Suppose production occurs according to a production function
F(K,L)=AK^((1)/(3))L^((2)/(3))
where A represents the total factor productivity of the economy and K,L are the inputs of
physical capital and labor used in production by a competitive, profit maximizing firm. Let
w and r represent the unit prices of capital and labor inputs, respectively.
(a) Write down the problem solved by a profit maximizing firm
(b) Solve for two equations which define the demand of capital and labor by the firm.
(c) Suppose A=1,w=6,r=3. What will be the capital-to-labor ratio, (K)/(L), demanded
by the firm?
2. Suppose production occurs according to a production function
F(K,L)=AKL3
where A represents the total factor productivity of the economy and K, L are the inputs of physical capital and labor used in production by a competitive, profit maximizing firm. Let w and r represent the unit prices of capital and labor inputs, respectively.
(a) Write down the problem solved by a profit maximizing firm
(b) Solve for two equations which define the demand of capital and labor by the firm.
(c) Suppose A = 1, w = 6, r = 3. What will be the capital-to-labor ratio, K, demanded by the firm?