Chapter Seventeen

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A PowerPointTutorialto Accompany macroeconomics, 5th ed.

N. Gregory Mankiw

Mannig J. Simidian

®

CHAPTER SEVENTEENInvestment

Chapter Seventeen

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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.

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• 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.

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The standard model of business fixed investment is called theneoclassical 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 capital2) the interest rate3) 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.

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To see what variables influence the equilibrium rental price, let’s consider the Cobb-Douglas production function as a good approximationof how the actual economy turns capital and labor into goods andservices. The Cobb-Douglas production function is: Y = AKL1- , where Y is output, K capital, L labor, and 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.

K Capital stock, K

Rea

l ren

tal

pric

e, R

/P

Capital demand (MPK)

Capital supply

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The marginal product of capital for the Cobb-Douglas production function is MPK = A(L/K)1-Because the real rental price equals the marginal product of capital in equilibrium, we can write R/P = A(L/K)1-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 improvethe technology, raise the equilibrium real rental price of capital.

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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 ofcapital PK times the interest rate, i, so i PK.2) The cost of the loss or gain on the price of capital denoted as -PK .3) Depreciation defined as the fraction of value lost per period because of the wear and tear, so PK .Therefore the total cost of capital = i PK - PK + PK or

= PK (i - PK/ PK + )Finally, we want to express the cost of capital relative to other goods inthe economy. The real cost of capital-- the cost of buying and rentingout a unit of capital measured in terms of the economy’s output is:The Real Cost of Capital = (PK / P )(r + ), where r is the real interestrate 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.

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Now consider a rental firm’s decision about whether to increase or decrease its capital stock. For each unit of capital, the firm earns realrevenue R/P and bears the real cost (PK / P )(r + ). The real profit per unit of capital is

Profit rate = Revenue - Cost = R/P - (PK / P )(r + ).

Because the real rental price equals the marginal product of capital, wecan write the profit rate as Profit rate = MPK - (PK / P )(r + ).The change in the capital stock, called net investment depends on thedifference between the MPK and the cost of capital. If the MPK exceedsthe cost of capital, firms will add to their capital stock. If the MPKfalls short of the cost of capital, they let their capital stock shrink, thus:

K = In [MPK - (PK / P )(r + )],where In ( ) is the function showing how much net investment respondsto the incentive to invest.

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We can now derive the investment function in the neoclassical model ofinvestment. 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 + )] + K.I = In [MPK - (PK / P )(r + )] + K.

investment

depends on

marginal product of capital

the cost of capitalamount 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.

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Investment, I

Rea

l in t

eres

t ra

t e, r

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.

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Finally, we consider what happens as this adjustment of the capitalstock continues over time. If the marginal product begins above thecost of capital, the capital stock will rise and the marginal product willfall. 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 + ).

Thus, in the long run, the MPK equals the real cost of capital. Thespeed of adjustment toward the steady state depends on how quicklyfirms adjust their capital stock, which in turn depends on how costlyit is to build, deliver and install new capital.

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The term stock refers to the shares in the ownership of corporations, andthe stock market is the market in which these shares are traded.The Nobel-Prize-winning economist James Tobin proposed that firmsbase their investment decisions on the following ratio, which is nowcalled Tobin’s q:

q = Market Value of Installed Capital Replacement Cost of Installed Capital

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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.

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1) Higher interest rates increase the cost of capital and reduce businessfixed investment.

2) Improvements in technology and tax policies such as the corporateincome 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.

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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 init 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.

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DemandRel

ativ

e P

rice

of

hou

sing

PH/P PH/P

The relative price of housing adjusts to equilibrate supply and demand for the existing stock of housing capital. The relative price thendetermines residential investment, the flow of new housing that construction firms build.

Stock of housing capital, KH Flow of residential investment, IH

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DemandRel

ativ

e P

rice

of

hou

sing

PH/P PH/P

Stock of housing capital, KH Flow of residential investment, IH

When the demand for housing shifts, the equilibrium price of housingchanges, and this change in turn affects residential investment. An increase in housing demand, perhaps due to a fall in the interestrate, raises housing prices and residential investment.

Demand'

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

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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.

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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 inprocess.

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The accelerator model assumes that firms hold a stock ofinventories that is proportional to the firm’s level of output. Thus, ifN is the economy’s stock of inventories and Y is output, then

N = Ywhere 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 N. Therefore, I = N = Y.

The accelerator model assumes that firms hold a stock ofinventories that is proportional to the firm’s level of output. Thus, ifN is the economy’s stock of inventories and Y is output, then

N = Ywhere 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 N. Therefore, I = N = Y.

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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.

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.

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Like other components of investment, inventory investment dependson 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 itcould 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 morecostly, so rational firms try to reduce their stock. Therefore, an increase in the real interest rate depresses inventory investment.

Like other components of investment, inventory investment dependson 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 itcould 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 morecostly, so rational firms try to reduce their stock. Therefore, an increase in the real interest rate depresses inventory investment.

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1) Higher interest rates increase the cost of holding inventories anddecrease inventory investment.

2) According to the accelerator model, the change in output shiftsthe inventory investment function.

3) Higher output during a boom raises the stock of inventories firmswish to hold, increasing inventory investment.

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Business fixed investmentResidual investmentInventory investmentNeoclassical model of investmentDepreciationReal cost of capitalNet investmentCorporate income taxInvestment tax creditStock

Stock marketTobin’s qFinancing constraintsProduction smoothingInventories as a factor of

productionStock-out avoidanceWork in processAccelerator model