Chapter 4: Consumption, Saving, and Investment

1. Chapter 4: Consumption, Saving, and Investment How the production is used: Y= C + I + G + NX Consumption and Saving Investment Goods Market Equilibrium 1

2. Goods Market Equilibrium Consumption (C), part of demand for goods and services = The aggregate supply of saving and capital (The decision of how much to consume is the same as the decision of how much to save ) Investment (I), part of demand for goods and services = The aggregate demand of saving and capital

3. Consumption and SavingAppendix 4.A The consumption and saving decision of an individual How Much Can the Consumer Afford? The Budget Constraint 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) cf = af + yf =(y + a � c)(1 + r) + yf Budget line cf + (1 + r)c = (y + a )(1 + r) + yf OR cf = - (1 + r)c + (y + a )(1 + r) + yf 3

4. Example Current income y=42,000; future income yf=33,000; initial wealth a=18,000 r=10% Draw the budget line 4

5. Figure 4.A.1 The budget Line 5

6. Present Values Present value: the value of payments to be made in the future in terms of today�s dollars or goods Present value = future value/(1 + i) Example: At an interest rate of 10%, $12,000 today invested for one year is worth $13,200 ($12,000 ? 1.10) the present value of $13,200 in one year later is ? $12,000 6

7. Present Value and the Budget Constraint Present value of lifetime resources: PVLR = y + a + yf/(1+r) (4.A.2) Present value of lifetime consumption: PVLC = c + cf/(1+r) The budget constraint means PVLC = PVLR c + cf/(1+r) = y + a + yf/(1+r) (4.A.3) Trade-off between current consumption and future consumption The price of 1 unit of current consumption is 1 + r units of future consumption, where r is the real interest rate 7

8. Lender vs borrower Lender: c<y+a Borrower: c>y+a 8

9. Exercise Suppose that a consumer has no current wealth (a = 0). The consumer�s current income, y = 960, and future income, yf = 1166. The real interest rate is 6%. a. Calculate the present value of lifetime resources (PVLR) for the consumer. b. Draw the consumer�s budget constraint, showing all relevant information. 9

10. What Does the Consumer Want? Consumer Preferences Utility = a person�s satisfaction or well-being Example: U(x1,x2) = x1x2 Consider the bundles (4,1), (2,3) and (2,2) U(2,3) = 6 > U(4,1) = U(2,2) = 4 An indifference curve shows combinations of c and cf that give the same utility A person is equally happy at any point on an indifference curve Example: Equation for one indifference curve is given by 4= x1 x2 10

11. Indifference curve U=6 U=4 11

12. What Does the Consumer Want? Consumer Preferences Three important properties of indifference curves Slope downward from left to right Indifference curves that are farther up and to the right represent higher levels of utility Indifference curves are bowed toward the origin consumption-smoothing motive (the desire to have a relatively even pattern of consumption over time) 12

13. The Optimal Level of Consumption Optimal consumption point is where the budget line is tangent to an indifference curve That�s the highest indifference curve that it�s possible to reach All other points on the budget line are on lower indifference curves 13

14. Figure 4.A.3 The optimal consumption combination 14

15. Exercise Suppose that a consumer has no current wealth (a = 0). The consumer�s current income, y = 960, and future income, yf = 1166. The real interest rate is 6%. This consumer wants perfect consumption smoothing (c = cf) b. Draw the budget line c. Find the consumer�s optimal lifetime consumption plan, (c, cf) and illustrate it on the graph for part (b). d. Is the consumer a current saver or a current borrower? Explain. 15

16. The Effects of Changes in Income and Wealth on Consumption and Saving Effect of changes in current income on consumption and saving Effect of changes in future income on consumption and saving Effect of changes in wealth on consumption and saving Budget line: c + cf/(1+r) = y + yf/(1+r) + a 16

17. An increase in current income Exercise: y increases by $1,000. Increases PVLR, so shifts budget line out parallel to old budget line If there is a consumption-smoothing motive, both current and future consumption will increase Then both consumption and saving rise because of the rise in current income Marginal propensity to consume (MPC) = fraction of additional current income consumed in current period; between 0 and 1 Aggregate level: When current income (Y) rises, Cd rises, but not by as much as Y, so Sd rises 17

18. An increase in future income Exercise: yf increases by $1,000. Same outward shift in budget line as an increase in current income With consumption smoothing, both current and future consumption increase Now saving declines, since current income is unchanged and current consumption increases

19. An increase in wealth Exercise: a increases by $1,000. Same parallel shift in budget line, so both current and future consumption rise Saving declines, since c rises and y is unchanged

20. Figure 4.A.4 An increase in income or wealth

21. The Effects of Changes in Fiscal Policy on Consumption and Saving Fiscal policy (Government purchase) Directly affects desired national saving Sd = Y � Cd � G Indirectly affects desired consumption through changes in current and expected future income c + cf/(1+r) = y-t+ (yf �tf)/(1+r) + a Higher G financed by higher current taxes reduces after-tax income, lowering desired consumption. Even true if financed by higher future taxes, if people realize how future incomes are affected . Since Cd declines less than G rises, national saving (Sd = Y � Cd � G) declines So government purchases reduce both desired consumption and desired national saving

22. Example A consumer�s income in the current period is y=100 , and income in the future period is yf=150 . He or she pays lump-sum taxes t=20 in the current period and tf=45 in the future period. The real interest rate is 0.05, or 5% per period. a. Determine the consumer�s PVLR b. Draw the consumer�s budget constraint. c. Suppose government changes tax such that lump-sum taxes t=10 in the current period and tf=55.5 in the future period, redo part a and b

23. Fiscal policy: Taxes Ricardian equivalence proposition: a change in the timing of taxes by the government is neutral. If tax change affects only the timing of taxes, not their ultimate amount (present value), that is, if future income loss exactly offsets current income gain, no change in consumption Does a tax cut increase current consumption in practice? People may not see that future taxes will rise if taxes are cut today, then a tax cut leads to increased desired consumption and reduced desired national saving 23

24. The Effects of Changes in the Real Interest Rate on Consumption and Saving The real interest rate and the budget line c + cf/(1+r) = y + yf/(1+r) + a When the real interest rate rises Slope of new budget line is steeper one point on the old budget line is also on the new budget line: the no-borrowing, no-lending point 24

25. Figure 4.A.6 The effect of an increase in the real interest rate on the budget line 25

26. Effect of an increase in real interest rate: two opposing effects c + cf/(1+r) = y + yf/(1+r) + a 1) Substitution effect: Positive effect on saving A higher real interest rate makes future consumption cheaper relative to current consumption Increasing future consumption and reducing current consumption increases saving recall the relative price of future consumption is 1/(1+r) Suppose a person is at the no-borrowing, no-lending point when the real interest rate rises 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 26

27. The substitution effectof an increase in the real interest rate

28. 2) The income effect If a person is planning to consume at the no-borrowing, no-lending point, then a rise in the real interest rate leads just to a substitution effect But if a person is planning to consume at a different point than the no-borrowing, no-lending point, there is also an income effect The intuition of the income effect If the person originally planned to be a lender, the rise in the real interest rate gives the person more income in the future period; the income effect works in the opposite direction of the substitution effect, since more future income increases current consumption If the person originally planned to be a borrower, the rise in the real interest rate gives the person less income in the future period; the income effect works in the same direction as the substitution effect, since less future income reduces current consumption further

29. The income and substitution effects together r ? for lender Substitution effect: c?, cf ? (recall the relative price of future consumption is 1/(1+r)) Income effect: c ?, cf ? Total effect: c?, cf ?, s? r ? for borrower Substitution effect: c?, cf ? (recall the relative price of future consumption is 1/(1+r)) Income effect: c?, cf ? Total effect: c?, cf ?, s ? 29

30. The income and substitution effects together

31. What is the aggregate effect of an increased real interest rate? For a saver: ambiguous effect on saving For a borrower: Positive effect on saving Empirical studies: a slight increase in aggregate saving Draw a diagram (aggregate saving vs real interest rate) 31

32. The Effects of Changes in the Tax of Interest Rate on Consumption and Saving Taxes and the real return to saving Expected after-tax real interest rate: ra-t = (1 � t)i � ?e (4.2) Q: how does a reduction in tax rate on interest affact aggregate saving? A reduction in tax rate increases after-tax real interest rate 32

33. Exercise How does each of the following changes affect national saving? An increase of current output An increase of future output An increase of national wealth An increase of expected real interest An increase of government purchases An increase of current tax 33

35. Investment Investment refers to the purchase or construction of capital goods, including residential and nonresidential buildings, equipment and software used in production, and additions to inventory stocks. 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 35

36. Investment How firms make investment decisions? The desired capital stock: the amount of capital that allows firms to earn the largest expected profit Desired capital stock depends on costs and benefits of additional capital Assumptions Capital stock in the current period is fixed Acquisition of new capital takes at least one period Firms choose next period�s capital stock to maximize the value of real profits in the future 36

37. Investment The benefit of investment: the future marginal product of capital (MPKf) User cost of capital = real cost of using a unit of capital for a specified period of time depreciation real interest cost uc = r pK + d pK = (r + d)pK (4.3) Example: pK = 200, r = 15%, d = 20% 37

38. Investment The desired capital stock If MPKf > uc (marginal benefits > marginal costs), profits rise as K is added If MPKf ? uc (marginal benefits < marginal costs), profits rise as K is reduced Profits are maximized where MPKf = uc 38

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40. A numerical example: Finding the Desired amount of Capital Let: MPk = 2000 - 4K Pk = 200 r = 15% d = 20% UC = ? K*=? 40

41. Investment Changes in the desired capital stock Factors that shift the MPKf curve or change the user cost of capital These factors are changes in the real interest rate, depreciation rate, price of capital, technological changes that affect the MPKf 41

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44. Investment Taxes and the desired capital stock With taxes, the return to capital is only (1 � ?) MPKf A firm chooses its desired capital stock so that the return equals the user cost, so (1 � ?) MPKf = uc An increase in ? reduces the desired capital stock 44

45. Investment From the desired capital stock to investment The capital stock changes from two opposing channels gross investment: It depreciation net investment: the change in the capital stock: Kt+1 � Kt Net investment = gross investment (I) minus depreciation: Kt+1 � Kt = It � dKt (4.5) 45

46. Figure 4.6 Gross and net investment, 1929-2005 46

47. Investment From the desired capital stock to investment If firms can change their capital stocks in one period, then the desired capital stock (K*) = Kt+1 It = K* � Kt + dKt (4.6) Desired net increase in the capital stock over the year (K* � Kt) Investment needed to replace depreciated capital (dKt) 47

48. Numerical Example 48

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50. Aggregate Desired Investment Add up all firms desired investment Aggregate investment is decreasing in the real interest rate Other determinates of investment MPK (expected future) price of capital tax rate depreciation rate 50

51. Goods Market Equilibrium The real interest rate adjusts to bring the goods market into equilibrium Y = Cd + Id + G (4.7) goods market equilibrium condition Sd = Y � Cd � G, Sd = Id 51

52. Figure 4.7 Goods market equilibrium 52

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54. Goods Market Equilibrium Shifts of the saving curve Example: Temporary increase in government purchases shifts S left Result of lower savings: higher r, causing crowding out of I (Fig. 4.8) 54

55. Figure 4.8 A decline in desired saving

56. Goods Market Equilibrium Shifts of the investment curve Investment curve shifts right due to a fall in the effective tax rate or a rise in expected future marginal productivity of capital Result of increased investment: higher r, higher S and I�(Fig. 4.9) 56

57. Figure 4.9 An increase in desired investment 57