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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). 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.

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  1. 3. Goods market equilibrium: the IS curve. Abel, Bernanke and Croushore (chapters 4 and 9.2).

  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)

  3. 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

  4. 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

  5. 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

  6. 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%

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. Figure 4.6Goods market equilibrium

  16. 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

  17. 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

  18. 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.

  19. 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

  20. 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

  21. 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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