A firm produces output according to the production function: Q = F (K, L) = 4K + 8L. a. How much output is produced when K = 2 and L = 3? unit (s) b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? Capital: Labor: c. If the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? Capital: Labor:

Production function: F (K, L) = 4K + 8L

Part a)

When K = 2 and L = 3, then Q = 4K + 8L

Q = 4 (2) + 8 (3)

Q = 32 units

Part b)

Since these are substitute goods, the firm can either use 23/4 = 8K or 32/8 = 4L

Cost of 8K = 8 (20) = $160 Cost of 4L = 4 (60) = $240

Since cost of using 8K is lower, the firm will use (SK, OL) to produce 32 units output.

Part c)

The firm can either use 23/4 = 8K or 32/8 = 4L

Cost of 8K = 8 (20) = $160 Cost of 4L = 4 (20) = $80

Since cost of using 4L is lower, the firm will use (01C, 4L) to produce 32 units output.