# 3. Goods market equilibrium: the IS curve.

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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 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.)
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 (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 (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 (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 (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) 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.) 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
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 (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 (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)
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 and Y=AD leads to Sd = Id

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

Figure 4.6 Goods market equilibrium

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)
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 (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 (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 (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

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

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