt (4.5) , where net investment equals the change in the capital stock Fig. 4.5 shows gross and net investment for the United States
4-26
4-27
4-28
4-29
4-30
4-31
4-32
4-33
4-34
4-35
4-36
4-37
Figure 4.9 Real U.S. stock prices and the ratio of consumption to GDP, 19872002
4-38
4-39
4-40
Appendix 4.A: A Formal Model of Consumption and Saving How much can the consumer afford? The budget constraint (BC)
Current income y; future income yf; initial wealth a Choice variables: af = wealth at beginning of future period; c = current consumption; cf = future consumption af = (y + a - c)(1 + r), so cf = (y + a - c)(1 + r) + yf (4.A.1) the BC
Present values
Present value is the value of payments to be made in the future in terms of today's dollars or goods Example: At an interest rate of 10%, $12,000 today invested for one year is worth $13,200 ($12,000 1.10); so the present value of $13,200 in one year is $12,000 General formula: Present value = future value / (1 + i), where amounts are in dollar terms and i is the nominal interest rate Alternatively, if amounts are in real terms, use the real interest rate r instead of the nominal interest rate i
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-42
4-43
Utility = a persons satisfaction or well-being (indifference curve, IC) Graph a persons preference for current vs. future consumption using IC An IC shows combinations of c and cf that give the same utility (Fig. 4.A.2) A person is equally happy at any point on an IC Three important properties of ICs Slope downward from left to right: Less consumption in one period requires more consumption in the other period to keep utility unchanged ICs that are farther up and to the right represent higher levels of utility, because more consumption is preferred to less ICs are bowed toward the origin, because people have a consumptionsmoothing motive, they prefer consuming equal amounts in each period rather than consuming a lot one period and little the other period
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-44
4-45
An increase in wealth
Same outward shift in budget line as an increase in current income Again, with consumption smoothing, both current and future consumption increase Now saving declines, since current income is unchanged and current consumption increases Same parallel shift in budget line, so both current and future consumption rise Again, saving declines, since c rises and y is unchanged
4-46
4-47
4-48
4-49
Looks at patterns of income, consumption, and saving over an individuals lifetime Typical consumers income and saving pattern shown in Fig. 4.A.5 Real income steadily rises over time until near retirement; at retirement, income drops sharply Lifetime pattern of consumption is much smoother than the income pattern In reality, consumption varies somewhat by age For example, when raising children, household consumption is higher than average The model can easily be modified to handle this and other variations Saving has the following lifetime pattern Saving is low or negative early in working life Maximum saving occurs when income is highest (ages 50 to 60) Dissaving occurs in retirement
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-50
4-51
4-52
Ricardian equivalence
We can use the two-period model to examine Ricardian equivalence The two-period model shows that consumption is changed only if the PVLR changes Suppose the government reduces taxes by 100 in the current period, the interest rate is 10%, and taxes will be increased by 110 in the future period Then the PVLR is unchanged, and thus there is no change in consumption
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-53
4-54
If a person wouldnt borrow anyway, the borrowing constraint is said to be nonbinding But if a person wants to borrow and cant, the borrowing constraint is binding
A consumer with a binding borrowing constraint spends all income and wealth on consumption
So an increase in income or wealth will be entirely spent on consumption This causes consumption to be excessively sensitive to current income changes
How prevalent are borrowing constraints? Perhaps 20% to 50% of the U.S. population faces binding borrowing constraints
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-55
4-56
An increase in the real interest rate unambiguously leads the person to increase future consumption and decrease current consumption The increase in saving, equal to the decrease in current consumption, represents the substitution effect
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-57
Figure 4.A.6 The effect of an increase in the real interest rate on the budget line
4-58
Figure 4.A.7 The substitution effect of an increase in the real interest rate
4-59
4-60
4-61
4-62
The substitution effect decreases current consumption, but the income effect increases current consumption; so saving may increase or decrease Both effects increase future consumption For a borrower, both effects decrease current consumption, so saving definitely increases but the effect on future consumption is ambiguous The effect on aggregate saving of a rise in the real interest rate is ambiguous theoretically Empirical research suggests that saving increases But the effect is small
Copyright 2005 Pearson Addison-Wesley. All rights reserved.
4-63
4-64