mankiw's macroeconomics modules A PowerPointTutorial to Accompany macroeconomics, 5th ed. N. Gregory Mankiw Mannig J. Simidian ® CHAPTER SEVENTEEN Investment

In this chapter, we’ll explain why investment is negatively related to the interest rate, what causes the investment function to shift and why investment rises during a boom and falls during a recession.

3 Types of Investment Spending Business fixed investment includes the 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 businesses put aside in storage, including materials and supplies, work in progress, and finished goods.

Business Fixed Investment The standard model of business fixed investment is called the neoclassical model of investment. It examines the benefits and costs of owning capital goods. Here are three variables that shift investment: 1) the marginal product of capital 2) the interest rate 3) tax rules To develop the model, imagine that there are two kinds of firms: production firms that produce goods and services using the capital that they rent and rental firms that make all the investments in the economy.

The Rental Price of Capital To see what variables influence the equilibrium rental price, let’s consider the Cobb-Douglas production function as a good approximation of how the actual economy turns capital and labor into goods and services. The Cobb-Douglas production function is: Y = AKaL1-a , where Y is output, K capital, L labor, and a a parameter measuring the level of technology, and a a parameter between 0 and 1 that measures capital’s share of output. The real rental price of capital adjusts to equilibrate the demand for capital and the fixed supply. Capital supply Real rental price, R/P Capital demand (MPK) K Capital stock, K

The marginal product of capital for the Cobb-Douglas production function is MPK = aA(L/K)1-a. Because the real rental price equals the marginal product of capital in equilibrium, we can write R/P = aA(L/K)1-a . This expression identifies the variables that determine the real rental price. It shows the following: the lower the stock of capital, the higher the real rental price of capital the greater the amount of labor employed, the higher the real rental price of capitals the better the technology, the higher the real rental price of capital. Events that reduce the capital stock, or raise employment, or improve the technology, raise the equilibrium real rental price of capital.

The Cost of Capital Let’s consider the benefit and cost of owning capital. For each period of time that a firm rents out a unit of capital, the rental firm bears three costs: 1) Interest on their loans, which equals the purchase price of a unit of capital PK times the interest rate, i, so i PK. 2) The cost of the loss or gain on the price of capital denoted as -DPK . 3) Depreciation d defined as the fraction of value lost per period because of the wear and tear, so d PK . Therefore the total cost of capital = i PK - DPK + dPK or = PK (i - D PK/ PK + d) Finally, we want to express the cost of capital 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 terms of the economy’s output is: The Real Cost of Capital = (PK / P )(r + d), where r is the real interest rate and PK / P equals the relative price of capital. To derive this equation, we assume that the rate of increase of the price of goods in general is equal to the rate of inflation.

The Determinants of Investment Now consider a rental 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 + d). The real profit per unit of capital is Profit rate = Revenue - Cost = R/P - (PK / P )(r + d). Because the real rental price equals the marginal product of capital, we can write the profit rate as Profit rate = MPK - (PK / P )(r + d). The change in the capital stock, called net investment depends on the difference between the MPK and the cost of capital. If the MPK exceeds the cost of capital, firms will add to their capital stock. If the MPK falls short of the cost of capital, they let their capital stock shrink, thus: DK = In [MPK - (PK / P )(r + d)], where In ( ) is the function showing how much net investment responds to the incentive to invest.

The Investment Function We can now derive the investment function in the neoclassical model of investment. Total spending on business fixed investment is the sum of net investment and the replacement of depreciated capital. The investment function is: I = In [MPK - (PK / P )(r + d)] + dK. investment depends on the cost of capital marginal product of capital amount of depreciation This model shows why investment depends on the real interest rate. A decrease in the real interest rate lowers the cost of capital.

Notice that business fixed investment increases when the interest rate falls-- hence the downward slope of the investment function. Also, an outward shift in the investment function may be a result of an increase in the marginal product of capital. Real interest rate, r Investment, I

Finally, we consider what happens as this adjustment of the capital stock continues over time. If the marginal product begins above the cost of capital, the capital stock will rise and the marginal product will fall. If the marginal product of capital begins below the cost of capital, the capital stock will fall and the marginal product will rise. Eventually, as the capital stock adjusts, the MPK approaches the cost of capital. When the capital stock reaches a steady state level, we can write: MPK = (PK / P )(r + d). Thus, in the long run, the MPK equals the real cost of capital. The speed of adjustment toward the steady state depends on how quickly firms adjust their capital stock, which in turn depends on how costly it is to build, deliver and install new capital.

The Stock Market and Tobin's q 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. The Nobel-Prize-winning economist James Tobin proposed that firms base their investment decisions on the following ratio, which is now called Tobin’s q: q = Market Value of Installed Capital 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 as if it were purchased today. Tobin conveyed that net investment should depend on whether q is greater or less than 1. If q >1, then firms can raise the value of their stock by increasing capital, and if q < 1, the stock market values capital at less than its replacement cost and thus, firms will not replace their capital stock as it wears out. Tobin’s q measures the expected future profitability as well as the current profitability.

Summary of Business Fixed Investment 1) Higher interest rates increase the cost of capital and reduce business fixed investment. 2) Improvements in technology and tax policies such as the corporate income tax and investment tax credit shift the business fixed investment function. 3) During booms higher employment increases the MPK and therefore, increases business fixed investment.

Residential Investment We will now consider the determinants of residential investment by looking at a simple model of the housing market. Residential investment includes the purchase of new housing both by people who plan to live in it themselves and by landlords who plan to rent it to others. There are two parts to the model: 1) the market for the existing stock of houses determines the equilibrium housing price 2) the housing price determines the flow of residential investment.

The Stock Equilibrium and the Flow Supply The relative price of housing adjusts to equilibrate supply and demand for the existing stock of housing capital. The relative price then determines residential investment, the flow of new housing that construction firms build. The Market for Housing The Supply of New Housing PH/P of housing PH/P Relative Price Demand Stock of housing capital, KH Flow of residential investment, IH

Changes in Housing Demand When the demand for housing shifts, the equilibrium price of housing changes, and this change in turn affects residential investment. An increase in housing demand, perhaps due to a fall in the interest rate, raises housing prices and residential investment. The Market for Housing The Supply of New Housing PH/P of housing PH/P Relative Price Demand' Demand Stock of housing capital, KH Flow of residential investment, IH

Summary of Residential Investment 1) An increase in the interest rate increases the cost of borrowing for home buyers and reduces residential housing investment. 2) An increase in population and tax policies shift the residential housing investment function. 3) In a boom, higher income raises the demand for housing and increases residential investment.

Inventory Investment Inventory investment, the goods that businesses put aside in storage, is at the same time negligible and of great significance. It is one of the smallest components of spending-- but its volatility makes it critical in the study of economic fluctuations.

Reasons for Holding Inventories When sales are high, the firm produces less that it sells and it takes the goods out of inventory. This is called production smoothing. Holding inventory may allow firms to operate more efficiently. Thus, we can view inventories as a factor of production. Also, firms don’t want to run out of goods when sales are unexpectedly high. This is called stock-out avoidance. Lastly, if a product is only partially completed, the components are still counted in inventory, and are called, work in process.

The Accelerator Model of Inventories The accelerator model assumes that firms hold a stock of inventories that is proportional to the firm’s level of output. Thus, if N is the economy’s stock of inventories and Y is output, then N = b Y where b is a parameter reflecting how much inventory firms wish to hold as a proportion of output. Inventory investment I is the change in the stock of inventories DN. Therefore, I = DN = b DY.

The Accelerator Model of Inventories The accelerator model predicts that inventory investment is proportional to the change in output. When output rises, firms want to hold a larger stock of inventory, so inventory investment is high. When output falls, firms want to hold a smaller stock of inventory, so they allow their inventory to run down, and inventory investment is negative. The model says that inventory investment depends on whether the economy is speeding up or slowing down.

Inventories and the Real Interest Rate Like other components of investment, inventory investment depends on the real interest rate. When a firm holds a good in inventory and sells it tomorrow rather than selling it today, it gives up the interest it could have earned between today and tomorrow. Thus, the real interest rate measures the opportunity cost of holding inventories. When the interest rate rises, holding inventories becomes more costly, so rational firms try to reduce their stock. Therefore, an increase in the real interest rate depresses inventory investment.

Summary of Inventory Investment 1) Higher interest rates increase the cost of holding inventories and decrease inventory investment. 2) According to the accelerator model, the change in output shifts the inventory investment function. 3) Higher output during a boom raises the stock of inventories firms wish to hold, increasing inventory investment.

Key Concepts of Ch. 17 Business fixed investment Stock market Residual investment Inventory investment Neoclassical model of investment Depreciation Real cost of capital Net investment Corporate income tax Investment tax credit Stock Stock market Tobin’s q Financing constraints Production smoothing Inventories as a factor of production Stock-out avoidance Work in process Accelerator model