The Cobb-Douglas production function is P(x, y) = k x^α y^(1−α) , where k ad α are constants representative of a particular firm or economy. (1) Show that doubling of both labor and capital results in doubling production P. (2) Suppose a particular firm has the production function for k = 120 and α =3/4 . Assume each unit of labor costs $250 and each unit of capital costs $400, and that the total expense for all costs cannot exceed $100,000. Find the maximum production level for the firm. (3) Compute the production level at x = 64 and y = 81. If the capital is decreased by 3 units, by how many units the labor should be adjusted to so that there is not change in production level.
During the 1920s, Charles Cobb and Paul Dougkas modeled total
production output P (of a firm, company or entire economy) as a function of labour
hours involved x and capital invested y (each includes the monetary worth of all
buildings and equipment). The Cobb-Douglas production function is
P(x, y) = k x^α y^(1−α)
,
where k ad α are constants representative of a particular firm or economy.
(1) Show that doubling of both labor and capital results in doubling production
P.
(2) Suppose a particular firm has the production function for k = 120 and
α =3/4
. Assume each unit of labor costs $250 and each unit of capital costs
$400, and that the total expense for all costs cannot exceed $100,000. Find
the maximum production level for the firm.
(3) Compute the production level at x = 64 and y = 81. If the capital is
decreased by 3 units, by how many units the labor should be adjusted to
so that there is not change in production level.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
