Download I. Basic Concepts of Input Markets

University of Pacific-Economics 53
Lecture Notes #10
I.
Basic Concepts of Input Markets
In this lecture we’ll look at the behavior of perfectly competitive firms in the input market.
Recall that firms demand inputs (land, labor and capital) and we will look at how firms decide
how much of each input they want. To start we will introduce several basic concepts that will be
useful in our analysis.
1.
2.
3.
4.
5.
Demand for inputs is a derived demand. What this means is that the demand for
inputs depends on the demand for the output sold. If nobody wants to purchase the firm’s
product, there will be no need for the firm to demand any labor or capital. On the other
hand, if the firm has a product that is in great demand, they will demand more inputs in
order to meet the high demand.
Productivity of inputs may differ. We define productivity as the amount of output
produced per unit of input. If Sam is able to produce 10 widgets while Dan can only
produce 5 widgets we say that Sam has a higher productivity than Dan. Some inputs may
have high productivity while others may have low productivity.
Inputs can be either complementary or substitutes.
a. Complements-Two inputs are complements if both are needed to produce an
output. For example in order to bus school children you need both a school bus
(capital) and a driver (labor). If you only have the school bus you won’t produce
any service.
b. Substitutes-Two inputs are substitutes if one input can be used to replace another.
There are cases, which we will soon see, in which capital can be used to replace
labor or where labor may be used to replace capital.
Inputs exhibit diminishing returns. In earlier chapters we have seen the law of
diminishing returns. Increasing the amount of an input in the production process, while
holding another input fixed, will increase output but at a decreasing rate. For example,
suppose a firm has a fixed level of capital and it starts increasing its workforce. The
marginal product of labor (MPL) is the extra output generated by each new worker hired.
The law of diminishing returns says that the MPL decreases as labor increases.
Firms make input demand decisions based on the marginal revenue product (MRP).
The marginal revenue product (MRP) is the extra revenue generated by a firm by
employing one additional unit of input, holding all else constant. For example, consider
labor. The marginal revenue product of labor is the extra revenue generated by a firm
when they hire one more worker. That extra worker will produce some output, the
marginal product of labor (MPL). If you multiply the MPL times the price of the output
you’ll get the marginal revenue product of labor.
MRPL = MPL x P
Where
MRPL = marginal revenue product of labor
MPL = marginal product of labor
P = price of the output
Let’s work through an example:
Example: Fred's Pizza Palace sells pizzas in a competitive market. The price of the pizzas is
$1.25 each. Complete the table
0
Total Product
(pizzas/hour)
0
1
20
2
35
3
47
4
55
5
59
# Workers
Marginal Product
of Labor
----
Marginal Revenue
Product
----
What is the marginal product of labor if the firm decides to hire the 1st worker? The total
output for the firm jumps from 0 to 20. Thus the MPL for the 1st worker is 20. When the
firm hires the 2nd worker, total output goes from 20 to 35. The extra output generated by
the 2nd worker is 15 which is the MPL and so on.
What is the MRP for the 1st worker? We know that the first worker will contribute 20
units of output for the firm. Since the price of each pizza is $1.25 (very cheap pizzas!)
the marginal revenue product will be MRP = 20 x $1.25= $25. The completed table is
shown below.
0
Total Product
(pizzas/hour)
0
Marginal Product
of Labor
----
Marginal Revenue
Product
----
1
20
20
$25.00
2
35
15
$18.75
3
47
12
$15.00
4
55
8
$10.00
5
59
4
$5.00
# Workers
Figure 1 shows the marginal revenue product curve for the above example.
Figure 1
MRP
30
25
Ouput
20
15
10
MRP
5
0
0
1
2
3
4
5
6
Number of Workers
Now that you understand MRP we’ll now see how firms are able to determine how many
workers they wish to hire.
First, we’ll assume that perfectly competitive firms are price takers in the input markets.
Wages are determined in the labor market. Individual firms can hire as many workers as
they want at the market real wage. Figure 2 shows the labor market and how wages are
determined.
Figure 2: The Labor Market
We see in Figure 2 that the wages
are determined by the supply of
labor and the demand for labor.
Where the curves intersect is the
market wage rate. In this example
the market wage rate is $10 an
hour. At that wage rate, 560,000
workers will be employed.
G
Given that the market wage rate is $10 an hour, how many workers will Fred’s Pizza
Place want to hire?
We can derive Fred’s demand for workers using the following marginal revenue product
analysis.
Should Fred hire the first worker? The first worker will generate revenues of $25, but
Fred only has to pay him $10. Thus Fred should definitely hire the 1st worker.
How about the 2nd worker? The second worker will generate revenues of $18.75 to the
pizza place. Again the revenue brought in by the worker is greater than the cost of hiring
that worker. Thus Fred should definitely hire the 2nd worker. The same will hold true for
the third and fourth worker. The 4th worker generates revenue of $10 which is offset by
the cost of hiring that worker. We’ll assume that when revenues equals the cost the firm
will still hire that worker.
Should Fred hire the 5th worker? The fifth worker will generate revenues of $5 to the
firm which is less than the cost of hiring the worker. The pizza parlor will lose money by
hiring that worker. Thus Fred will not hire that worker and will stop at the 4th worker.
We can see that Fred will stop hiring when the market wage is equal to the MRP. This is
true in general
**Firms will hire workers until MRP = market wage rate***
Looking back at Figure 1 we can see that the MRP tells us how much labor a firm will
hire at each potential market wage rate. We see that if the wage is $25 the firm will hire
1 worker, when the wage rate is $15 it will hire 3 workers, etc… Notice that as the wage
rate falls the demand for workers will be higher. When the wage rate rises the quantity of
labor will fall. This fact leads to a downward sloping demand curve for labor.
The above analysis applies for any factor of production, and not just labor.
II.
Choosing Two Variable Inputs
So far we’ve looked at a situation where a firm had to decide how much labor to hire holding
everything else constant. In that case the decision for the firm was a simple choice of choosing
the amount of one input. What if we were to add another input to the firms’ decision matrix.
How would firms decide how much input to demand?
Suppose that a firm had to choose the level of capital and labor.
Suppose also that the price of capital is PK while the price of labor is PL
Suppose that the firm has to choose between two technologies to produce its output.
Technology
A
B
Units of Capital
(K)
300
1000
Units of Labor
(L)
1000
500
Variable Costs if
PL =$1; PK =1
$1300
$1500
Variable Costs if
PL =$2; PK =1
Technology A is more labor intensive than Technology B. What if the price of inputs were $1
per unit for both capital and labor.
The total variable costs using technology A will be (300 x $1) + (1000 x $1) = $1300 while
The total variable costs using technology B will be (1000 x $1) + (500 x $1) = $1500
Recall that firms want to minimize costs, so the firm will choose the technology that results in
the least-cost which is Technology A. However, what will happen if the price of labor doubles
so PL=$2.
The total variable costs using technology A will be (300 x $1) + (1000 x $2) = $2300 while
The total variable costs using technology B will be (1000 x $1) + (500 x $2) = $2000.
The firm now will choose Technology B. As labor costs increase, the firm will move away from
the expensive input and substitute labor with capital. Relative input prices are a important
determinant of input demand. This fact that we just observed is called the factor substitution
effect. The factor substitution effect states that when the price of an input rises, firms have a
tendency to substitute away from that factor. Conversely, when the price of an input has fallen,
firms will substitute toward that factor. The factor substation effect helps explains why the
demand curve for inputs is downward sloping. As the price of labor decreases, firms will
substitute away from other factors of production (such as labor) and increase demand for labor.
There is another factor behind the downward sloping demand curve. Notice in our example that
the least-cost technology before the price of labor increase was Technology A at $1300. After
the price increase in labor the least-cost technology was Technology B at $2000. To produce the
same amount of output, the cost for the firm has increased and the firm may be losing money.
We would expect that most firms will respond by producing less. But recall that demand for
inputs is a derived demand. If the firm will be producing less, they’ll need less inputs such as
capital and labor and thus the demand for both capital and labor will decline due to the increase
in the price of labor. This is called the output effect of a factor price increase. A decrease in
the price of a factor production will have the opposite effect. The output effect is another
explanation behind the downward sloping demand curve.
III.
Land Markets
Much of our analysis of the labor markets can be easily extended to the land markets. The only
real difference between land and labor markets is the supply curves. In the land market, we
assume that the amount of land is fixed. At any given location, the supply of land is fixed. Thus
the supply curve is vertical. See Figure 3
The price of land is demand determined. That is the price of land is determined solely by shifts
in the demand curve. Suppose we start at Point A and the price of land is P0. If demand for land
is higher, this will drive up the price of land to Point B. If the demand for land is lower, this will
drive down the price of land to Point C. The lesson here is that land will be sold to the user who
is willing to pay the most for it.
Figure 3
The demand for land is derived exactly the same as it was for labor. The firm will continue to
demand land as long as the marginal revenue product of land is greater than the price of a unit of
land. If an extra acre of farmland would generate $50 for the farmer and the price of an acre of
land is $40, the farmer should purchase that acre of land. If, on the other hand, the extra acre of
farmland would generate only $30, the farmer would not purchase the acre of land.
PA = MRPA
Where PA = Price of land in acres
MRPA = Marginal revenue product of land in acres.
IV. Profit-Maximization Rule in Input Markets
Although we will talk about the capital market in the next lecture, you can probably guess that
the firm will demand capital based on the following rule:
PK = MRPK
Where PK = Price of capital
MRPK = Marginal revenue product of capital.
We can look at our three input demand rules for land, labor and capital and derive a general
profit maximization rule.
(1) PL = MRPL → PL = MPL x P
(2) PA = MRPA → PA = MPA x P
(3) PK = MRPK → PK = MPK x P
Where P = price of output
Doing some rearranging we get
(1) P = PL/MPL
(2) P = PA/MPA
(3) P = PK/MPL
Which lead to the following relationship: P = PL/MPL = PA/MPA = PK/MPK
The final step is to take the reciprocal of each term to get
1/P = MPL/PL = MPA/PA = MPK/PK
This is the profit maximizing rule for input demand. Firms will continue to demand inputs until
they reach this equilibrium. Why must this condition hold? Think about what would happen if it
did not hold.
Suppose that MPL/PL > MPK/PK
This inequality implies that if the firm spent an extra $1 on labor as opposed to capital the firm
would get more output from labor. Thus the firm will demand more labor and less capital. As
demand for labor increases, the marginal product of labor decreases (law of diminishing returns).
As the demand for capital decreases, the marginal product of capital increases. This will continue
until the ratios are equal.
V.
Shifts in Input Demand Curves
There are several factors that would cause the demand curves for land, labor and capital to shift.
These include
(1) Demand for Outputs. If the demand for output increases, the firm will demand more
units of inputs to meet the higher output demand. At any given input price, the firm will
demand more of the input. Thus the demand curve would shift to the right.
(2) Quantity of Complementary and Substitutable Inputs. Suppose that a school district
has 5 new school buses to transport children. Those buses will be useless unless they hire
5 new drivers. Thus for complementary inputs, if there is an increase in the number of
one of the inputs, this will increase the demand for its complement. As another example
suppose that a textile firm can either use labor to cut cloth or a cutting machine. If the
firm were to get a whole shipment of cutting machines, that will reduce its demand for
labor. Thus for substitutable inputs, if there is an increase in the quantity of one of the
inputs, this will decrease the demand for its substitute.
(3) The Price of Other Inputs. An increase in the price of one input, may lead firms to
substitute away from that input and towards another. The demand for that other input
will increase as this occurs.
(4) Technological Change. Technological change means that new methods of production
are now available that allows firms to be able to produce more output using the same
amount of input as before. The marginal product of input will be greater. Each unit of
input will be able to generate more revenue for the firm than before which should
increase the demand for inputs.