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Chapter 4: Consumption, Saving, and Investment

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**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 Saving Appendix 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 effect of 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

**39. **39

**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

**42. **42

**43. **43

**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

**49. **49

**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

**53. **53

**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