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Chapter 17

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York University
ECON 2000
Mokhles Hossain

Chapter 17 There are three types of investment spending: Business fixed investment includes the machinery, equipment, and structures that businesses buy to use in production. Residential investment includes the new housing that people buy to live in and that landlords buy to rent out. Inventory investment includes those goods that business put aside in storage, including materials and supplies, work in process, and finished goods. Business fixed investment The largest piece of investment spending. Includes everything from fax machines to factories, computers to company cars. The standard model of business fixed investment is called the neoclassical model of investment. This model examines the benefits and costs to firms of owning capital goods. To develop the model, imagine that there are two kinds of firms in the economy. Production firms produce goods and services using capital that they rent. Rental firms make all the investments in the economy; they buy capital and rent it out to the production firms. This is not usually the case in the real world, however it simplifies our analysis. The firm rents capital at a rental rate R and sells its output at a price P; the real cost of a unit of capital to the production firm is R/P. The real benefit of a unit of capital is the marginal product of capital MPK, the slope of the production function. The firm rents capital until the marginal product of capital MPK falls to equal the real rental price of capital R/P in order to maximize profit. The downward sloping demand for capital (MPK) curve reaches equilibrium with the vertical capital supply curve, and the real rental price of capital (Y-axis) adjust to equilibrate supply and demand. The marginal product of capital for the Cobb-Douglas production function is MPK = 1-α αA(L/K) . 1-α Since MPK = R/P in equilibrium, we can write R/P = αA(L/K) . This expression shows the following: the lower the stock of capital, the higher the real rental price of capital; the greater the amount of labour employer, the higher the real rental price of capital; the better the technology, the higher the real rental price of capital. Firms that rent out capital have three costs for each period of time that it rents out capital: 1. When a rental firm borrows to buy a unit of capital it intends to rent out, it must pay interest on the loan. If P is the purchase price of a unit of capital and i is the nominal K interest rate, then iK is the interest cost. iPKis the interest cost whether the rental firm buys capital with loans or with its own cash. If it uses its own cash, it loses out on the interest it could have earned by depositing this cash in the bank. In either case, the interest cost equals iPK. 2. While the rental firm is renting out the capital, the price of capital can change. The cost of this loss or gain is –ΔPK(the minus sign is here because we are measuring costs, not benefits.) 3. While the capital is rented out, it suffers depreciation. If δ is the rate of depreciation, Jessica  Gahtan     CH  17   1   then the dollar cost of depreciation is δPK. The total cost of renting out a unit of capital for one period is therefore: Cost of Capital = iP K ΔP K +δP K = P Ki - ΔP K P K δ) The cost of capital depends on the price of capital, the interest rate, the rate at which capital prices are changing, and the depreciation rate. In this case, ΔPK/ PKequals the overall rate of inflation π. Because i – π equals the real interest rate r, we can write the cost of capital as: Cost of Capital = P Kr + δ) We want to express the cost relative to other goods in the economy. The real cost of capital, the cost of buying and renting out a unit of capital measured in units of the economy’s output, is: Real Cost of Capital = (P KP)(r + δ) This equation states that the real cost of capital depends on the relative price of a capital good P KP, the real interest rate r, and the depreciation rate δ. Determinants of investment Consider a firm’s decision about whether to increase or decrease its capital stock. For each unit of capital, the firm earns real revenue R/P and bears the real cost (PK/P)(r + δ). The real profit per unit of capital is: Profit Rate = Revenue – Cost = R/P – (P /PK(r + δ) = MPK – (P /P)(K + δ) The rental firm makes a profit if the marginal product of capital is greater than the cost of capital. It incurs a loss if the marginal product is less than the cost of capital. The change in the capital stock, called net investment, depends on the difference between the marginal product of capital and the cost of capital. If the marginal product of capital exceeds the cost of capital, firms find it profitable to add to their capital stock. If the marginal product of capital falls short of the cost of capital, they let their capital stock shrink. ΔK = I nMPK – (P /P)Kr + δ)], where I is nhe function showing how much net investment responds to the incentive to invest. We can now derive the investment function. Total spending on business fixed investment is the sum of net investment and the replacement of depreciated capital. The investment function is: I = n [MPK – (P /K)(r + δ)] + δK Business fixed investment depends on the marginal product of capital, the cost of capital, and the amount of depreciation. The investment curve slopes downward because a decrease in the real interest rate lowers the cost of capital, increasing the incentive to invest. Any event that raises what business managers expect the marginal product of capital to be increases the profitability of investment and causes the investment schedule to shift outward. When the capital stock reaches a steady state, we can write: MPK = (PK/P)(r + δ). In the long run, the marginal product of capital equals the real cost of capital. Taxes and investment Jessica  Gahtan     CH  17   2   Tax laws influence firms’ incentives to accumulate capital in many ways. Here are the three most important provisions of corporate taxation: Corporate profit tax, the tax levied on the accounting profit of corporations. A tax on profit, measured in the way that the rental price of capital equals the cost of capital, would not alter investment incentives. The depreciation allowance is based on the price of capital when it was originally purchased (historical cost) under tax laws, whereas our definition of profit deducts the current (replacement) value of depreciation as a cost. In periods of inflation, replacement cost is greater than historical cost, so the tax law sees a profit and levies a tax even when economic profit is zero, which makes owning capital less attractive. The investment tax credit is a tax provision that encourages the accumulation of capital. It reduces a firm’s taxes by a certain amount for each dollar spent on capital goods. Thus, it reduces the cost of capital nad raises investment. Investment subsidies and other tax incentives for investment are one tool that policymakers can use to control aggregate demand. The term stock refers to the shares in the ownership of corporations, and the stock market is the market in which these shares are traded. Stock prices tend to be high when firms have many opportunities for profitable investment, as they mean higher future income for shareholders. Thus, stock prices reflect the incentives to invest. Economist Janes Tobin proposed that firms base their investment decisions on the following ratio, now called Tobin’s q: 𝑴𝒂𝒓𝒌𝒆𝒕  𝑽𝒂𝒍𝒖𝒆  𝒐𝒇  𝑰𝒏𝒔𝒕𝒂𝒍𝒍𝒆𝒅  𝑪𝒂𝒑𝒊𝒕𝒂𝒍 𝒒 = 𝑹𝒆𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕  𝑪𝒐𝒔𝒕  𝒐𝒇  𝑰𝒏𝒔𝒕𝒂𝒍𝒍𝒆𝒅  𝑪𝒂𝒑𝒊𝒕𝒂𝒍 The numerator of Tobin’s q is the value of the economy’s capital as determined by the stock market. The denominator is the price of capital if it were purchased today. Tobin reasoned that net investment should depend on whether q is greater or less than 1. If q is greater than 1, then the stock market values installed capital at more than its replacement cost. In this case, managers can raise the market value of their firms stock by buying more capital. Conversely, if q is less than 1, the stock market values capital at less than its replacement cost. In this case, managers will not re
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