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-minimizationproblem when
capital is fi?xed at a quantity of 5 units (i.e., K = 5), and w = 1and 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:
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-minimizationproblem when
capital is fi?xed at a quantity of 5 units (i.e., K = 5), and w = 1and 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:
