Cost Mani and ProfiT max
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 = 800+100Q0.2 +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
4 K
1
4 , price of labor (w) = 3 and price of capital (r) = 12. The
market price for the output produced is P = 128. 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 = 81. Write down and solve this firms SHORT-RUN cost minimization problem.
[Note: Capital is fixed here, so the firm chooses only labor to minimize cost.] Find out the short-run cost of
the firm for producing 18 units of output.
Part b
ii. Write down the functional forms of the short-run average total cost, average variable cost and marginal cost.
Draw them in a diagram.
iii. 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 firms 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.] Solving the long-run cost minimization
problem, we get the long-run cost function C (Q) = 3Q2. Find out the long-run cost of the firm for producing
18 units of output.
iii. Write down the functional forms of the long-run average cost and marginal cost.
iv. Find out the profit maximizing choice of output 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?
