Answer to Question #143480 in Microeconomics for Ananya

Question

A firm is in the business of assembling computers and it has the following production function q=l^1/3k^1/2, where l and k are measures of labor and capital input used to produce q number of pcs that are sold in the market at a fixed price= p per pc. Cost of one unit of l and k are w and v respectively.
a) Does this production function exhibits increasing, decreasing or constant returns to scale.
b) Find the firm's conditional demand for labor in the short run when capital is fixed at k(bar)=81.
c) Find the firm's conditional demand function for labor and capital in the long run.
d) Find also the profit maximising level of output.{in unconditional profit function}

Answer 1

a) This production function exhibits decreasing returns to scale.

b) The firm's conditional demand for labor in the short run when capital is fixed at k(bar)=81 is:

$q = l^{1/3} × 81^{1/2} = 9l^{1/3},$

$q'(l) = 3/l^{2/3} = 0.$

c) The firm's conditional demand function for labor and capital in the long run will be the same.

d) The profit maximising level of output is when the marginal product of labor divided by wage is equal to the marginal product of capital divided by rent.