1. 17
Investment
This chapter begins by reviewing the three components of investment, and presents a time series graph of all three components, and total investment, to show the relative size of each component and to show their behavior over business cycles.
Then, the chapter presents the leading theory of each component of investment.
The chapter is of average length and difficulty.

2. 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
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3. 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.
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4. U.S. investment and its components
Billions of dollars
2000
Total investment
1750
Business fixed investment
1500
Residential investment
1250
Change in inventories
1000
750
500
Figure 17-1, p Source: U.S. Dept of Commerce.
What we learn from this graph:
1. Business fixed investment is the largest of the three types of investment
2. Investment varies with the business cycle, rising in booms and falling in recessions.
250
-250
1970
1975
1980
1985
1990
1995
2000
2005
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5. 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
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6. 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.
Note: Many students find it easier to learn the following material by separating the investment decision from the production decision.
Of course, the lessons apply to real-world firms that actually do both functions.
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7. The capital rental market
capital stock
real rental price, R/P
Production firms must decide how much capital to rent.
Recall from Chap. 3: Competitive firms rent capital to the point where MPK = R/P.
capital supply
capital demand (MPK)
equilibrium rental rate
The graph of the rental market for capital is review from chapter 3. As you present it to your students, it might be worthwhile to briefly review each piece (why the supply curve is vertical, why demand = MPK).
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8. Factors that affect the rental price
For the Cobb-Douglas production function,
the MPK (and hence equilibrium R/P ) is
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)
(It might be worth reminding students that A represents the level of technology, and  is a number between 0 and 1 that equals capital’s share of national income.)
We use the C-D function for two reasons: First, we can make the ideas here more concrete with a specific functional form, and second, because the C-D function will be familiar to most students from earlier chapters (the appendix to Chapter 3, and the economic growth chapters).
If students are wondering where the MPK equation comes from, either refer them to the Appendix to chapter 3, or, if they are acquainted with basic calculus, take the derivative of the C-D production function with respect to K.
Regarding the impact of an increase in A on R/P: We usually associate A with technology. However, A represents anything that affects the amount of output that can be produced from a given bundle of inputs. For example, firms use resources (in this context, L and/or K) to comply with regulations (some labor time is used to fill out forms; some capital is used to reduce emissions of nasty things into the air or rivers). A relaxation of regulations would allow firms to divert these resources from compliance with regulations to production, causing output to increase. Hence, a deregulation could cause A to rise.
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9. 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.
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10. The cost of capital Components of the cost of capital:
interest cost: i PK, where PK = nominal price of capital
depreciation cost:  PK, where  = rate of depreciation
capital loss:  PK (a capital gain, PK > 0, reduces cost of K )
The total cost of capital is the sum of these three parts:
Notes:
Interest cost-- If firms borrow in the loanable funds market (from chapter 3) to finance their purchases of capital, then they incur interest. But even if firms use their own funds, they incur an opportunity cost equal to the interest they could have earned had they purchased Pk worth of bonds instead of spending Pk to buy a piece of capital.
Depreciation cost--
Remind students that  is the depreciation rate, the percentage of capital that wears out each period. If the firm starts the period with $1000 worth of capital and the depreciation rate = 0.03, then at the end of the period, the value of the firm’s capital equals (1-0.03)$1000 = $970.
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11. Nominal cost of capital
The cost of capital
Nominal cost of capital
Example: car rental company (capital: cars)
Suppose PK = $10,000, i = 0.10,  = 0.20, and PK/PK = 0.06
Then, interest cost = depreciation cost = capital loss = total cost =
If the price of capital, Pk, falls during the period, then firm incurs a capital loss, which increases its cost of capital.
In this example, the price of capital rises, so the “capital loss” is negative. (Or, there’s a capital gain which we subtract from the cost, because the increase in the price of new capital reduces the cost of capital.)
$1000
$2000
 $600
$2400
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12. The cost of capital For simplicity, assume PK/PK = .
Then, the nominal cost of capital equals PK(i +   ) = PK(r + )
and the real cost of capital equals
The real cost of capital depends positively on:
the relative price of capital
the real interest rate
the depreciation rate
The assumption in the first line says that the price of capital rises as fast as the general price level.
The real cost of capital equals the nominal cost divided by the price level, just as the real wage equals the nominal wage divided by P.
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13. The rental firm’s profit rate
A firm’s net investment depends on its profit rate:
If profit rate > 0, then increasing K is profitable
If profit rate < 0, then the firm increases profits by reducing its capital stock.
(Firm reduces K by not replacing it as it depreciates.)
In plain English, the profit rate equals
(the rental price of capital) minus (the user cost of capital)
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14. Net investment & gross investment
Hence,
where In[ ] is a function that shows how net investment responds to the incentive to invest.
Total spending on business fixed investment equals net investment plus replacement of depreciated K:
The equation in the yellow box simply states “net investment depends on the profit rate.”
It might be useful to remind students that gross investment is simply net investment plus depreciation.
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15. The investment function
An increase in r
raises the cost of capital
reduces the profit rate
and reduces investment: I r r2
Finally, we see where our familiar investment function comes from. I1 r1 I2
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16. The investment function
An increase in MPK or decrease in PK/P
increases the profit rate
increases investment at any given interest rate
shifts I curve to the right. I r
Here’s a challenge for particularly bright students:
Ask what happens to the investment curve given an increase in the depreciation rate. Tell them to justify their answer based on the investment equation we have derived.
Answer: The impact on the curve is ambiguous.
The depreciation rate appears in two different places in the equation.
First, it appears in the expression for the profit rate, which is the argument of the net investment function. An increase in the depreciation rate would raise the cost of capital and hence reduce the profit rate and the incentive to invest (*net* investment). This would tend to shift the curve left.
Second, the depreciation rate appears as a coefficient on K. An increase in the depreciation rate means that more investment (*gross* investment) is needed to replace depreciating capital and keep the total capital stock at its optimal level. This effect would shift the curve right.
The net impact of the two opposing forces is ambiguous, without knowing the specific form of the In( ) function.
Note: This exercise is simply for practice, and does not correspond to a real-world policy example. I1 r1 I2
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17. Taxes and investment
Two of the most important taxes affecting investment:
Corporate income tax
Investment tax credit
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18. Corporate Income Tax: A tax on profits
Impact on investment depends on definition of “profit”
In our definition (rental price minus cost of capital), depreciation cost is measured using current price of capital, and the CIT would not affect investment
But, the legal definition uses the historical price of capital.
If PK rises over time, then the legal definition understates the true cost and overstates profit,
so firms could be taxed even if their true economic profit is zero.
Thus, corporate income tax discourages investment.
Why the corporate income tax doesn’t affect investment when profits are defined as in the textbook: Let  be the tax rate and--for this note only--let  denote the profit rate as defined above. The after-tax profit rate equals (1). The firm’s investment decision depends on whether its profit rate is positive. As long as  < 1, then the sign of (1) equals the sign of . I.e., if an investment project is profitable without the tax, it will be profitable (though less so) with the tax.
Why using the historical price to compute depreciation understates the true cost of capital:
Consider the car rental example from a few slides ago. Suppose that when the car was originally purchased, the price was only $ Then, according to the government, depreciation is only $1600 = 0.2 (the depreciation rate) times $8000 (the historical price of capital). So, according to the government, the total cost of capital is only $2000, which is $400 less than the true economic cost of capital. Thus, the government is taxing the car rental firm ( + 400) instead of .
(Please forgive my use of  to represent profit in this note when everywhere else we are using it to represent inflation!)
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19. The Investment Tax Credit (ITC)
The ITC reduces a firm’s taxes by a certain amount for each dollar it spends on capital.
Hence, the ITC effectively reduces PK
which increases the profit rate and the incentive to invest.
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20. Tobin’s q
numerator: the stock market value of the economy’s capital stock.
denominator: the actual cost to replace the capital goods that were purchased when the stock was issued.
If q > 1, firms buy more capital to raise the market value of their firms.
If q < 1, firms do not replace capital as it wears out.
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21. Relation between q theory and neoclassical theory described above
The stock market value of capital depends on the current & expected future profits of capital.
If MPK > 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.
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22. The stock market and GDP
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
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23. The stock market and GDP
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
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24. The stock market and GDP
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.
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25. The stock market and GDP
Real GDP (right scale)
Percent change from 1 year earlier 50 10
Percent change from 1 year earlier
Stock prices (left scale) 40 8 30 6 20 4 10 2
Figure 17-4 on p Source: U.S. Department of Commerce and Global Financial Data. The measure of the stock market is the Dow Jones Industrial Average.
The figure shows that the stock market and GDP tend to move together, but the association is far from precise.
-10 -2
-20 -4
-30 -6
1970
1975
1980
1985
1990
1995
2000
2005
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26. Alternative views of the stock market: 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.
This and the next two slides correspond to new material in the 6th edition, on pp
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27. Alternative views of the stock market: Keynes’s “beauty contest”
Idea based on newspaper beauty contest in which a reader wins a prize if he/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”).
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28. Alternative views of the stock market: EMH vs. Keynes’s beauty contest
Both views persist.
There is evidence for the EMH and random-walk theory (see p.498).
Yet, some stock market movements do not seem to rationally reflect new information.
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29. 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.
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30. 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.
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31. How residential investment is determined
(a) The market for housing
Demand
Supply
Supply and demand for houses determines the equilib. price of houses.
The equilibrium price of houses then determines residential investment: KH
Stock of housing capital
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32. How residential investment is determined
(a) The market for housing
(b) The supply of new housing
Demand
Supply
Supply KH IH
Stock of housing capital
Flow of residential investment
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33. How residential investment responds to a fall in interest rates
(a) The market for housing
(b) The supply of new housing
Demand
Supply
Supply
The main point of this slide is to establish more formally the dependence of investment (in this case, residential investment) on the interest rate.
A fall in interest rates increases the demand for houses, bidding up the price of houses (relative to the general level of prices).
The higher relative price of houses motivates firms to increase residential investment. KH IH
Stock of housing capital
Flow of residential investment
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34. The tax treatment of housing
The tax code, in effect, subsidizes home ownership by allowing people to deduct mortgage interest.
The deduction applies to the nominal mortgage rate,
so this subsidy is higher when inflation and nominal mortgage rates are high than when they are low.
Some economists think this subsidy causes over-investment in housing relative to other forms of capital
But eliminating the mortgage interest deduction would be politically difficult.
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35. 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.
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36. Motives for holding inventories
1. production smoothing
Sales fluctuate, but many firms find it cheaper to produce at a steady rate.
When sales < production, inventories rise.
When sales > production, inventories fall.
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37. Motives for holding inventories
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
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38. Motives for holding inventories
1. production smoothing
2. inventories as a factor of production
3. stock-out avoidance
To prevent lost sales when demand is higher than expected.
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39. Motives for holding inventories
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.
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40. The Accelerator Model
A simple theory that explains the behavior of inventory investment, without endorsing any particular motive
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41. The Accelerator Model
Notation: N = stock of inventories N = inventory investment
Assume: Firms hold a stock of inventories proportional to their output
N =  Y, where  is an exogenous parameter reflecting firms’ desired stock of inventory as a proportion of output.
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42. The Accelerator Model Result: N =  Y
Inventory investment is proportional to the change in output.
When output is rising, firms increase inventories.
When output is falling, firms allow their inventories to run down.
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43. Evidence for the Accelerator Model
Inventory investment (billions of 1996 dollars)
100
1982
2001
2004
1998
1984
1978
1996
1983
1967
1974 80 60 40 20
A near-replica of Figure 17-7, p.506, except that the data Mankiw gave me to construct this graph are in 1996 dollars, whereas the data used to construct Figure 17-7 in the textbook are in 2000 dollars.
This scatterplot shows that inventory investment is high in years when real GDP rises and low in years when real GDP falls, just as the accelerator model predicts.
-20
-40
-200
-100
100
200
300
400
500
Change in real GDP (billions of 1996 dollars)
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44. Inventories and the real interest rate
The opportunity cost of holding goods in inventory: the interest that could have been earned on the revenue from selling those goods.
Hence, inventory investment depends on the real interest rate.
Example: High interest rates in the 1980s motivated many firms to adopt just-in-time production, which is designed to reduce inventories.
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45. Chapter Summary
All types of investment depend negatively on the real interest rate.
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.
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46. Chapter Summary
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.
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