Cost Minimization for special production functions.
Part a and b are for perfect substitutes.
Suppose a widget manufacturer has an infinitely substitute production function, q=3L+2K, given that MPL= 3, MPK= 2. If both the wage rate and rental rate are $10.
a. What is the cost-minimizing combination of L and K to produce 60 units of output. How much is the minimum cost?
b. What is the cost-minimizing combination of L and K to produce 90 units of output? How much is the minimum cost?
Part c and d are for perfect complements
Suppose an automobile manufacturer has a fixed proportions production function that requires it always uses 2 workers and 1 machine to produce 1 car belt. If the wage rate w= $10 and rental rate are r= $15.
c. What is the cost-minimizing combination of L and K to produce 50 units of output. How much is the minimum cost?
d. What is the cost-minimizing combination of L and K to produce 100 units of output. How much is the minimum cost?