Answers to Textbook Questions and Problems CHAPTER 17 The Theory of Investment Questions for Review 1. In the neoclassical model of business fixed investment, firms will find it profitable to add to their capital stock if the marginal product of capital is greater than the cost of capital. The cost of capital depends on the real interest rate, the depreciation rate, and the relative price of capital goods. 2. Tobin’s q is the ratio of the market value of installed capital to its replacement cost. Tobin reasoned that net investment should depend on whether q is greater or less than one. If q is greater than one, then the stock market values installed capital at more than it costs to replace. This creates an incentive to invest, because managers can raise the market value of their firms’ stock by buying more capital. Conversely, if q is less than one, then the stock market values installed capital at less than its replacement cost. In this case, managers will not replace capital as it wears out. This theory provides an alternative way to express the neoclassical model of investment. If the marginal product of capital exceeds the cost of capital, for example, then installed capital earns profits. These profits make the firms desirable to own, which raises the market value of these firms’ stock, implying a high value of q. Hence, Tobin’s q captures the incentive to invest because it reflects the current and expected future profitability of capital. 3. An increase in the interest rate leads to a decrease in residential investment because it reduces housing demand. Many people take out mortgages to purchase their homes, and a rise in the interest rate increases the cost of the loan. Even for people who do not borrow to buy a home, the interest rate measures the opportunity cost of holding their wealth in housing rather than putting it in the bank. Figure 17-1 shows the effect of an increase in the interest rate on residential investment. The higher interest rate shifts the demand curve for housing to the left, as shown in Figure 17-1(A). This causes the relative price of housing to fall, and as shown in Figure 17-1(B), the lower relative price of housing decreases residential investment. 4. Reasons why firms might hold inventories include: a. Production smoothing. A firm may hold inventories to smooth the level of production over time. Rather than adjust production to match fluctuations in sales, it may be cheaper to produce goods at a constant rate. Hence, the firm increases inventories when sales are low and decreases them when sales are high. b. Inventories as a factor of production. Holding inventories may allow a firm to operate more efficiently. For example, a retail store may hold inventories so that it always has goods available to show customers. A manufacturing firm may hold inventories of spare parts to reduce the time an assembly line is shut down when a machine breaks. c. Stock-out avoidance. A firm may hold inventories to avoid running out of goods when sales are unexpectedly high. Firms often have to make production decisions before knowing how much customers will demand. If demand exceeds production and there are no inventories, the good will be out of stock for a period, and the firm will lose sales and profit. d. Work in process. Many goods require a number of steps in production and, therefore, take time to produce. When a product is not completely finished, its components are counted as part of a firm’s inventory. Problems and Applications 1. In answering parts (a) to (c), it is useful to recall the neoclassical investment function: I = In[MPK – (PK/P)(r + δ)] + δK. This equation tells us that business fixed investment depends on the marginal product of capital (MPK), the cost of capital (PK/P)(r + δ), and the amount of depreciation of the capital stock (δK). Recall also that in equilibrium, the real rental price of capital equals the marginal product of capital. a. The rise in the real interest rate increases the cost of capital (PK/P)(r + δ). Investment declines because firms no longer find it as profitable to add to their capital stock. Nothing happens immediately to the real rental price of capital because the marginal product of capital does not change. b. If an earthquake destroys part of the capital stock, then the marginal product of capital rises because of diminishing marginal product. Hence, the real rental price of capital increases. Because the MPK rises relative to the cost of capital (which does not change), firms find it profitable to increase investment. c. If an immigration of foreign workers increases the size of the labor force, then the marginal product of capital and, hence, the real rental price of capital increase. Because the MPK rises relative to the cost of capital (which does not change), firms find it profitable to increase investment. d. Advances in computer technology that cause production to be more efficient will increase the marginal product of capital. The result will be an increase the real rental price of capital and investment. The cost of capital will not change. 2. Recall the equation for business fixed investment: I = In[MPK – (PK/P)(r + δ)] + δK. This equation tells us that business fixed investment depends on the marginal product of capital, the cost of capital, and the amount of depreciation of the capital stock. A one-time tax levied on oil reserves does not affect the MPK; the oil companies must pay the tax no matter how much capital they have. Because neither the benefit of owning capital (the MPK) nor the cost of capital is changed by the tax, investment does not change either. If the firm faces financing constraints, however, then the amount it invests depends on the amount it currently earns. Because the tax reduces current earnings, it also reduces investment. 3. a. There are several reasons why investment might depend on national income. First, from the neoclassical model of business fixed investment, we know that an increase in employment increases the marginal product of capital. Hence, if national income is high because employment increases, then the MPK is high, and firms have an incentive to invest. Second, if firms face financing constraints, then an increase in current profits increases the amount that firms are able to invest. Third, increases in income raise housing demand, which increases the price of housing and, therefore, the level of residential investment. Fourth, the accelerator model of inventories implies that when output rises, firms wish to hold more inventories; this may be because inventories are a factor of production or because firms wish to avoid stock-outs. b. In the Keynesian cross model of Chapter 11, we assumed that I = I. We found the governmentpurchases multiplier by considering an increase in government expenditure of ΔG. The immediate effect is an increase in income of ΔG. This increase in income causes consumption to rise by MPC ΔG. This increase in consumption increases expenditure and income once again. This process continues indefinitely, so the ultimate effect on income is ΔY = ΔG[1 + mpc + mpc2 + mpc3 + . . . ] = (1/(1 – MPC))ΔG. Hence, the government spending multiplier we found in Chapter 11 is ΔY/ΔG = 1/(1 – MPC). Now suppose that investment also depends on income, so that I = I + aY. As before, an increase in government expenditure by ΔG initially increases income by ΔG. This initial increase in income causes consumption to rise by MPC ΔG; now, it also causes investment to increase by a ΔG. This increase in consumption and investment increases expenditure and income once again. The process continues until ΔY = ΔG[1 + (mpc + a) + (mpc + a)2 + (mpc + a)3 + . . . ] = [1/(1 – MPC – a)]ΔG. Hence, the government-purchases multiplier becomes ΔY/ΔG = 1/(1 – MPC – a). Proceeding the same way, we find that the tax multiplier becomes ΔY/ΔT = – MPC/(1 – MPC – a). Note that the fiscal-policy multipliers are larger when investment depends on income. c. The government-purchases multiplier in the Keynesian cross tells us how output responds to a change in government purchases, for a given interest rate. Therefore, it tells us how much the IS curve shifts out in response to a change in government purchases. If investment depends on both income and the interest rate, then we found in part (b) that the multiplier is larger, so that we know the IS curve shifts out farther than it does if investment depends on the interest rate alone. This is shown in Figure 17-2 by the shift from IS1 to IS2. From the figure, it is clear that national income and the interest rate increase. Since income is higher, consumption is higher as well. We cannot tell whether investment rises or falls: the higher interest rate tends to make investment fall, whereas the higher national income tends to make investment rise. In the standard model where investment depends only on the interest rate, an increase in government purchases unambiguously causes investment to fall. That is, government purchases “crowd out” investment. In this model, an increase in government purchases might instead increase investment in the short run through the temporary expansion in Y. 4. A stock market crash implies that the market value of installed capital falls. Tobin’s q—the ratio of the market value of installed capital to its replacement cost—also falls. This causes investment and hence aggregate demand to fall. If the Fed seeks to keep output unchanged, it can offset this aggregate-demand shock by running an expansionary monetary policy. 5. If managers think the opposition candidate might win, they may postpone some investments that they are considering. If they wait, and the opposition candidate is elected, then the investment tax credit reduces the cost of their investment. Hence, the campaign promise to implement an investment tax credit next year causes current investment to fall. This fall in investment reduces current aggregate demand and output: the recession deepens. Note that this deeper recession makes it more likely that voters vote for the opposition candidate instead of the incumbent, making it more likely that the opposition candidate wins. 6. a. In the 1970s, the baby-boom generation reached adulthood and started forming their own households. This implies that in our model of residential investment, demand for housing rose. As shown in Figure 17-3, this causes housing prices and residential investment to rise. b. Using data from the Federal Reserve Economic Data (FRED) Web site, the real price of housing in 1970—the ratio of the residential investment deflator to the GDP deflator—was 16.25/22.78, or 0.71. In 1980, this ratio had risen to 38.91/44.38, or 0.88. Thus, between 1970 and 1980 the real price of housing rose 24 percent. This finding is consistent with the prediction of our model. 7. Consider the Solow growth model from Chapters 8 and 9. The Solow model shows that the saving rate is a key determinant of the steady-state capital stock. If the tax laws encourage investment in housing but discourage investment in business capital, this implies that the fraction of output devoted to business investment is lower because of the tax consequences. Figure 17-4 shows the outcome of the Solow model for low and high saving rates. At the lower saving rate, business capital-per-worker and business output-per-worker is also lower. Thus, the tax system distorts the economy’s choice of business output versus housing. An alternative way to see this effect is to think of the labor market. With less capital for each worker, the marginal product of labor is lower. Hence, in the long run, the real wage of workers is lower because of the distortions of the tax system. IN THIS CHAPTER, YOU WILL LEARN: ▪ leading theories to explain each type of investment ▪ why investment is negatively related to the interest rate ▪ things that shift the investment function ▪ why investment rises during booms and falls during recessions 1 Three types of investment ▪ Business fixed investment: businesses’ spending on equipment and structures for use in production. ▪ Residential investment: purchases of new housing units (either by occupants or landlords). ▪ Inventory investment: the value of the change in inventories of finished goods, materials and supplies, and work in progress. Understanding business fixed investment ▪ The standard model of business fixed investment: the neoclassical model of investment ▪ Shows how investment depends on: ▪ MPK ▪ interest rate ▪ tax rules affecting firms Two types of firms ▪For simplicity, assume two types of firms: 1. Production firms rent the capital they use to produce goods and services. 2. Rental firms own capital, rent it to production firms. In this context, “investment” is the rental firms’ spending on new capital goods. The capital rental market Production firms real rental price, R/P K capital stock Factors that affect the rental price For the Cobb-Douglas production function, the MPK (and hence equilibrium R/P ) is Y =AK L 1− R1− =MPK ALK= ( ) P The equilibrium R/P would increase if: ▪ K (e.g., earthquake or war) ▪ L (e.g., pop. growth or immigration) ▪ A (technological improvement or deregulation) Rental firms’ investment decisions ▪ Rental firms invest in new capital when the benefit of doing so exceeds the cost. ▪ The benefit (per unit capital): R/P, the income that rental firms earn from renting the unit of capital to production firms. Components of the cost of capital: interest cost: i × PK, where PK = nominal price of capital depreciation cost: δ × PK, where δ = rate of depreciation capital loss: −ΔPK (a capital gain, ΔPK > 0, reduces cost of K ) Add these three parts to get the total cost of capital: Nominal cost PK of capital =iP P PK+K− K = P iK + − PK Example: car rental company (capital: cars) Suppose PK = $10,000, i = 0.10, δ = 0.20, and ΔPK/PK = 0.06 Then, interest cost = $1000 depreciation cost = 2000 capital loss = −600 total cost = $2400 For simplicity, assume ΔPK/PK = π. Then, the nominal cost of capital equals PK(i + δ − π) = PK(r + δ) PK and the real cost of capital equals (r+) P The real cost of capital depends positively on: ▪ the relative price of capital ▪ the real interest rate ▪ the depreciation rate The rental firm’s profit rate A firm’s net investment depends on its profit rate: R P P Profit rate = − K (r+) = MPK− K (r+) P P P ▪ If profit rate > 0, then increasing K is profitable ▪ If profit rate 1, firms buy more capital to raise the market value of their firms. ▪ If q cost of capital, then profit rate is high, which drives up the stock market value of the firms, which implies a high value of q. ▪ If MPK < cost of capital, then firms are incurring losses, so their stock market values fall, so q is low. Reasons for a relationship between the stock market and GDP: 1. A wave of pessimism about future profitability of capital would: ▪ cause stock prices to fall ▪ cause Tobin’s q to fall ▪ shift the investment function down ▪ cause a negative aggregate demand shock Reasons for a relationship between the stock market and GDP: 2. A fall in stock prices would: ▪ reduce household wealth ▪ shift the consumption function down ▪ cause a negative aggregate demand shock Reasons for a relationship between the stock market and GDP: 3. A fall in stock prices might reflect bad news about technological progress and long-run economic growth. This implies that aggregate supply and full-employment output will be expanding more slowly than people had expected. The efficient markets hypothesis ▪ Efficient markets hypothesis (EMH): The market price of a company’s stock is the fully rational valuation of the company, given current information about the company’s business prospects. ▪ Stock market is informationally efficient: each stock price reflects all available information about the stock. ▪ Implies that stock prices should follow a random walk (be unpredictable) and should only change as new information arrives. Keynes’s “beauty contest” ▪ Idea based on newspaper beauty contest in which a reader wins a prize if he or she picks the women most frequently selected by other readers as most beautiful. ▪ Keynes proposed that stock prices reflect people’s views about what other people think will happen to stock prices; the best investors could outguess mass psychology. ▪ Keynes believed stock prices reflect irrational waves of pessimism/optimism (“animal spirits”). EMH vs. Keynes’s beauty contest Both views persist. ▪ There is evidence for the EMH and random-walk theory (see p.508). ▪ Yet, some stock market movements do not seem to rationally reflect new information. Financing constraints ▪ Neoclassical theory assumes firms can borrow to buy capital whenever doing so is profitable. ▪ But some firms face financing constraints: limits on the amounts they can borrow (or otherwise raise in financial markets). ▪ A recession reduces current profits. If future profits expected to be high, investment might be worthwhile. But if firm faces financing constraints and current profits are low, firm might be unable to obtain funds. Residential investment ▪ The flow of new residential investment, IH , depends on the relative price of housing PH /P. ▪ PH /P determined by supply and demand in the market for existing houses. How residential investment is determined How residential investment is determined Stock of Flow of residential investment How residential investment responds to a fall in interest rates Stock of Flow of residential investment Inventory investment Inventory investment is only about 1% of GDP. Yet, in the typical recession, more than half of the fall in spending is due to a fall in inventory investment. 1. production smoothing Sales fluctuate, but many firms find it cheaper to produce at a steady rate. ▪ When sales production, inventories fall. 1. production smoothing 2. inventories as a factor of production Inventories allow some firms to operate more efficiently. ▪ samples for retail sales purposes ▪ spare parts for when machines break down 1. production smoothing 2. inventories as a factor of production 3. stock-out avoidance To prevent lost sales when demand is higher than expected. 1. production smoothing 2. inventories as a factor of production 3. stock-out avoidance 4. work in process Goods not yet completed are counted in inventory. Inventories, the real interest rate, and credit conditions ▪ Inventories and the real interest rate ▪ The real interest rate is the opportunity cost of holding inventory (instead of bonds, e.g.) ▪ Example: High interest rates in the 1980s motivated many firms to adopt just-in-time production, which is designed to reduce inventories. ▪ Inventories and credit conditions ▪ Many firms purchase inventories using credit. ▪ Example: The credit crunch of 2008–09 helped cause a huge drop in inventory investment. C H A P T E R S U M M A R Y 1. All types of investment depend negatively on the real interest rate. 2. Things that shift the investment function: ▪ Technological improvements raise MPK and raise business fixed investment. ▪ Increase in population raises demand for, price of housing and raises residential investment. ▪ Economic policies (corporate income tax, investment tax credit) alter incentives to invest. C H A P T E R S U M M A R Y 3. Investment is the most volatile component of GDP over the business cycle. ▪ Fluctuations in employment affect the MPK and the incentive for business fixed investment. ▪ Fluctuations in income affect demand for, price of housing and the incentive for residential investment. ▪ Fluctuations in output affect planned & unplanned inventory investment. Solution Manual for Macroeconomics Gregory N. Mankiw 9781464182891, 9781319106058
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