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3. Goods market equilibrium: the IS curve. Abel, Bernanke and Croushore (chapters 4 and 9.2). I. Consumption and Saving (Sec. 4.1). A) The importance of consumption and saving 1. Desired consumption: consumption amount desired by households

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3 goods market equilibrium the is curve

3. Goods market equilibrium: the IS curve.

Abel, Bernanke and Croushore

(chapters 4 and 9.2).

i consumption and saving sec 4 1
I. Consumption and Saving (Sec. 4.1)
  • A) The importance of consumption and saving
    • 1. Desired consumption: consumption amount desired by households
    • 2. Desired national saving: level of national saving when consumption is at its desired level

Sd = Y – Cd – G

(Note that NFP=0, Y=GDP=GNP due to the closed economy assumption)

i consumption and saving cont
I. Consumption and Saving (cont.)
  • B) The consumption and saving decision of an individual
    • 1. A person can consume less than current income (saving is positive)
    • 2. A person can consume more than current income (saving is negative)
    • 3. Trade-off between current consumption and future consumption
      • a. The price of 1 unit of current consumption is 1 + r units of future consumption, where r is the real interest rate
      • b. Consumption-smoothing motive: the desire to have a relatively even pattern of consumption over time
i consumption and saving cont1
I. Consumption and Saving (cont.)
  • C) Effect of changes in current income
    • 1. Increase in current income: both consumption and saving increase (vice versa for decrease in current income)
    • 2. Marginal propensity to consume (MPC) = fraction of additional current income consumed in current period.
    • 3. Aggregate level: When current income (Y) rises, Cd rises, but not by as much as Y, so Sd also rises. MPC between 0 and 1.
    • 4. Keynesian consumption equation
      • Cd=C0+C1(Y-T),

Sd = Y – Cd – G= Y – C0– C1(Y-T) – G

Sd =-(C0+G- C1T)+ (1– C1)Y

i consumption and saving cont2
I. Consumption and Saving (cont.)
  • D) Effect of changes in expected future income
    • 1. Higher expected future income leads to more consumption today, so saving falls
    • 2. Application: consumer sentiment and the 1990–91 recession; sharp contraction in consumer sentiment in 1990 led to fall in consumer spending
  • E) Effect of changes in wealth
    • 1. Increase in wealth raises current consumption, so lowers current saving
i consumption and saving cont3
I. Consumption and Saving (cont.)
  • F) Effect of changes in real interest rate
    • 1. Increased real interest rate has two opposing effects
      • a. Substitution effect: Positive effect on saving, since rate of return is higher; greater reward for saving elicits more saving
      • b. Income effect
        • (1) For a saver: Negative effect on saving, since it takes less saving to obtain a given amount in the future (target saving)
        • (2) For a borrower: Positive effect on saving, since the higher real interest rate means a loss of wealth
      • c. Empirical studies have mixed results; probably a slight increase in aggregate saving
    • 2. Taxes and the real return to saving
      • a. Expected after-tax real interest rate:
  • rat = (1 – t)i – e
      • b. Simple examples: i = 5%, e = 2%; if t = 30%, rat= 1.5%; if t = 20%, rat= 2%
i consumption and saving cont4
I. Consumption and Saving (cont.)
  • G) Fiscal policy
    • 1. Affects desired consumption through changes in current and expected future income.
    • 2. Directly affects desired national saving, Sd = Y – Cd – G
    • 3. Government purchases (temporary increase)
      • a. Higher G financed by higher current taxes reduces after-tax income, lowering desired consumption Cd=C0+C1(Y-T), by less than the decline in current income
      • b. Even true if financed by higher future taxes, if people realize how future incomes are affected
      • c. Since Cd declines less than G rises, national saving declines

Sd =-(C0+G- C1T)+ (1– C1)Y

      • d. So government purchases reduce both desired consumption and desired national saving
    • 4. Taxes
      • a. Lump-sum tax cut today, financed by higher future taxes
      • b. Decline in future income may offset increase in current income; desired consumption could rise or fall
      • c. Ricardian equivalence proposition
        • (1) If future income loss exactly offsets current income gain, no change in consumption
        • (2) Tax change affects only the timing of taxes, not their ultimate amount (present value)
        • (3) 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
ii investment sec 4 2
II. Investment (Sec. 4.2)
  • A) Why is investment important?
    • 1. Investment fluctuates sharply over the business cycle, so we need to understand investment to understand the business cycle
    • 2. Investment plays a crucial role in economic growth
ii investment cont
II. Investment (cont.)
  • B) The desired capital stock
    • 1. Desired capital stock is the amount of capital that allows firms to earn the largest expected profit
    • 2. Desired capital stock depends on costs and benefits of additional capital
    • 3. Since investment becomes capital stock with a lag, the benefit of investment is the future marginal product of capital (MPKf)
    • 4. The user cost of capital
      • a. Examples of Kyle’s Bakery (textbook) and vending machines (class)
      • b. User cost of capital = real cost of using a unit of capital for a specified period of time
      • c. uc = rpK + dpK = (r + d)pK
ii investment cont determining the desired capital stock
II. Investment (cont.). Determining the desired capital stock
  • a. Desired capital stock is the level of capital stock at which MPKf = uc
  • b. MPKf falls as K rises due to diminishing marginal productivity
  • c. uc doesn’t vary with K, so is a horizontal line
  • d. If MPKf > uc, profits rise as K is added (marginal benefits > marginal costs)
  • e. If MPKfuc, profits rise as K is reduced (marginal benefits < marginal costs)
  • f. Profits are maximized where MPKf = uc
ii investment cont1
II. Investment (cont.)
  • C) Changes in the desired capital stock
    • 1. Factors that shift the MPKf curve or change the user cost of capital cause the desired capital stock to change
    • 2. These factors are changes in the real interest rate, depreciation rate, price of capital, or technological changes that affect the MPKf (text Figure 4.3 shows effect of change in uc)
    • 3. Taxes and the desired capital stock
      • a. With taxes, the return to capital is only (1 – )MPKf
      • b. Setting the return equal to the user cost gives

MPKf = uc/(1 – ) = (r + d)pK/(1 – )

      • c. Tax-adjusted user cost of capital is uc/(1 – )
      • d. An increase in τ raises the tax-adjusted user cost and reduces the desired capital stock
ii investment cont2
II. Investment (cont.)
  • D) From the desired capital stock to investment
    • 1. The capital stock changes from two opposing channels
      • a. New capital increases the capital stock; this is gross investment
      • b. The capital stock depreciates, which reduces the capital stock
      • c. Net investment = gross investment (I) minus depreciation:

Kt+1 – Kt = It – dKt (4.5)

where net investment equals the change in the capital stock

    • 2. Rewriting (4.5) gives It = Kt+1 – Kt + dKt
      • a. If firms can change their capital stocks in one period, then the desired capital stock (K*) = Kt+1
      • b. So It = K* – Kt + dKt (4.6)
      • c. Thus investment has two parts
        • (1) Desired net increase in the capital stock over the year (K* – Kt)
        • (2) Investment needed to replace depreciated capital (dKt)
    • 3. Lags and investment
      • a. Some capital can be constructed easily, but other capital may take years to put in place
iii goods market equilibrium sec 4 3
III. Goods Market Equilibrium (Sec. 4.3)
  • A) The real interest rate adjusts to bring the goods market into equilibrium, Y = AD, in a closed economy without rest of the world (NX=NFP=0)
    • 1. Y = AD = Cd + Id + G goods market equilibrium condition
    • 2. Differs from income-expenditure identity, as goods market equilibrium condition need not hold; undesired goods may be produced, so goods market won’t be in equilibrium
    • 3. Alternative representation from National Saving definition:
      • Sd = Y – Cd – G andY=AD leads to

Sd = Id

iii goods market equilibrium cont
III. Goods Market Equilibrium (cont.)
  • 1. Equilibrium where Sd = Id
  • 2. How to reach equilibrium? Adjustment of r
  • 3. Shifts of the saving curve

a.Saving curve shifts right due to a rise in current output, a fall in expected future output, a fall in wealth, a fall in government purchases, a rise in taxes (unless Ricardian equivalence holds, in which case tax changes have no effect)

    • b. Example: Temporary increase in government purchases shifts S left
    • c. Result of lower savings: higher r, causing crowding out of I
  • 4. Shifts of the investment curve
    • a. Investment curve shifts right due to a fall in the effective tax rate or a rise in expected future marginal productivity of capital
    • b. Result of increased investment: higher r, higher S and I

B)The saving-investment diagram

iv the is curve equilibrium in the goods market sec 9 2
IV. The IS Curve: Equilibrium in the Goods Market (Sec. 9.2)
  • A) The goods market clears when desired investment equals desired national saving
    • 1. Adjustments in the real interest rate bring about equilibrium
    • 2. For any level of output Y, the IS curve shows the real interest rate r for which the goods market is in equilibrium
    • 3. Derivation of the IS curve from the saving-investment diagram (Figure 9.2)
    • In situations of disequilibrium adjustment between desired amounts and effective amounts takes place through inventory investment
      • C=Cd I=Id+Inventory investment.
      • As a result: Excess Supply is absorved as inventory investment:
      • Y-AD=C+I+G –Cd-Id-G=Inventory investment
iv the is curve equilibrium in the goods market cont
IV.The IS Curve: Equilibrium in the Goods Market (cont)

B) Derivation of the IS curve from the saving-investment diagram

(1) The saving curve slopes upward because a higher real interest rate increases saving (SE>IE)

  • (2) The investment curve slopes downward because a higher real interest rate reduces the desired capital stock, thus reducing investment
  • (3) An increase in output shifts the saving curve to the right, because people save more when their income is higher
  • (4) Since the investment curve is downward sloping, equilibrium at the higher level of output has a lower real interest rate
  • (5) Thus a higher level of output must lead to a lower real interest rate, so the IS curve slopes downward
iv the is curve equilibrium in the goods market cont1
IV.The IS Curve: Equilibrium in the Goods Market (cont)
  • C) Result:
    • The IS curve shows the relationship between the real interest rate and output for which desired investment equals desired saving.
    • Alternatively, The IS curve is the set of combinations (r,Y) that clear the goods market.
iv the is curve equilibrium in the goods market cont2
IV.The IS Curve: Equilibrium in the Goods Market (cont)
  • D) Alternative interpretation in terms of goods market equilibrium (Y=AD)
    • (1) Beginning at a point of equilibrium, suppose the real interest rate rises
    • (2) The increased real interest rate causes people to increase desired saving and thus reduce consumption, and causes firms to reduce desired investment
    • (3) So the quantity of goods demanded declines
    • (4) To restore equilibrium, the quantity of goods supplied would have to decline
    • (5) So higher real interest rates are associated with lower output, that is, the IS curve slopes downward
iv the is curve equilibrium in the goods market cont3
IV.The IS Curve: Equilibrium in the Goods Market (cont)
  • E) Factors that shift the IS curve
    • 1.Any change that reduces desired national saving relative to desired investment shifts the IS curve to the right
      • a. Intuitively, imagine constant output, so a reduction in saving (e.g. due to an increase in wealth) means more investment relative to saving; the interest rate must rise to reduce investment and increase saving (see Figure in classroom blackboard)
    • 2. Similarly, a change that increases desired national saving relative to desired investment shifts the IS curve to the left
    • 3. An alternative way of stating this is that a change that increases aggregate demand for goods shifts the IS curve to the right
      • a. In this case, the increase in aggregate demand for goods exceeds the supply
      • b. The real interest rate must rise to reduce desired consumption and investment and restore equilibrium
      • c. Verify this result graphically for the three components of AD
slide23

IV.The IS Curve: Equilibrium in the Goods Market (cont)

  • F) Summary. Table 12 in page 315 of the textbook lists the factors that shift the IS curve
    • a. The IS curve shifts to the right because of
      • (1) an increase in expected future output
      • (2) an increase in wealth
      • (3) a temporary increase in government purchases
      • (4) a decline in taxes (if Ricardian equivalence doesn’t hold)
      • (5) an increase in the expected future marginal product of capital
      • (6) a decrease in the effective tax rate on capital
    • b. The IS curve shifts to the left when the opposite happens to the six factors above