Question

1. A monopoly is facing an inverse demand curve that is p=200-5q. There is no fixed cost and the marginal cost of production is given and it is equal to 50.

1. Find the total revenue function.
2. Find marginal revenue (MR).
3. Draw a graph showing inverse demand, MR, and marginal cost (MC).
4. Find the quantity (q) that maximizes the profit.
5. Find price (p) that maximizes the profit.
6. Find total cost (TC), total revenue (TR), and profit made by this firm.
7. Find DWL in this market.

2. Consider a competitive market with short run demand and supply of p=200-Q/1000000 and p=Q/1000000. There is a firm in this market with a MC=q for q>50.

1. Find the market equilibrium.
2. Find the firm’s output.
3. Is this market efficient?

3. Fill all the blank cells in the following table.

FC VCTC AFC AVC ATC MCP Profit 190 100 280 250 25 112.5 98 130 260 1390 1750

Answer 1

(1)

(a)

TR = p x q = 200q - 5q²

(b)

MR = dTR/dq = 200 - 10q

(c)

From demand function, when q = 0, p = 200 (vertical intercept) & when p = 0, q = 200/5 = 40 (horizontal intercept).

From MR function, when q = 0, MR = 200 (vertical intercept) & when MR = 0, q = 200/10 = 20 (horizontal intercept).

(d)

Profit is maximized when MR = MC.

200 - 10q = 50

10q = 150

q = 15

(e)

p = 200 - 5 x 15 = 200 - 75 = 125

(f)

TC = MC x q = 50 x 15 = 750

TC = p x q = 125 x 15 = 1875

Profit = TR - TC = 1875 - 750 = 1125

(g)

In efficient outcome, p = MC.

200 - 5q = 50

5q = 150

q = 30

p = MC = 50

Deadweight loss = (1/2) x Difference in p x Difference in q = (1/2) x (125 - 50) x (30 - 15) = (1/2) x 75 x 15 = 562.5

NOTE: As HOMEWORKLIB Answering Policy, 1st question has been answered.