Suppose a technology is described by the production function 
a. For a price taking producer who faces output price p and wage w, derive the first order condition and interpret it.
b. Without knowing more about the function f, is the condition you derived in (a) either necessary or sufficient for deriving the profit maximizing production plan? Explain.
c. Suppose 
. Derive the first order condition you illustrated in (a) and solve for 
.
d. For what values of 
is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain.
What will be an ideal response?
which gives us the first order condition 
. Since the 
, this first order condition can be written as 
In words, this means that the marginal revenue product -- i.e. the increase in revenue from the last worker hired -- is equal to the wage.b. No. The condition is necessary and sufficient only if we know that the solution is an interior solution and that there are no local minima that have the same tangency between isoprofits and the production frontier.
c.
-- so the first order condition is 
This solves to
d. The answer above is correct for
In that case, the producer choice set is fully convex and a single interior solution exists. For 
, we have increasing marginal product of labor throughout -- implying that the profit maximizing solution would be to produce an infinite amount.You might also like to view...
In recent years, Japan's capital stock has increased by about 6 percent from one year to the next. As a result, we would expect
A) a leftward shift in Japan's aggregate demand curve. B) a movement up along Japan's short-run aggregate supply curve. C) only Japan's long-run aggregate supply curve to shift rightward. D) rightward shifts in both Japan's short-run aggregate supply and long-run aggregate supply curves.
The difference between the marginal expenditure and the wage is greater when the supply curve of labor is
A) less elastic at the monopsony optimum. B) more elastic at the monopsony optimum. C) more elastic than the demand curve. D) The difference does not depend on any elasticity.
Total planned consumption
a. exceeds total income at very low levels of output. b. is always less than total income. c. exceeds total income at very high levels of output. d. always equals total income.
A free-rider problem exists for any good that is not
a. rival in consumption. b. a private good. c. free. d. excludable.