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: