Input Demand: Labor and Land Markets
9.1
Demand for Inputs: A Derived Demand
Derived demand is demand for resources (inputs) that is
dependent on the demand for the outputs those resources
can be used to produce.
Inputs are demanded by a firm if, and only if, households
demand the good or service produced by that firm
 this means that firms will layoff employees when the
demand for its product falls and will hire fewer workers
when the price of labor (wages) increases.
9.2
Inputs: Complementary and Substitutable
9.3
The productivity of an input is the amount of output produced
per unit of that input.
Labor Productivity: Q/L (output per hour of labor)
Inputs can be complementary or substitutable. This means
that a firm’s input demands are tightly linked together.
• Complements: as the firm hires more workers, it will need to
employ more machinery (computers, etc.) for labor to use.
• Substitutes: as labor becomes more costly firms will automate
by buying machinery that can do what labor does.
Marginal Product and Marginal Revenue Product
Faced with a capacity constraint in the short-run, a firm
that decides to increase output will eventually encounter
diminishing marginal product.
• Marginal product of labor (MPL) is the additional output
produced by one additional unit of labor.
• Marginal Revenue Product of Labor (MRPL) is the
additional revenue a firm earns by employing one
additional unit of labor, holding all else constant.
Suppose Px is the price of output  MRPL = Px * MPL
9.4
9.5
Marginal Revenue Product Per Hour of Labor
in Sandwich Production (One Grill)
(1)
TOTAL LABOR
UNITS
(EMPLOYEES)
aThe
(2)
TOTAL
PRODUCT
(SANDWICHES
PER HOUR)
(3)
MARGINAL
PRODUCT OF
LABOR (MPL)
(SANDWICHES
PER HOUR)
(4)
PRICE (PX)
(VALUE
ADDED PER
SANDWICH)a
(5)
MARGINAL REVENUE
PRODUCT (MPL X PX)
(PER HOUR)
0
0
-
-
-
1
10
10
$ .50
$ 5.00
2
25
15
.50
7.50
3
35
10
.50
5.00
4
40
5
.50
2.50
5
42
2
.50
1.00
6
42
0
.50
0
“price” is essentially profit per sandwich; see discussion in text.
Marginal Revenue Product Per Hour of Labor
in Sandwich Production (One Grill)
9.6
MRPL = Px*MPL
• When output price is constant,
the behavior of MRPL depends
only on the behavior of MPL.
• Under diminishing returns,
both MPL and MRPL
eventually decline.
Determining the Profit-Max Level of Labor:
What is the Firms’ Demand for Labor?
9.7
• A competitive firm using only one
variable factor of production will
use that factor as long as its
marginal revenue product exceeds
its unit cost.
• If the firm uses only labor, then it
will hire labor as long as MRPL is
greater than the going wage, W*.
Suppose W = $2.50 
9.8
In General
Labor Market
Representative Firm
S
W
D
Labor
Profit-max rule: hire
L* where MRPL = W
MRPL
L*
labor
When a firm uses only one variable
factor of production, that factor’s
marginal revenue product curve is the
firm’s demand curve for that factor in the
short run.
Comparing Marginal Revenue and Marginal Cost
to Maximize Profits
We have 2 profit-maximizing rules:
The output rule: choose q* where MR = MC
The input rule: choose L* where MRPL = W
These two rules should be consistent: the L* from the
input rule should be capable of producing the q* units
from the output rule.
• Assuming that labor is the only variable input, if society
values a good more than it costs firms to hire the workers
to produce that good, the good will be produced.
• Firms weigh the value of outputs as reflected in output
price against the value of inputs as reflected in marginal
costs.
9.9
The Two Profit-Maximizing Conditions
• The two profit-maximizing conditions are simply two views of the
same choice process.
9.10
Many Labor Markets
If labor markets are competitive, the wages in those
markets are determined by the interaction of supply and
demand.
Firms will hire workers only as long as the value of their
product exceeds the relevant market wage. This is true in
all competitive labor markets.
• Examples:
9.11
Land Markets
9.12
• Unlike labor and capital, the
total supply of land is strictly
fixed (perfectly inelastic).
Demand Determined Price
9.13
• The price of a good that is in fixed
supply is demand determined.
• Because land is fixed in supply, its
price is determined exclusively by
what households and firms are willing
to pay for it.
The return to any factor of production in fixed supply is
called pure rent.
Land in a Given Use Versus Land of a Given
Quality
• The supply of land in a given
use may not be perfectly
inelastic or fixed.
9.14
• The supply of land of a given
quality at a given location is
truly fixed in supply.
Rent and the Value of Output
Produced on Land
• A firm will pay for and use land as long as the revenue
earned from selling the output produced on that land is
sufficient to cover the price of the land.
• The firm will use land (A) up to the point at which:
MRPA = PA
Where MRPA is defined as Px*MPA
9.15
The Firm’s Profit-Maximization Condition in
Input Markets
• Profit-maximizing conditions for the perfectly
competitive firm with 3 types of variable inputs: are
PL = MRPL = Px*MPL
PA = MRPA = Px*MPA
PK = MRPK = Px*MPK
where L is labor, K is capital, A is land (acres), X is
output, and PX is the price of that output.
9.16
The Firm’s Profit-Maximization Condition in
Input Markets
• Profit-maximizing condition for the perfectly competitive
firm, written another way is:
MPL MPk MPA 1



PL
Pk
PA
Px
• In words, the marginal product of the last dollar spent
on labor must be equal to the marginal product of the
last dollar spent on capital, which must be equal to the
marginal product of the last dollar spent on land, and so
forth.
9.17
9.18
Input Demand Curves
MRPL=PX*MPL
If product demand increases (Px ), product price will rise and
marginal revenue product will increase
 The Firm’s demand for inputs increases.
Input Demand Curves
9.19
MRPL=PX*MPL
If the productivity of labor increases (due to more, better
machinery/computers), marginal product increases causing marginal revenue
product will increase
 The firm’s demand for labor will increase.
Impact of Technological Change
• Technological change refers to the introduction of new
methods of production or new products intended to
increase the productivity of existing inputs or to raise
marginal products.
• Technological change can, and does, have a powerful
influence on factor demands.
• When we aggregate up all the firms’ higher demand
curves for labor, we see the entire demand curve for labor
shift right, pushing up wages.
9.20