1. MANKIW'S MACROECONOMICS MODULES
MANKIW'S MACROECONOMICS MODULES
CHAPTER 18
Production & Investment
A PowerPointTutorial
To Accompany
MACROECONOMICS, 7th. ed.
N. Gregory Mankiw
Tutorial written by:
Mannig J. Simidian,modified by meb
B.A. in Economics with Distinction, Duke University
M.P.A., Harvard University Kennedy School of Government
M.B.A., Massachusetts Institute of Technology (MIT) Sloan School of Management

2. Learning objectives In this chapter, you will learn:
leading theories to explain each type of investment
why investment is negatively related to the interest rate
factors that shift the investment function
why investment rises during booms and falls during recessions

3. Investment Spending Investment spending is aimed at
providing a higher standard of income in the future. 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.
Investment Spending

4. 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.

5. P T
Source: U.S. Department of Commerce. P and T denote dates of peaks and troughs, respectively.
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.
Source: U.S. Department of Commerce. P and T denote dates of peaks and troughs, respectively.

6. What we learn from this graph:
1. Business fixed investment is the largest of the three types of investment
Investment varies with the business cycle, rising in booms and falling in recessions.
Investment is fundamental for long-run growth
Investment is also fundamental for short-run business cycle
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.
Source: U.S. Department of Commerce. P and T denote dates of peaks and troughs, respectively.
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.

7. What is the Classical Model?
It is a quite simple but powerful analytical model built around
buyers and sellers pursuing their own self-interest (within
rules set by government). It’s emphasis is on the consequences
of competition and flexible wages/prices for total employment
and real output. Its roots go back to 1776—to Adam Smith’s
Wealth of Nations. The Wealth of Nations suggested that the economy was controlled by the “invisible hand” whereby the market system, instead of government would be the best mechanism for a healthy economy.
Copyright 1997 Dead Economists Society

8. Why is the Classical Model Important?
The heart of the market system lies in the “market clearing” process and the consequences of individuals pursuing self-interest. Prices adjust to balance demand and supply.
We will use this model to show how income is distributed among factors of production.

9. Understanding business fixed investment
The standard model of business fixed investment: the neoclassical model of investment (more recent, nineteenth-century) based on the idea that the demand for each factor of production depends on the marginal productivity of that factor.
Shows how investment depends on
Marginal productivity of capital (MPK)
interest rate
tax rules affecting firms

10. 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.

11. What determines the Total Production of Goods and Services?
An economy’s output of goods and services (GDP) depends on:
quantity of inputs
ability to turn inputs into output
Let’s go over both now.
The Factors of Production
The Production Function

12. The Factors of Production
The factors of production are the inputs used to produce goods
and services. The two most important factors of production are
capital and labor.
K = capital, tools, machines, and structures used in production
L = labour, the physical and mental efforts of workers
We think of capital as plant & equipment. In the real world, capital also includes inventories and residential housing. “Land” or “land and natural resources” is an additional factor of production. In macro, we mainly focus on labor and capital, though. So, to keep our model simple, we usually omit land as a factor of production, as we can learn much of what we need to know about macroeconomics without the factor of production land.

13. The Production Function
The available production technology determines how much output is produced from given amounts of capital (K) and labor (L). The production function represents the transformation of inputs into outputs. A key assumption is that the production function has constant returns to scale, meaning that if we increase inputs by z, output will also increase by z.
We write the production function as: Y = F ( K , L )
Output is
some function of
our given inputs
To see an example of a production function–let’s visit Mankiw’s Bakery…

14. Mankiw’s Bakery The loaves of bread are its output.
The workers hired to
make the bread are its
labor.
The kitchen and its
equipment are Mankiw’s
Bakery capital.
Mankiw’s Bakery production function shows that the number of loaves produced depends on the amount of the equipment and the number of workers. If the production function has constant returns to scale, then doubling the amount of equipment and the number of workers doubles the amount of bread produced.

15. The production function
denoted Y = F (K, L)
shows how much output (Y ) the economy can produce from K units of capital and L units of labour.
reflects the economy’s level of technology.
exhibits constant returns to scale.

16. Returns to scale: a review
Initially Y1 = F (K1 , L1 )
Scale all inputs by the same factor z:
K2 = zK1 and L2 = zL1
(If z = 1.25, then all inputs are increased by 25%)
What happens to output, Y2 = F (K2 , L2 ) ?
If constant returns to scale, Y2 = zY1
If increasing returns to scale, Y2 > zY1
If decreasing returns to scale, Y2 < zY1

17. Assumptions of the model
Technology is fixed.
The economy’s supplies of capital and labour are fixed at:
Output is determined by the fixed factor supplies and the fixed state of technology:
Emphasize that “K” and “L” (without bars on top) are variables - they can take on various magnitudes. On the other hand, “Kbar” and “Lbar” are specific values of these variables. Hence, “K = Kbar” means that the variable K equals the specific amount Kbar.
Regarding the assumptions:
In chapters 7 and 8 (Economic Growth I and II), we will relax these assumptions: K and L will grow in response to investment and population growth, respectively, and the level of technology will increase over time.

18. How is National Income Distributed to the Factors of Production?
Recall that the total output of an economy equals total income.
The income is paid to the workers, capital owners, land owners, etc….
Because the factors of production and the production function
together determine the total output of goods and services, they also
determine national income.
We will discuss distribution in the next lectures…..

19. Factor Prices
The distribution of national income is determined by factor prices.
Factor prices are the amounts paid to the factors of production:
the wages workers earn  the wage is the price of L
the rent the owners of capital collect  the rental rate is the price of K.

20. Capital
Labor
To make a product, the firm needs two factors of production, capital and labor. Let’s represent the firm’s technology by the usual production function:
Y = F (K, L)
The firm sells its output at price P, hires workers at a wage W, and rents capital at a rate R.

21. Notation W = nominal wage R = nominal rental rate P = price of output
W /P = real wage (measured in units of output)
R /P = real rental rate
It might be worthwhile to refresh students’ memory about nominal and real variables.
The nominal wage & rental rate are measured in currency units.
The real wage is measured in units of output.
To see this, suppose W = €10/hour and P = €2 per unit of output.
Then, W/P = (€10/hour) / (€2/unit of output) = 5 units of output per hour of work.
It’s true, the firm is paying the workers in money units, not in units of output. But, the real wage is the purchasing power of the wage - the amount of stuff that workers can buy with their wage.

22. How factor prices are determined
Since the distribution of income depends on factor prices, we need to see how factor prices are determined.
Factor prices are determined by supply and demand in factor markets. For instance, supply and demand for capital determine the rent.
Recall: Supply of each factor is fixed.
What about demand?
Since the distribution of income depends on factor prices, we need to see how factor prices are determined.
Each factor’s price is determined by supply and demand in a market for that factor. For instance, supply and demand for labour determine the wage.

23. The price paid to any factor of production depends on the supply and
demand for that factor’s services. Because we have assumed that
the supply is fixed, the supply curve is vertical. The demand curve
is downward sloping. The intersection of supply and demand
determines the equilibrium factor price.
FACTOR PRICES
Factor
price
(Wage or
rental
rate)
Quantity of factor
Factor demand
Factor supply
Equilibrium
factor price
This vertical supply curve
is a result of the
supply being fixed.

24. The goal of the firm is to maximize profit. Profit is revenue minus
cost. Revenue equals P × Y. Costs include both labor and capital
costs. Labor costs equal W × L, the wage multiplied by the amount
of labor L. Capital costs equal R × K, the rental price of capital R times
the amount of capital K.
Profit = Revenue - Labor Costs - Capital Costs
= PY - WL - RK
Then, to see how profit depends on the factors of production, we use
production function Y = F (K, L) to substitute for Y to obtain:
Profit = P × F (K, L) - WL - RK
This equation shows that profit depends on P, W, R, L, and K.

25. Assume that markets are competitive:
each firm takes W, R, and P as given
The competitive firm takes the product price and factor prices as given
and chooses the amounts of labor and capital that maximize profit.
Basic idea: A firm hires each unit of labour if the cost does not exceed the benefit.
cost = real wage that is paid
benefit = marginal product of labour (MPL)
A firm rents each unit of capital if the cost does not exceed the benefit.
cost = real cost of renting a unit of K for one period of time
benefit = marginal product of capital (MPK)

26. The Firm's Demand for Factors
We know that the firm will hire labor and rent capital in the quantities that maximize profit. But what are those maximizing quantities? To answer this, we must consider the quantity of labor
and then the quantity of capital.

27. The Marginal Product of Labor
The marginal product of labor (MPL) is the extra amount of output the
firm gets from one extra unit of labor, holding the amount of
capital fixed and is expressed using the production function:
MPL = F(K, L + 1) - F(K, L).
Most production functions have the property of
diminishing marginal product (or return): holding the amount of capital
fixed, the marginal product of labor decreases as the amount of labor
increases.

28. Diminishing marginal returns
As a factor input is increased, its marginal product falls (other things equal).
Intuition: L while holding K fixed
 fewer machines per worker
lower productivity
An increase in labor while holding capital fixed causes there to be fewer machines per worker, which causes lower productivity.”
Tell class: Many production functions have this property.
This slide introduces some short-hand notation that will appear throughout the PowerPoint presentations of the remaining chapters:
The up and down arrows mean increase and decrease, respectively.
The symbol “” means “causes” or “leads to.”
Hence, the text after “Intuition” should be read as follows:
“An increase in labor while holding capital fixed causes there to be fewer machines per worker, which causes lower productivity.”
Many instructors use this type of short-hand (or something very similar), and it’s much easier and quicker for students to write down in their notes.

29. The production function and its slope (MPL)Y
output 1
MPL
As more labour is added, MPL  1
MPL
(Figure 3-3 on p.49)
To the instructor:
It’s straightforward to see that the MPL = the prod function’s slope (i.e. its first derivative): The definition of the slope of a curve is the amount the curve rises when you move one unit to the right. On this graph, moving one unit to the right simply means using one additional unit of labor. The amount the curve rises is the amount by which output increases: the MPL.
Slope of the production function equals MPL
MPL 1 L
labour

30. The MPL is the change in output when the labor input is increased by 1 unit. As the amount of labor
increases, the production function becomes flatter, indicating diminishing marginal product.
It’s straightforward to see that the MPL = the production function’s slope (i.e. its first derivative): The definition of the slope of a curve is the amount the curve rises when you move one unit to the right. On this graph, moving one unit to the right simply means using one additional unit of labor. The amount the curve rises is the amount by which output increases: the MPL.

31. From the MPL to Labor Demand
When the competitive, profit-maximizing firm is
deciding whether to hire an additional unit of labor, it
considers how that decision would affect profits. It
therefore compares the extra revenue from the increased
production that results from the added labor to the extra
cost of higher spending on wages. The increase in revenue
from an additional unit of labor depends on two variables:
the marginal product of labor, and the price of the output.
Because an extra unit of labor produces MPL units of output
and each unit of output sells for P dollars, the extra revenue
is P × MPL. The extra cost of hiring one more unit of labor
is the wage W. Thus, the change in profit from hiring
an additional unit of labor is D Profit = D Revenue - D Cost
= (P × MPL) - W

32. Thus, the firm’s demand for labor is determined by P × MPL = W,
or another way to express this is MPL = W/P, where W/P is the
real wage– the payment to labor measured in units of output rather
than in dollars. To maximize profit, the firm hires up to the point
where the extra revenue equals the real wage.
Units of
output
Units of labor, L
MPL, labor demand
Quantity of labor demanded
Real
wage
The MPL depends on the amount of labor.
The MPL curve slopes downward because
the MPL declines as L increases. This
schedule is also the firm’s labor demand
curve.

33. The MPK and Capital Demand
The firm decides how much capital to rent in the same way it decides
how much labor to hire.
The marginal product of capital, or MPK,
is the amount of extra output the firm gets from an extra unit of
capital, holding the amount of labor constant:
MPK = F (K + 1, L) – F (K, L).
Thus, the MPK is the difference between the amount of output produced
with K+1 units of capital and that produced with K units of capital.
Like labor, capital is subject to diminishing marginal product.
The increase in profit from renting an additional machine is the extra
revenue from selling the output of that machine minus the machine’s
rental price: D Profit = D Revenue - D Cost = (P × MPK) – R.

34. falls to equal the real rental price, MPK = R/P.
To maximize profit, the firm continues to rent more capital until the MPK
falls to equal the real rental price, MPK = R/P.
The real rental price of capital is the real cost of renting a unit of K for one period of time, measured in units of goods rather than in dollars.
The firm demands each factor of production
until that factor’s marginal product falls to equal its real factor price.
The same logic shows that MPK = R/P :
diminishing returns to capital: MPK  as K 
The MPK curve is the firm’s demand curve for renting capital.
Firms maximize profits by choosing K such that MPK = R/P .
In our model, it’s easiest to think of firms renting capital from households (the owners of all factors of production). In the real world, of course, many firms own some of their capital. But, for such a firm, the market rental rate is the opportunity cost of using its own capital instead of renting it to another firm. Hence, R/P is the relevant “price” in firms’ capital demand decisions, whether firms own their capital or rent it.

35. The Rental Price of Capital
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)
equilibrium rental rate
K Capital stock, K

36. To see what variables influence the equilibrium rental price, let’s
consider the Cobb-Douglas production function (we will come back to it in the next lecture) 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,
A a parameter measuring the level of technology,
and a a parameter between 0 and 1 that measures capital’s share of output (or of national income … see next lecture…)

37. The real rental price equals MPK in equilibrium:
The marginal product of capital for the Cobb-Douglas production function is MPK = aA(L/K)1-a.
The real rental price equals MPK in equilibrium:
R/P =MPK= aA(L/K)1-a .
This expression identifies the variables that determine the real rental price. The equilibrium R/P would increase:
the lower the stock of capital K (due, e.g., to earthquake or war)
the greater the amount of labor employed L (due, e.g., to pop. growth or immigration)
the better the technology A (technological improvement, or deregulation).
Note that actually A represents anything that affects the amount of output that can be produced from a given bundle of inputs. For ex., firms use resources (L and/or K) to compliance with regulations (some labour 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.

38. 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 out to production firms.

39. The Cost of Capital
For each period of time that a firm rents out a unit of capital, the rental firm bears three costs:
Interest on their loans, i PK , which equals the purchase price of a unit of capital PK times the nominal interest rate
2) The cost of the loss or gain on the price of capital denoted as -DPK
(a capital gain, PK > 0, reduces cost of K )
3) Depreciation cost ,  PK defined as the fraction of value lost per period d (rate of depreciation).

40. Interest cost. If firms borrow in the loanable funds market 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.  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 = € Capital loss. If the price of capital, Pk, falls during the period, then firm incurs a capital loss, which increases its cost of capital (PK < 0 with - PK in the formula) A capital gain (PK > 0) is subtracted from the cost, because the increase in the price of new capital reduces the cost of capital.

41. The cost of capital Example car rental company (capital: cars)
Nominal cost of capital
Example car rental company (capital: cars)
Suppose PK = €10,000, i = 0.10,  = 0.20, and PK/PK = 0.06
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.)
Then, interest cost = depreciation cost = capital loss = total cost =
€1000
€2000
 €600
€2400

42. The real cost of capital
For simplicity, assume PK/PK = , the rate of inflation.
The price of capital is assumed to rise as fast as the general price level.
Then, the nominal cost of capital equals PK(i +   ) = PK(r + )
and the real cost of capital equals
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.
The real cost of capital depends positively on:
the relative price of capital
the real interest rate
the depreciation rate
We use real cost as in the W/P and labour case.

43. 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 profit rate equals
(the rental price of capital) minus (the user cost of capital)
The nominal interest rate is the interest rate as usually reported; it is the
rate of interest that investors pay to borrow money.
The real interest rate is the nominal interest rate corrected for
the effects of inflation and investment depends on real interest rate.

44. 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 profit rate > 0, then it’s profitable for firm to increase K
If the MPK falls short of the cost of capital, they let their capital stock shrink. If profit rate < 0, then firm increases profits by reducing its capital stock.
(Firm reduces K by not replacing it as it depreciates)

45. Net investment & gross investment
Hence,
where In( ) is a function showing how net investment responds to the incentive to invest.
Total spending on business fixed investment equals net investment plus the replacement of depreciated capital:
It might be useful to remind students that gross investment is simply net investment plus depreciation.

46. 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.

47. The investment function
An increase in r
raises the cost of capital
reduces the profit rate
and reduces investment: I r r2 I1 r1 I2

48. 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 I1 r1 I2

49. 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.

50. Taxes and Investment
Two of the most important taxes affecting investment:
Corporate income tax
Investment tax credit

51. Corporate Income Tax: A tax on profits
Impact on investment depends on definition of “profits”
If the law used our definition (rental price minus cost of capital), then the tax doesn’t affect investment.
In our definition, depreciation cost is measured using the current price of capital.
But, 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 the use of  to represent profit in this note when everywhere else we are using it to represent inflation!)

52. Why the corporate income tax doesn’t affect investment when profits are defined as in the textbook:
Let  be the tax rate and  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  .
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 the use of  to represent profit in this note when everywhere else we are using it to represent inflation!)

53. Corporate Tax Rates in Europe, US and Japan
Note that the 3 largest economies have the highest corporate tax rates.
With its 12.5% rate, Ireland is the clear outlier within the Eurozone. This may explain much of its remarkable income growth in the last years.
Ireland outlier within the Eurozone; this may explain much of its remarkable income growth in the last years.

54. Investment Tax Credit
Policymakers often change the rules governing corporate income
tax in an attempt to encourage investment, or at least mitigate the
disincentive the tax provides.
An investment tax credit is a tax provision that reduces a firm’s
taxes by a certain amount for each dollar spent on capital goods.
Because a firm recoups part of its investment in capital goods in the
form of lower taxes, a credit reduces the effective purchase price of
a unit of capital PK
which increases the profit rate and the incentive to invest.

55. 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
Tobin’s q measures the expected future profitability as well as the current profitability.

56. 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 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.

57. 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.

58. 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 loses, so their stock market value falls, and q is low.

59. Efficient-Market Hypothesis: the market price of a company’s
The Stock Market:
The Efficient-Market Hypothesis
vs. Keynes's Beauty Contest
Efficient-Market Hypothesis: the market price of a company’s
stock is the fully rational valuation of the company’s value, given
current information about the company’s business prospects.
Keynes’ beauty contest is a metaphor for stock speculation. In this view, the stock market fluctuates for no good reason, and because the stock market influences the aggregate demand for goods and services, these fluctuations are a source of short-run economic fluctuations.

60. The stock market and GDP
Why one might expect 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

61. The stock market and GDP
Why one might expect 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

62. The stock market and GDP
Why one might expect 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.

63. The stock market and GDP
The figure shows that the stock market and GDP tend to move together, but the association is far from precise.
The stock market and GDP tend to move together, but the association is far from precise

64. 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, it might be worthwhile to continue to invest. But if firm faces financing constraints, then firm might be unable to obtain funds due to current profits being low.

65. 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.

66. 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

67. 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

68. 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.

69. The tax treatment of housing
In some countries 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.

70. 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.

71. Reasons 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.

72. 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

73. Motives for holding inventories
1. production smoothing
2. inventories as a factor of production
3. stock-out avoidance
To prevent lost sales in the event of higher than expected demand.

74. 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 as part of inventory.

75. 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.

76. 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.

77. Evidence for the Accelerator Model
100
Inventory investment
(billions of 1996 80
1998
dollars)
1984
1997 60
2000
1999 40
1977
1974 20
1971
1991
1993
1983
-20
1982
1975
1980
-40
-200
-100
100
200
300
400
500
Change in real GDP (billions of 1996 dollars)

78. 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.
Example: High interest rates in the 1980s motivated many firms
to adopt just-in-time production, which is designed to reduce inventories.

79. 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.

80. Chapter summary
All types of investment depend negatively on the real interest rate.
Factors 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.

81. 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.

82. Key Concepts of Chapter 18
Business fixed investment
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