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Input Demand:
The Labor and Land Markets
10
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.
The productivity of an input
is the amount of output produced per unit of
that input.
Inputs can be complementary or
substitutable.
This means that a firm’s input demands are
tightly linked together.
Inputs: Complementary and Substitutable
Diminishing Returns
Faced with a capacity constraint in the
short-run, a firm that decides to increase
output will eventually encounter diminishing
returns.
Marginal product of labor (MPL )
is the additional output produced by one
additional unit of labor.
Diminishing Returns
Marginal Revenue Product per Hour of Labor in Sandwich Production (One Grill)
(1)Total Labor Units
(Employees)
(2)Total
Product (Sandwiches
per Hour)
(3)Marginal
Product Of Labor (MPL) (Sandwiches
per Hour)
(4)Price (PX)
(Value Added per
Sandwich)a
(5)MarginalRevenueProduct
(MPL X PX)(per Hour)
0 0 - - -
1 10
10 $0.50
$5.00
2 25
15 0.50
7.50
3 35
10 0.50
5.00
4 40
5 0.50
2.50
5 42
2 0.50
1.00
6 42
0 0.50
0
aThe “price” is essentially profit per sandwich.
Marginal Revenue Product
The marginal revenue product (MRP)
of a variable input is the additional revenue
a firm earns by employing one additional
unit of input, ceteris paribus.
MRPL equals the price of output, PX, times
the marginal product of labor, MPL.
Marginal Revenue Product Per Hour of Labor in Sandwich Production (One Grill)
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.
MRPL = PX MPL
A Firm Using One Variable
Factor of Production: Labor
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*.
Marginal Revenue Product and Factor Demand
for a Firm Using One Variable Input (Labor)
The hypothetical firm will demand 210 units of labor.
W* =MRPL = 10
Short-Run Demand Curve for a Factor of Production
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
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.
The Two Profit-Maximizing Conditions
The two profit-maximizing conditions are
simply two views of the same choice
process.
The Trade-Off Facing Firms
Firms weigh the cost of labor as reflected in wage rates against the value of labor’s marginal product. Assume that labor is the only variable factor of production. Then, if
society values a good more than it costs firms to hire the workers to
produce that good, the good will be produced.
A Firm Employing Two Variable Factors of
Production
Land, labor, and capital
are used together to produce outputs.
When an expanding firm adds to its stock of
capital, it raises the productivity of its labor,
and vice versa.
Each factor complements the other.
Substitution and Output Effects of a Change in Factor Price
Response of a Firm to an Increasing Wage Rate
Technology
Input Requirements
Per Unit Of Output
Unit Cost ifPL = $1PK = $1
(PL x L) + (PK x K)
Unit Cost ifPL = $2PK = $1
(PL x L) + (PK x K)K L
A (capital intensive)
10 5 $15 $20
B (labor intensive)
3 10 $13 $23
When PL = PK = $1, the labor-intensive method of producing output is less costly.
Substitution and Output Effects of a Change
in Factor Price
Two effects occur when the price of an input
changes:
Factor substitution effect: The
tendency of firms to substitute away from
a factor whose price has risen and toward
a factor whose price has fallen.
Output effect of a factor price
increase (decrease): When a firm
decreases (increases) its output in
response to a factor price increase
(decrease), this decreases (increases) its
demand for all factors.
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.
Land Markets
Unlike labor and capital,
the total supply of land
is strictly fixed
(perfectly inelastic).
Demand Determined Price
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
QualityThe supply of land in a given use may not be perfectly inelastic or
fixed.
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
The Firm’s Profit-Maximization Condition in
Input Markets
Profit-maximizing condition for the perfectly competitive firm is:
where L is labor, K is capital, A is land (acres),
X is output, and PX is the price of that output.
PL = MRPL = (MPL X PX)
PK = MRPK = (MPK X PX)
PA = MRPA = (MPA X PX)
The Firm’s Profit-Maximization Condition in
Input Markets
Profit-maximizing condition for the perfectly competitive firm, written another way is:
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.
Input Demand Curves
If product demand increases, product price will rise and marginal revenue product will
increase.
If the productivity of labor increases, both marginal product and marginal revenue
product will increase.
Input Demand Curves
Impact of Capital Accumulation on Factor
Demand
The production and use of capital enhances the productivity of labor, and normally
increases the demand for labor and drives up wages.
Shifts in Factor Demand Curves
The Demand for Outputs
If product demand increases, product price will rise and
marginal revenue product (factor demand) will increase—
the MRP curve will shift to the right.
If product demand declines, product price will fall and
marginal revenue product (factor demand) will decrease
—the MRP curve will shift to the left.
The Quantity of Complementary and
Substitutable Inputs
The production and use of capital enhances the productivity
of labor and normally increases the demand for labor and
drives up wages.
The Prices of Other Inputs
When a firm has a choice among alternative
technologies, the choice it makes depends to some
extent on relative input prices.
Technological Change
The introduction of new methods of production or new
products intended to increase the productivity of
existing inputs or to raise marginal products.
Shifts in Factor Demand Curves
Resource Allocation and the Mix of Output in Competitive Markets
marginal productivity theory of income
distribution
At equilibrium, all factors of production end up
receiving rewards determined by their
productivity as measured by marginal
revenue product.
PROBLEM # 1The table below shows the number of cakes that could be baked daily at a local bakery, depending on the number of
bakers.
a. Calculate the marginal product of labor. b. Do you observe the law of diminishing marginal returns? c. Suppose each cake sells for $10. Calculate the marginal revenue product of labor. d. If each baker is paid $80 per day, how many bakers will the bakery owner hire, given that the goal is to maximize profits? How many cakes will be baked and sold each day?
Solution:
The marginal product of labor (MPL) is calculated in the third column, using the following formula: MPL = Δ(Number of cakes)/ΔL
b. Yes, the marginal product of labor declines as more bakers are hired.
c. The marginal revenue product of labor (MRPL) is calculated in the fourth column, using the following formula: MRPL = MPL × P
d. If each baker is paid $80 per day, 2 bakers would be hired and 18 cakes would be baked and sold daily.
PROBLEM # 2
Fill in the gaps in the table below:
Solution:
Suppose a firm with some market power faces a downward-sloping demand curve for the product it
produces. Using the information on demand given in the table below,
complete the table.
PROBLEM # 3
Solution: