Cost Minimization and Profit Maximization

Week 4 - Cost Minimization and Profit Maximization

Part a

1. What is economic cost? How is it different from accounting cost?

2. What is sunk cost? What is the difference between the fixed cost and a sunk cost?

3. What do we mean by a cost function?

4. Suppose a short-run total cost function is given by C = 100+50Q0.2 +Q2.

(a) Find out the fixed cost, variable cost, marginal cost, average variable cost and average total cost.

(b) Plot them in a diagram and interpret the relationship between average and marginal cost.

5. Prove that, in the short-run, APL and AVC are inversely related. Similarly, MPL and MC are inversely related.

6. Suppose the production function is given by Q = 2L 1 2 K

1 3 , price of labor (w) = 2 and price of capital (r) = 3. The

market price for the output produced is P = 6. Answer parts a(i)−a(iv) and b(i) to b(v) based on this information.

(a) Short-run production:

i. Suppose capital is fixed at K = 27. Write down this firm’s SHORT-RUN cost minimization problem. [Note: Capital is fixed here, so the firm chooses only labor to minimize cost.]

ii. Solve the short-run cost minimization problem to get the short-run cost function C (Q) |K=27 . Find out the short-run cost of the firm for producing 60 units of output.

Part b

iii. Write down the functional forms of the short-run average total cost, average variable cost and marginal cost. Draw them in a diagram.

iv. Find out the profit maximizing choice of output and labor in the short-run. How much is the profit?

(b) Long-run production:

i. What is an iso-cost? ii. Write down this firm’s LONG-RUN cost minimization problem. [Note: In long-run, nothing is fixed, so the firm can choose both labor and capital optimally to minimize its cost.]

iii. Solving the long-run cost minimization problem, we get the long-run cost function C (Q) = 15 2 · ( Q 3

)6 5

. Find

out the long-run cost of the firm for producing 60 units of output. iv. Write down the functional forms of the long-run average cost and marginal cost. v. Find out the profit maximizing choice of output and labor in the long-run. How much is the profit?

7. What is the relationship between the slope of the long-run average cost and returns to scale?