Eco205 Chapter 13 - Pricing in Input Markets 6 April 2013
Marginal Productivity Theory Of Input Demand
Profit-Maximizing Behavior and the Hiring of Inputs
A profit-maximizing firm will hire additional units of any input up to the point at which the additional revenue from
hiring one more unit of the input is exactly equal to the cost of hiring that unit.
ME L MR L
ME K MR K
If the firm is a price take in the input markets:
w =ME =LMR L
v = ME K MR K
Marginal Revenue Product
The extra revenue earned from selling the output produced by hiring an extra input is the marginal revenue product.
w = ME = MR = MP x MR
L L L
v = ME =KMR = MK x MR K
If the firm sells its output in a perfectly competitive market:
w = MP xLP = MVP L
v = MP xKP = MVP K Responses to Changes in Input Prices
MVP is the marginal value product - The extra revenue obtained from selling the output produced by hiring an extra
worker or machine MVP
Responses to Changes in Input Prices
Single Variable Input Case
Suppose the price of an input fell. What would happen?
Fixed capital and variable labor 2
As more labor is hired, MVP wiLl fall due to diminishing marginal MVP L
physical product. L1 L2
As the wage rate falls, the firm is able to hire more workers even if they add less to total output than previous workers
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At a wage rate w ,1profit maximization requires that L lab1r input be hired. If the wage rate falls to w , mor2 labor (L ) 2
will be hired because of the assumed negative slope of the MVP curve.L
Two-Variable Input Case
If w falls, there will be a change not only in labor input but also in capital input as a new cost-minimizing combination of
inputs is chosen. When capital input changes, the entire MP functLon shifts (workers now have a different amount of
capital to work with), and our earlier analysis of how wages affect hiring cannot be made.
In the theory of production, the substitution of one input for another while holding output constant in response to a change in the input’s price.
To study the substitution effect, we hold q constant at 1 . With a fall in w, there will be a tendency to substitute labor
for capital in the production of q . Because the condition for minimizing the cost of producing q requires that RTS =
w/v, a fall in w will necessitate a movement from input combination A to combination B. It is clear from the diagram that
this substitution effect must cause labor input to rise in response to the fall in w because of the convex shape of t1e q
isoquant. The firm now decides to produce q 1n a more labor-intensive way.
The effect of an input price change on the amount of the input that the firm hires that results from a change in the firm’s
The change in w will affect the firm’s costs, and this will prompt the firm to alter its output. The reason the output effect
breaks down for this is that consumers have budget constraints, but firms do not. Firms produce as much as profit
Responses to Changes in Input Prices
maximization requires; their need for inputs is derived from these production decisions. A fall in w, because it changes
relative factor costs, will shift the firm’s expansiCapital Price MC
path. Consequently, all the firm’s cost curves will Input choice
be shifted, and probably some output level other decision
than q1will be chosen 1
The combined result of both the substitution and q
the output effects is to move the input choice to q
point C on the firm’s isoquant for output level2q .
L1 L2 q1 q2 Output
Both effects work to increase L in response to a Labor
decrease in w.
When the price of labor falls, the substitution ef© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.
This is shown as a movement from point A to point B in panel a. The change in w will also shift the firm’s marginal cost
curve. A normal situation might be for the MC curve to shift downward in response to a decrease in w. With this new
curve (MC ) a higher level of output (2 ) will be chosen. The hiring of labor will increase 2to L ) from this output effect.
We conclude therefore that a profit-maximizing firm will increase its hiring of labor for two reasons. First, the firm will
substitute the now-cheaper labor for other inputs that are now relatively more expensive. This is the substitution effect.
Second, the wage decline will reduce the firm’s marginal costs, thereby causing it to increase output and to increase the
hiring of all inputs including labor. This is the output effect.
Responsiveness Of Input Demand To Input Price Changes
Suppose the wage rate rose - less labor will be demanded but by how much?
Ease of Substitution