Problem 1. Perfect Substitutes Production
The firm's technology is such that one unit of output can be produced either using 2 units of capital or 3 units of labour. Denote with L the amount of labor, K - the amount of capital. The wage rate is 2, the rental rate on capital is 3.
a) Write down the firm's production function. Is it CRS, DRS or IRS?
b) What is the optimal way to produce 1 unit of output?
c) What is this firm's cost function C(y)?
Problem 2. Perfect Complements Production
The firm must use 2 unit of capital with 3 units of labour to produce each unit of output. Denote with L the amount of labor, K - the amount of capital. The wage rate is 2, the rental rate on capital is 3.
a) Write down the firm's production function. Is it CRS, DRS or IRS?
b) What is the optimal way to produce 1 unit of output?
c) What is this firm's cost function C(y)?
Problem 3. Cobb-Douglas Production with Constant Returns to Scale.
The firm has a technology of f(l,k) = L1/4k1/4 , where L is the amount of labor, K is the amount of capital. The wage rate is 2, the rental rate on capital is 3.
a) Is this technology CRS, DRS or IRS.
b) Write down the equation that describes the firms optimal choice of capital and labor. Show that a combination of inputs such that K=2L is optimal.
c) What is the optimal way to produce 1 unit of output? How about 10 units?
d) What is this firm's cost function C(y)?
Problem 4. Production
Acme hunting supplies makes roadrunner traps for coyotes using labor and capital according to the following production function
Traps = L1/2 + k1/3.
a. What are the marginal products? What is the marginal rate of technical substitution?
b. Draw a few isoquants.
c. If Acme has orders for 100 traps what is the least costly combination of labor and capital to use if labor costs $10 per hour and capital can be rented for $20 per hour?
d. Is this technology of decreasing, increasing or constant returns to scale?