Transcript Document

Production & Investment
A PowerPointTutorial
To Accompany
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
Chapter Eighteen
Learning objectives
In this chapter, you will learn:
• leading theories to explain each type of
• 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
Chapter Eighteen
• 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
U.S. Investment and its components, 1970-2002
Billions of 1996 dollars
Business fixed investment
Residential investment
Change in inventories
Chapter Eighteen
Source: U.S. Department of Commerce. P and T denote dates of peaks and troughs,
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.
3. Investment is fundamental for long-run growth
4. Investment is also fundamental for short-run business
5. 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.
Chapter Eighteen
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.
Chapter Eighteen
Copyright 1997 Dead Economists Society
The heart of the market system lies in the
“market clearing” process and the
consequences of individuals pursuing selfinterest. Prices adjust to balance demand
and supply.
We will use this model to show how income
is distributed among factors of production.
Chapter Eighteen
Understanding business fixed
• 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
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.
Chapter Eighteen
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
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 =
tools, machines, and structures used in production
L =
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
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)
is some function of our given inputs
To see an example of a production function–let’s visit Mankiw’s
Chapter Eighteen
The workers hired to
The kitchen and its
equipment are Mankiw’s make the bread are its
Bakery capital.
The loaves of bread
are its output.
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.
Chapter Eighteen
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
• exhibits constant returns to scale.
Chapter Eighteen
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
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
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…..
Chapter Eighteen
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
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
W /P
= nominal wage
= nominal rental rate
= price of output
= real wage
(measured in units of output)
R /P = real rental rate
Chapter Eighteen
How factor prices are determined
• Since the distribution of income depends on factor
prices, we need to see how factor prices are
• 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
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.
(Wage or
factor price
Chapter Eighteen
Factor supply
This vertical supply curve
is a result of the
supply being fixed.
Factor demand
Quantity of factor
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
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
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
cost = real cost of renting a unit of K for one period of time
benefit = marginal product of capital (MPK)
Chapter Eighteen
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.
Chapter Eighteen
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
Chapter Eighteen
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.”
Chapter Eighteen
The production function and its slope
As more labour
is added, MPL 
Chapter Eighteen
Slope of the production
function equals MPL
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
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
Chapter Eighteen
= (P × MPL) - W 31
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
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
Quantity of labor demanded
MPL, labor demand
Chapter Eighteen
Units of labor, L
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.
Chapter Eighteen
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.
Chapter Eighteen
The real rental price of capital
adjusts to equilibrate the demand for capital and the fixed supply.
Capital supply
Capital demand (MPK)
rental rate
Chapter Eighteen
Capital stock, K
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…)
Chapter Eighteen
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
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
A toEighteen
Rental firms’ investment
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.
Chapter Eighteen
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 -DPK
(a capital gain, DPK > 0, reduces cost of K )
3) Depreciation cost ,  PK defined as the fraction of value lost per
period  (rate of depreciation).
Chapter Eighteen
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 (DPK < 0 with - DPK in the formula)
A capital gain (DPK > 0) is subtracted from the cost, because the increase in the
price of new capital reduces the cost of capital.
Chapter Eighteen
The cost of capital
Nominal cost
of capital
Example car rental company (capital: cars)
Suppose PK = €10,000, i = 0.10,  = 0.20,
and DPK/PK = 0.06
Chapter Eighteen
interest cost = €1000
depreciation cost = €2000
capital loss =  €600
total cost = €2400
The real cost of capital
For simplicity, assume DPK/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 PK  r   
The real cost of capital depends positively on:
Chapter Eighteen
• the relative price of capital
• the real interest rate
• the depreciation rate
We use real cost as in the W/P and labour case.
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 + ).
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, we
can 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 the
rate of interest that investors pay to borrow money.
The real
interest rate is the nominal interest rate corrected for
Chapter Eighteen
the effects of inflation and investment depends on real interest rate.
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
Net investment & gross investment
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
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 + )] + K.
the cost of capital
depends on
amount of depreciation
marginal product of capital
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
The investment function
An increase in r
• raises the cost
of capital
• reduces the
profit rate
• and reduces
Chapter Eighteen
The investment function
An increase in MPK
or decrease in PK/P
• increases the profit
• increases investment
at any given interest
• shifts I curve to the
Chapter Eighteen
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 + ).
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.
Chapter Eighteen
Taxes and Investment
Two of the most important taxes
affecting investment:
1. Corporate income tax
2. Investment tax credit
Chapter Eighteen
Corporate Income Tax: A tax on
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
• Thus, corporate income tax discourages investment.
Chapter Eighteen
• 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
Corporate Tax Rates in Europe,
an SA any nce Italy ece nds
U rm ra
G her
Chapter Eighteen
ay den ga and and and ary and
m orw e
rtu inl erl Pol ung Irel
F itz
Ireland outlier within the Eurozone; this may explain much of its
remarkable income growth in the last years.
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.
Chapter Eighteen
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
Chapter Eighteen
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.
Chapter Eighteen
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 fixedinvestment function.
3) During booms higher employment increases the MPK and therefore,
increases business fixed investment.
Chapter Eighteen
Relation between q theory and neoclassical
theory described above
Market value of installed capital
Replacement cost of installed capital
• 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.
Chapter Eighteen
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.
Chapter Eighteen
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
Chapter Eighteen
cause stock prices to fall
cause Tobin’s q to fall
shift the investment function down
cause a negative aggregate demand shock
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
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 fullemployment output will be expanding more
slowly than people had expected.
Chapter Eighteen
The stock market and GDP
Panel (a) Annual Percentage Change in Stock Prices
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Panel (b) Annual Percentage Change in Real GDP
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
The stock
market and GDP tend to move together, but the association is far from precise
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
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.
Chapter Eighteen
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.
Stock of housing capital, KH
Chapter Eighteen
Flow of residential investment, IH
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.
Stock of housing capital, KH
Chapter Eighteen
Flow of residential investment, IH
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.
Chapter Eighteen
The tax treatment of housing
• In some countries the tax code, in effect, subsidizes
home ownership by allowing people to deduct mortgage
• 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 overinvestment in housing relative to other forms of capital
• But eliminating the mortgage interest deduction would
be politically difficult.
Chapter Eighteen
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
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
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
Chapter Eighteen
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.
Chapter Eighteen
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.
Chapter Eighteen
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
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.
Chapter Eighteen
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
Evidence for the Accelerator Model
Inventory investment
(billions of 1996
Chapter Eighteen
Change in real GDP (billions of 1996 dollars)
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.
High interest rates in the 1980s motivated many firms
to adopt just-in-time production, which is designed to reduce inventories.
Chapter Eighteen
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.
Chapter Eighteen
Chapter summary
1. All types of investment depend negatively on
the real interest rate.
2. Factors that shift the investment function:
Chapter Eighteen
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 summary
3. Investment is the most volatile component of
GDP over the business cycle.
Chapter Eighteen
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
Fluctuations in output affect planned &
unplanned inventory investment.
Business fixed investment
Residual investment
Inventory investment
Neoclassical model of investment
Real cost of capital
Net investment
Corporate income tax
Investment tax credit
Chapter Eighteen
Stock market
Tobin’s q
Financing constraints
Production smoothing
Inventories as a factor of
Stock-out avoidance
Work in process
Accelerator model