Question

2、Suppose a monopoly is facing two different types of consumers with inverse demand functions ?=200−?1 and ?=150−2?2. Monopoly cannot observe who belongs to which group. Monopoly’s marginal cost is zero and there is no fixed cost.（20 points）

(1) Suppose the monopoly offers two options specifying quantity and total price. The first offer is targeted at consumer 1 with ?1=200 such that it makes consumer 1 indifferent between the two offers. The second offer is targeted at consumer 2 with ?2=75 and extracts all of consumer 2’s surplus. Find the total prices in each option offered. Find the overall profit of the monopoly（Hint: draw a graph.）.

(2) Can the monopoly increase its profit level in part (a) by offering a new pair of options? Show your work.

Answer 1

1)

Q1 = 200 - P

Q2 = (150 - P)/2 = 75 - P/2

Q = 0, for P>=200

Q = 200 - P for 150=<P<200

Q = Q1 + Q2 = 275 - 3*P/2 for P<150

Now for q1 = 200, amd for q2 = 75

P = 2/3*(275 - Q)

for q1

P = 2/3*(275 - 200) = 50

for q2

P = 2/3*(275 - 75) = 133.33

As there are no costs, total revenue will be total profit.

Profit = 200*50 + 75*133.33 = 20000

2)

Yes, profit can be increased by using different pair of q1 and q2.

Suppose,

q1=q2=137

P = 92

So total revenue will be

137*92 + 137*92 = 12604

q1 and q2 are set to 137, as the total demand is 275 and half of total demand is 137.5