A fi?rm produces a product with labor and capital. Its production function is de

Question

A fi?rm produces a product with labor and capital. Its production function
is described by Q = 2L + 3K: Let w and r be the prices of labor and capital,
respectively.

(a) Find the equation for the ?firm's long-run total cost curves as a function
of quantity Q, for input prices, w = 1 and r = 1.

(b) Find the equation for the firm's long-run total cost curves as a function of
quantity Q and input prices, w and r (and so as a function of three parameters).

c) Find the solution to the ?firm's short-run cost-minimization problem when
capital is fi?xed at a quantity of 5 units (i.e., K = 5), and w = 1 and r = 1.
Derive the equation for the ?firm's short-run total cost curve as a function of
quantity Q. Graph this curve together with the long-run total cost curve for
the same input prices.

(d) Redo parts a) and c) for w = 1 and r = 2:

Explanation / Answer

a) w is the price of labor, r is the price of capital in the long run you can switch both labor and capital so the function is the function that produuces this at the lowest cost, as in all capital in this linear case b)again same idea, the function uses all capital or all labor based on which will minimize total cost, i.e. is 2w>

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