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Chapter Eighteen 1
CHAPTER 18Production & Investment
A PowerPointTutorial
To Accompany
MACROECONOMICS, 7th. ed.
N. Gregory MankiwTutorial written by:
Mannig J. Simidian,modified by mebB.A. in Economics with Distinction, Duke University
M.P.A., Harvard University Kennedy School of GovernmentM.B.A., Massachusetts Institute of Technology (MIT) Sloan School of
Management
®
Chapter Eighteen 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
Chapter Eighteen 3
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.
Chapter Eighteen 4
• 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.
Chapter Eighteen 5
U.S. Investment and its components, 1970-2002
-250
0
250
500
750
1000
1250
1500
1750
2000
1970 1975 1980 1985 1990 1995 2000
Bill
ion
s o
f 1
99
6 d
olla
rs
TotalBusiness fixed investmentResidential investmentChange in inventories
P T PT P T PT P
Source: U.S. Department of Commerce. P and T denote dates of peaks and troughs, respectively.
Chapter Eighteen 6
What we learn from this graph:1. Business fixed investment is the largest of the three types of investment2.Investment varies with the business cycle, rising in booms and falling in recessions.3.Investment is fundamental for long-run growth4.Investment is also fundamental for short-run business cycle5.5.Inventory investment is only about 1% of GDP. Yet, in Inventory investment is only about 1% of GDP. Yet, in the typical recession, more than half of the fall in spending the typical recession, more than half of the fall in spending is due to a fall in inventory investment. is due to a fall in inventory investment.
Chapter Eighteen 7Copyright 1997 Dead Economists Society
It is a quite simple but powerful analytical model built aroundbuyers and sellers pursuing their own self-interest (withinrules set by government). It’s emphasis is on the consequencesof competition and flexible wages/prices for total employmentand real output. Its roots go back to 1776—to Adam Smith’sWealth 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.
Chapter Eighteen 8
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.
Chapter Eighteen 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
Chapter Eighteen 10
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.
Chapter Eighteen 11
An economy’s output of goods and services (GDP) depends on:
(1) quantity of inputs
(2) ability to turn inputs into output
Let’s go over both now.
Chapter Eighteen 12
The factors of production are the inputs used to produce goodsand services. The two most important factors of production arecapital 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.
Chapter Eighteen 13
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 )
OutputOutput isis some function ofsome function of our given inputsour given inputsTo see an example of a production function–let’s visit Mankiw’s Bakery…
Chapter Eighteen 14
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.
The workers hired to make the bread are itslabor.
The kitchen and itsequipment are Mankiw’sBakery capital.
The loaves of breadare its output.
Chapter Eighteen 15
The production function
• denoted Y = F (K, L)
• shows how much output (Y ) the economy can produce fromK units of capital and L units of labour.
• reflects the economy’s level of technology.
• exhibits constant returns to scale.
Chapter Eighteen 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
Chapter Eighteen 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:
Chapter Eighteen 18
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 functiontogether determine the total output of goods and services, they alsodetermine national income.
We will discuss distribution in the next lectures…..
Chapter Eighteen 19
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.
Chapter Eighteen 20
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.
Chapter Eighteen 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
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
Chapter Eighteen 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?
Chapter Eighteen 23
The price paid to any factor of production depends on the supply anddemand for that factor’s services. Because we have assumed thatthe supply is fixed, the supply curve is vertical. The demand curveis downward sloping. The intersection of supply and demanddetermines the equilibrium factor price.
FactorFactorpriceprice(Wage or(Wage orrentalrentalrate)rate)
Quantity of factor
Factor demand
Factor supply
Equilibriumfactor price
This vertical supply curve is a result of thesupply being fixed.
Chapter Eighteen 24
The goal of the firm is to maximize profit. Profit is revenue minuscost. Revenue equals P × Y. Costs include both labor and capitalcosts. Labor costs equal W × L, the wage multiplied by the amountof labor L. Capital costs equal R × K, the rental price of capital R timesthe 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.
Chapter Eighteen 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 givenand 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 paidbenefit = 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 timebenefit = marginal product of capital (MPK)
Chapter Eighteen 26
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 laborand then the quantity of capital.
Chapter Eighteen 27
The marginal product of labor (MPL) is the extra amount of output thefirm gets from one extra unit of labor, holding the amount ofcapital 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.
Chapter Eighteen 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 productivityAn increase in labor while holding capital fixed causes there to be
fewer machines per worker, which causes lower productivity.”
Chapter Eighteen 29
Youtput
The production function and its slope (MPL)
Llabour
1
MPL
1
MPL
1MPL As more
labour is added, MPL
Slope of the production function equals MPL
Chapter Eighteen 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.
Chapter Eighteen 31
When the competitive, profit-maximizing firm isdeciding whether to hire an additional unit of labor, itconsiders how that decision would affect profits. Ittherefore compares the extra revenue from the increasedproduction that results from the added labor to the extracost of higher spending on wages. The increase in revenuefrom 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 outputand each unit of output sells for P dollars, the extra revenueis P × MPL. The extra cost of hiring one more unit of laboris the wage W. Thus, the change in profit from hiringan additional unit of labor is Profit = Revenue - Cost
= (P × MPL) - W
Chapter Eighteen 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 thereal wage– the payment to labor measured in units of output ratherthan in dollars. To maximize profit, the firm hires up to the pointwhere the extra revenue equals the real wage.
The MPL depends on the amount of labor.The MPL curve slopes downward becausethe MPL declines as L increases. Thisschedule is also the firm’s labor demandcurve.
Units ofoutput
Units of labor, L
MPL, labor demand
Quantity of labor demanded
Realwage
Chapter Eighteen 33
The firm decides how much capital to rent in the same way it decideshow 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 extrarevenue from selling the output of that machine minus the machine’srental price: Profit = Revenue - Cost = (P × MPK) – R.
Chapter Eighteen 34
To maximize profit, the firm continues to rent more capital until the MPKfalls 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 productionuntil 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.
Chapter Eighteen 35
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
equilibrium equilibrium rental raterental rate
Chapter Eighteen 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 = AKL1- ,
where Y is output, K capital, L labor, A a parameter measuring the level of technology, and a parameter between 0 and 1 that measures capital’s share of output (or of national income … see next lecture…)
Chapter Eighteen 37
The marginal product of capital for the Cobb-Douglas production function is MPK = A(L/K)1-The real rental price equals MPK in equilibrium: R/P =MPK= A(L/K)1-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.
Chapter Eighteen 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 outto production firms.
Chapter Eighteen 39
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, 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 -PK
(a capital gain, PK > 0, reduces cost of K )
3) Depreciation cost , PK defined as the fraction of value lost per period (rate of depreciation).
Chapter Eighteen 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 = €970.
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.
Chapter Eighteen 41
Then,
interest cost =
depreciation cost =
capital loss =
total cost =
The cost of capital
Example car rental company (capital: cars)
Suppose PK = €10,000, i = 0.10, = 0.20,
and PK/PK = 0.06
Nominal cost of capital
€1000€2000 €600
€2400
Chapter Eighteen 42
The real cost of capitalFor 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
KPr
P
The real cost of capital depends positively on:• the relative price of capital• the real interest rate• the depreciation rateWe use real cost as in the W/P and labour case.
Chapter Eighteen 43
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 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 therate 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.
Chapter Eighteen 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)
Chapter Eighteen 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:
Chapter Eighteen 46
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.
Chapter Eighteen 47
The investment function
An increase in r • raises the cost
of capital • reduces the
profit rate • and reduces
investment: I
r
I2 I1
r1
r2
Chapter Eighteen 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
Chapter Eighteen 49
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.
Chapter Eighteen 50
Taxes and Investment
Two of the most important taxes Two of the most important taxes affecting investment:affecting investment:
1.1. Corporate income taxCorporate income tax
2.2. Investment tax creditInvestment tax credit
Two of the most important taxes Two of the most important taxes affecting investment:affecting investment:
1.1. Corporate income taxCorporate income tax
2.2. Investment tax creditInvestment tax credit
Chapter Eighteen 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.
Chapter Eighteen 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 €8000. 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 .
Chapter Eighteen 53Ireland outlier within the Eurozone; this may explain much of its remarkable income growth in the last years.
Corporate Tax Rates in Europe, US and Japan
0
5
10
15
20
25
30
35
40%
Chapter Eighteen 54
Policymakers often change the rules governing corporate incometax in an attempt to encourage investment, or at least mitigate thedisincentive the tax provides.
An investment tax credit is a tax provision that reduces a firm’staxes 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 ofa unit of capital PK
which increases the profit rate and the incentive to invest.
Chapter Eighteen 55
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
Tobin’s q measures the expected future profitability as well as the current profitability.
Chapter Eighteen 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 byincreasing 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.
Chapter Eighteen 57
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.
Chapter Eighteen 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.
Market value of installed capitalReplacement cost of installed capital
q
Chapter Eighteen 59
Efficient-Market Hypothesis: the market price of a company’sstock is the fully rational valuation of the company’s value, givencurrent 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.
Chapter Eighteen 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
Chapter Eighteen 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
Chapter Eighteen 62
The stock market and GDPWhy 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.
Chapter Eighteen 63The stock market and GDP tend to move together, but the association is far from precise
The stock market and GDPPanel (a) Annual Percentage Change in Stock Prices
-30
-20
-10
0
10
20
30
40
50
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
UK
EU-15
US
Panel (b) Annual Percentage Change in Real GDP
0
1
2
3
4
5
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Chapter Eighteen 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.
Chapter Eighteen 65
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.
Chapter Eighteen 66
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
Chapter Eighteen 67
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'
Chapter Eighteen 68
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.
Chapter Eighteen 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.
Chapter Eighteen 70
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.
Chapter Eighteen 71
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.
Chapter Eighteen 72
Motives for holding inventories
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
1. production smoothing
Chapter Eighteen 73
Motives for holding inventories
3. stock-out avoidance
To prevent lost sales in the event of higher than expected demand.
2. inventories as a factor of production
1. production smoothing
Chapter Eighteen 74
Motives for holding inventories
4. work in process
Goods not yet completed are counted as part of inventory.
3. stock-out avoidance
2. inventories as a factor of production
1. production smoothing
Chapter Eighteen 75
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.
Chapter Eighteen 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.
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.
Chapter Eighteen 77
Evidence for the Accelerator Model
1982
1991
1974 1971
1977
19751980
1983
1993
19981984
1997 2000
1999
Inventory investment(billions of 1996 dollars)
100
80
60
40
20
0
-20
-40
Change in real GDP (billions of 1996 dollars)-200 -100 300 400 5002001000
Chapter Eighteen 78
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.Example: High interest rates in the 1980s motivated many firms to adopt just-in-time production, which is designed to reduce inventories.
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.Example: High interest rates in the 1980s motivated many firms to adopt just-in-time production, which is designed to reduce inventories.
Chapter Eighteen 79
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.
Chapter Eighteen 80
Chapter summary
1. All types of investment depend negatively on the real interest rate.
2. 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.
Chapter Eighteen 81
Chapter summary
3. 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.
Chapter Eighteen 82
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
