Question

Problem 1: A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product: Market demand function: Q = 200 - 2P (direct form, which shows Q as a function of P) Market demand function in the indirect form: P = 100 – 0.5Q (indirect form because it shows P as a function of Q). Marginal revenue function: MR = 100 – Q (Notice that the slope of the MR function is twice the slope of the inverse demand function). Total Cost function: TC = 5Q Average Cost function: AC = (TC/Q) = 5 Marginal Cost function: MC = 5 [Note that whenever marginal cost is a constant number, MC will always be equal to AC.]

(a) Plot the demand and marginal revenue functions given. Plot the marginal cost and average cost information given.

(b) Find the output level that will be produced by a profit maximizing monopolist in a market equilibrium. Label it QM.

(c) Once you have found the monopolist’s profit maximizing quantity, find the price the monopolist will charge in the market. Label it PM.

(d) Find the numerical value of the total revenue earned by the monopolist at QM. Label the area on your graph.

(e) Find the numerical value of the total cost earned by the monopolist at QM. Label the area on your graph.

(f) Find the numerical value of the profit earned by the monopolist at QM. Label the area on your graph.

(g) Can you identify the area of the market consumer surplus at QM? Label the area of your graph. (Note you have to read the textbook chapter15 before doing this part. If you do not remember what is consumer surplus, take a quick look at chapter 7.?

(h) Label the producer surplus earned by the monopolist at QM.

(i) You are given the inverse demand function and the marginal cost value. Can you find the total industry output that would have been produced if this industry had been a perfectly competitive industry (instead of being a monopoly)? Label the perfectly competitive level of industry output on your graph as QC.

(j) Label the total market consumer surplus in the case of a perfectly competitive industry. Can you identify the area that shows the difference in consumer surplus amount between the monopoly industry and the perfectly competitive industry?

(k) Label the total market producer surplus in the case of a perfectly competitive industry. Can you identify the area that shows the difference in producer surplus amount between the monopoly industry and the perfectly competitive industry?

Answer 1

Market demand function: Q = 200 - 2P ----- (i)

Market demand function in the indirect form: P = 100 – 0.5Q ----- (ii)

Marginal revenue function: MR = 100 – Q ------ (iii)

Cost function: TC = 5Q ----- (iv)

Average Cost function: AC = (TC/Q) = 5 ----- (v)

Marginal Cost function: MC = 5 ------- (vi)

(a) The graph is given in the image below

(b) At profit maximization for a monopolist, MR = MC

Thus, we have 100 - Q = 5

or, QM = 95

(c) Substituting QM = 95 in (ii) gives,

PM = 100 - 0.5(95)

or, PM = 52.5

QM and PM are shown in the graph below:

(d) Total Revenue or TR = PM*QM

or, TR = 52.5*95

or, TR = 4987.5

(e) TC = 5Q (from (iv))

or, TC = 5*95

or, TC = 475

TR and TC are shown in the graph below:

(f) Profit = TR - TC

or, Profit = 4987.5 - 475

or, Profit = 4512.5

(g) and (h)

Profit, consumer surplus and producer surplus are shown below:

(i) In perfect competition, at equilibrium, P = MC

or, 100 – 0.5Q = 5

or, 0.5Q = 95

or, QC = 190

Thus, PC=5

(j) and (k)

QC, consumer surplus and producer surplus in perfectly competitive market are shown below:

No producer surplus here.

Difference between consumer surplus amount and producer surplus amount between the monopoly industry and the perfectly competitive industry are shown below: