Suppose that you are a monopolist selling widgets. You face costs of C(Q) = 10 +

Question

Suppose that you are a monopolist selling widgets. You face costs of C(Q) = 10 + 2Q. Suppose that there are two types of consumers that buy your widgets.

Group 1 has demand: Q1(p) = 20 - p1

Group 2 has demand: Q2(p) = 40 - p2

(a) What is the overall market demand that you face?

(b) If you cannot price discriminate, what price will you charge? How many widgets will you sell?

(c) Graph you answer to (b). Include MC, MR, and demand curves. Shade and label consumer surplus, producer surplus, and deadweight loss (if it exists).

(d) If you cannot price discriminate, what will be your total profits?

(e) If you can price discriminate, what prices will you charge? How many widgets will you sell?

(f) If you can price discriminate, what will be your total profits?

(g) Graph you answer to (e) using two separate graphs (one for each group of consumer). Include MC, MR, and demand curves. Shade and label consumer surplus, producer surplus, and deadweight loss (if it exists).

Explanation / Answer

C(Q) = 10 + 2Q , So Marginal Cost=10

a>Overall Market Demand=Q1(p) +Q2(p)= 20 - p1+40 - p2=60-p1-p2

b> 20-p1=10 or p1=20-10=10 , 40-p2=10 or p2=40-10=30

Q1=20-p1=20-10=10 , Q2=40-p2=40-30=10

d>If no price discrimination , the price will be 30 ( that is the higher of the two prices)

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