Syllabus

Lecutres

Outlines

Assignments

Learning Objectives
1. Examine the factors that affect the economy-wide demand for goods and services

2. Focus on consumption demand and investment demand

3. Examine equilibrium condition in the goods market (desired saving equals desired investment)

4. Examine the role of real interest rates in bringing goods market to equilibrium

Lecture Outline

I. Consumption and Saving
1. Desired consumption (Cd): How much consumption households want to make;
2. Desired national saving (Sd): level of national saving when consumption is at its desired level;
Sd = Y - Cd - G

Determinants of Cd and Sd
(Current income, expected future income, wealth, expected real interest rate, fiscal policy)

A. Current income
Keynesian consumption function: Cd =c0+cy Y
a. Positive relation between Cd and Y
b. cy = marginal propensity to consume (MPC); between 0 and 1

B. Expected future income (Ye)
1. Positive relation between Ye and Cd
2. Negative relation between Ye and Sd
3. Application: the 1990-91 fall in consumer sentiment, fall in consumer spending, and recession

C. Wealth
1. Positive relation between wealth and consumption
2. Negative relation between wealth saving
3. Application: the 1987 stock market crash
a. Wealth fell approximately $1 trillion
b. C fell but less than expected - no recession
c. Temporary fall in confidence, but quickly reversed
d. The small response may due to large previous run up in stock prices between December 1986 and August 1987, so it reduced earlier gains

D. The expected real interest rate (re)

1. An rise in re has two opposing effects on saving
a. Positive effect: higher reward for saving; higher saving
b. Negative effect: takes less saving to achieve a target level future wealth; less saving
c. Empirical results: a slight increase in saving; a slight decrease in Cd

2. Taxes and the real after tax interest rate
a. Expected after-tax real interest rate: rat = (1-t) i - pe
b. A rise in taxes reduces the after tax real return on savings, and reduces savings
c. Example: i = 5%, pe = 2%, if t = 30%, then rat = 1.5%; if t = 20%, then rat = 2%

E. Fiscal policy
1. Consists of changes in taxes (T) and spending (G)
2. We assume the economy at full-employment output Y*
3. Affects Cd and Sd by changing current and/or expected future income

Case 1: A one-time increase in G:
a. If financed by higher current taxes, then after-tax income falls, which reduces Cd and Sd

b. If financed by borrowing, then future taxes will have to increase, which reduces expected future income, which reduces Cd and Sd

c. Consumption function: Cd = C0+cy (Y-T),
Desired national saving: Sd = Y - Cd - G

A $1 rise in G increases T by $1, reduces Y-T by $1, reduces Cd by cy (less than a $), and reduces Sd by 1-cy (less than a $). A rise in G reduces both Cd and Sd.

Case 2: Changes in Taxes: A lump-sum tax cut today financed by higher future taxes

a. The rise in current after tax income is offset by the decline in future after tax income.
Thus no change in Cd and Sd

b. Ricardian equivalence proposition
(1) If loss in future income equals gain in current income, then no change in Cd and Sd
(2) A tax change affects only the timing of taxes, not their ultimate amount (present value)
(3) In practice, people may not see the rise in future taxes (myopia); then a tax cut leads to increased Cd

II. Investment
A. Importance
1. Sharp fluctuation in investment over the business cycle; important to understand cycles
2. Plays a crucial role in economic growth

B. The desired capital stock (K*)
1. The amount of capital stock that allows firms to maximize expected profit
2. K* depends on MC and MB of additional capital
3. MB is the MPK
4. MC is known as the real user cost of capital (uc)
a. uc is the real cost of using an additional unit of capital for a specified time period
b. Formula: uc = r pk + d pk = (r+d)pk
c. Example (Kyle Bakery): Cost of capital, depreciation rate, expected real interest rate

5. How to find K*
a. MPK falls as k rises due to diminishing marginal productivity
b. uc does not change with k, thus is horizontal
c. If MPK > uc, profits rise as k is added
d. If MPK < uc, profits fall as K is added
e. If MPK = uc, profits are maximized
f. K* is the level of K where MPK = uc

C. Changes in the K*
1. Factors that change MPK or uc cause K* to change
(real interest rate, depreciation rate, price of capital, technological change)

2. Tax rate and K*
a. After-tax return to capital = (1-t) MPKf
b. Setting it equal to real user cost: MPKf = (r+d)pk/(1-t)
c. Tax adjusted real user cost of capital is uc/(1-t)
d. A rise in t raises the tax-adjusted user cost and reduces the desired capital stock

D. Box: investment and the stock market
1. Firms change investment in the same direction as the stock market: Tobin's q theory of investment
2. If market value of a firm > its replacement cost, then firm should invest more
3. Tobin's q = the value of firm's capital / its replacement cost
a. If q <1 do not invest
b. If q>1, invest more

4. Value of firm capital=V = market value = stock price times the number of shares outstanding
5. Replacement cost = price of a new capital times the amount of capital = pk K
6. Formula: q = V / (pk K)
7. Stock market boom raises V, causing q to rise, increasing investment

E. From desired capital stock (K*) to investment (I)
Formula: Kt+1 = Kt + It- d Kt

1. Capital stock changes for two reasons
a. Gross investment: purchases of new capital goods
b. Depreciation: which reduces capital stock

2. If firms adjust their capital stock in one period, then desired capital stock K t+1 =K* and It = K* - Kt + d Kt.

Thus, firms invest for two reasons:
a. Net Investment: To raise the desired capital stock (K* - Kt)
b. To replace depreciated capital (d Kt)

3. Factors that affect desired investment
a. Any factor that affects desired capital stock K*;
Those that affect the user cost of capital:
real interest rate (r), depreciation rate (d), price of capital goods (Pk), tax rate;

Those that affect MPK:
Technological change

III. Goods market Equilibrium
1. Equilibrium Conditions:
Condition 1.
Aggregate quantity of goods supplied (Y) equals aggregate quantity of goods demanded (Cd + Id + G):
Y = Cd + Id + G
Condition 2:
Desired investment (Sd) equals desired national saving (Id): Sd = Id

2. The two conditions are equivalent:
Proof: Start from Y = Cd + Id + G.
Subtract Cd + G from both sides. Y - Cd - G = Id
The left-side is the desired national saving Sd.

3. How Goods Market Reaches Equilibrium?
Through adjustments in real interest rate (r ).

Proof: Look at the Sd, Id diagram.
Sd is upward sloping: higher r encourages saving
Id is downward sloping: higher r discourages investment.

If actual r < rE then desired investment > desired national saving. Investors want to borrow more which raises r to rE.

If actual r > rE then desired saving > desired investment. Thus r will fall to rE.

4. Factors that shift the saving curve: A change in:
a. current output,
b. expected future output,
c. wealth,
d. government purchases,
e. taxes (unless Ricardian equivalence holds)

5. Example: A Temporary Increase in G (budget deficit): shifts S left, raises r, crowds-out I

6. Factors that shift the investment curve: A change in:
a. effective tax rate
b. expected future marginal productivity of capital
c. depreciation rate

7. Example: A fall in tax rate on capital:
Reduces real user cost of capital, increases desired I, raises r, and raises desired saving.

Determinants of Desired National Saving

Determinants of Desired Investment

Factors that affect desired consumption Cd and desired naional saving Sd

Cd = c0 + c1 (Y-T) + c2 (Ye - Te) + c3 Wealth + c4 re + c5 G
c1>0, c2 >0, c3 >0, c4 <0, c5 = 0

Sd = Y - Cd - G

1. Y up by DY then Cd up by c1.DY and Sd up by (1-c1).DY

2. Ye up by DYe then Cd up by c2.DYe and Sd down by -c2.DYe

3. Wealth up by DWealth then Cd up by c3.DWealth and Sd down by c3.DY

4. re up by Dre then Cd down by c4. Dre and Sd up by c4.D re

5. G up by DG but does not affect Cd directly. However, its method of finance does. In the long run, higher G must be financed by either T or Te.

· If government raises T, then Cd falls by c1.DT and Sd falls by (1-c1).DT
· If government raises Te, then Cd falls by c2.DTe and Sd goes down by c2.DTe.

6. T up but Te expected to fall, then no change in Cd and Sd
(Ricardian Equivalence proposition)

· With myopia, people see the rise in current taxes (T) but not the cut in future taxes (Te). That is, they consider DTe = 0. Thus, they respond to current tax hike by reducing Cd by c1.DT and raise Sd by c1.DT.