Question

# Suppose an agricultural firm has the production function: f(l; k; a) = l^(1/4) * k^(1/4) *...

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

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.

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