Question

1. Calculate the returns to scale for the following production functions.

a. Q = AL + BK (A and B are constants)

b. Q = AL^(1/2)K^(1/2)

c. Q= AL^(1/2)K^(3/2)

d. Q= AL^(1/2)K^(1/4)

e. Q= ALK

2. Calculate the elasticity of substitution (ε) between L and K for the following production functions. [ Formula: ε = dlog(K/l)/dlog(MRTS _L,K) ]

a. Q = AL^(1/2)K^(1/2)

B. Q= [AL^(η) + (1-A)K^(η)] ^(1/η)

c. Q= AL^(1/2)K^(3/2)

d. Q= AL^(1/2)K^(1/4)

3. The Production function of a firm is given by Q = AL^(1/2)K^(1/2). The Wage rate is $2 per hour and the rental rate is $3 per hour. The firm cannot exceed it's cost above $600. Find out the optimal amounts of L and K the firm should hire. What is maximum amount of output the firm ends up producing.

4. The Production function of a firm is given by Q = LK. The Wage rate is $2 per hour and the rental rate is $3 per hour. The firm has to produce at least 15,000 units of output.

a. Find out the optimal amounts of L and K the firm should hire.

b. What is the minimum cost the firm ends up incurring?