4. Consider a monopolist with the following long run costs: TC=Q -SQ + 100 The i

Question

4. Consider a monopolist with the following long run costs: TC=Q -SQ + 100 The inverse demand curve is given by Use the twice as steep rule to find the equation of the marginal revenue curve corresponding to the market demand curve.(5 points) a. Find the profit maximizing quantity of output for the monopoly and the price the monopolist will set. (5 points) b. c. Calculate the monopolist's profits. (5 points) What level of output would be produced by this industry under perfect competition? What would the perfectly competitive price be? (5 points) d.

Explanation / Answer

a) Inverse demand function is P = 55 - 4Q. Now MR has twice the slope of demand function with same intercept so MR will be 55 - 2*4Q or MR = 55 - 8Q

b) Profit is maximized when MR = MC. We have 55 - 8Q = 2Q - 5

60 = 10Q and so Q = 60/10 = 6 units. The relevant price is P = 55 - 4*6 = $31 per unit

c) Profits = Revenue - cost = PQ - TC

= 6*31 - (6^2 - 5*6 + 100)

= $80

d) A perfectly competitive firm uses a production rule P = MC

55 - 4Q = 2Q - 5

60 = 6Q

Q = 10 units

Perfectly competitive price is P = 55 - 4*10 = $15 per unit.

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