Question

Suppose an agricultural firm has the production function:
f(l; k; a) = l^(1/4) * k^(1/4) * a^(1/4)
where the price of labor is w, the price of capital is r and acreage (a) has price s.

(a) Verify that this is a valid production function.

(b) Solve the rm's cost minimization problem for the conditional input demands,
cost function, average cost function, and marginal cost function.

(c) Suppose that there was a tax on one or more inputs. For each of the following
cases explain how the tax would a ect the eciency of taxation. Hint: think
about both the cost minimization problem, which you have solved, and the pro t
maximization problem, which you have not.
i. Only on labor
ii. On both labor and acreage
iii. On all three inputs

Answer 1

A. The production function is valid beacause the production function states the relation between inputs and outputs and the value of these inputs and outputs can be varying.

B.