Question 1 Given the production function for good X is Q = 2K 1/4 L 1/2 In the s

ID: 1112649 • Letter: Q

Question

Question 1 Given the production function for good X is Q = 2K1/4L1/2

In the short run, the amount of capital is fixed at K=16. The capital rental rate is r = $2.5, and wage rate is w = $10.

1) Derive the short-run total cost function.

2) Derive the short-run average cost (AC), average fixed cost (AFC), and average variable cost (AVC). Show them on the same graph.

3) Derive short-run marginal cost curve. Show on the same graph as 2).

4) Derive the short-run supply function of good x.

5) Suppose now the firm is selling good X at a fixed price $15, will the firm making any profit at this price? If so, how much profit does it make?

6) What will be the price level if the firm does not earn any profit?

Question 2 True or False. Explain.

1) Whenever the price of a good equals its marginal cost, the firm will have a positive profit.

2) For an upward sloping linear supply curve, the price elasticity of supply will be different at varies points.

Question 3 (Optional) Consider a total cost function of TC = 0.5Q2 +10Q + 20, and the market demand equation is Q=70-P.

a. What is the profit-maximizing output and price for the perfect competition? Calculate its profit.

b. What is the profit-maximizing output and price for the monopolist? Calculate its profit.

3. a) Under perfect competition, profit is maximized where: P = MC

P = 70 - Q

MC = Q + 10

So, 70 - Q = Q + 10

70 - 10 = 2Q

60 = 2Q

Q = 30 units

P = 70 - 30 = $ 40

Profit = TR - TC = P.Q - 0.5Q2 - 10Q - 20 = 40 x 30 - 450 - 300 - 20 = 1200 - 770 = 430

b) Under monopoly, profit is maximised where MR = MC

TR = P.Q = (70 - Q)Q = 70Q -Q2

MR =70 - 2Q

MC =Q + 10

At equilibrium, 70 - 2Q = Q + 10

60 = 3Q

Q = 20 units

P = 70 - 20 = $ 50

Profit = 50 x 20 - 0.5(20)2 - 10(20) - 20 = 1000 - 200 - 200 - 20 = 1000 - 420 = $ 580

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