Question

In: Economics

Consider a monopolist selling sweets to two types of consumers (assume sweets are infinitely divisible, so...

Consider a monopolist selling sweets to two types of consumers (assume sweets are

infinitely divisible, so that the monopolist can sell any nonnegative, real quantity).

The demand function of consumers of type 1’s is p1(q1) = 9 − 3q1.

The demand function of consumers of type 2’s is p2(q2) = 8 − 5q2.

The monopolist can produce sweets at no cost.

There are equal numbers of both types of consumers.

SOLVE by using calculus please

SHOW STEP-BY-STEP solution please

(a) Suppose the monopolist can distinguish between the two types of consumers and is also able to offer them fixed-quantity packages, so that they cannot continuously choose any amount they want.

What packages will the monopolist offer to each type (state quantities and fees)?

What profit will the monopolist earn per consumer?

Solutions

Expert Solution

The demand function of consumer-1 is p1= 9 - 3q1, p1*q1 = 9q1 - 3q12 . MR = 9 - 6q1, As monopolist can distinguish the two type customer so monopolist can extract the consumer surplus fully. Now if P = MC , then q1=3, as MC=0. If monopolist equal the MC with MR then price would have 4.5. As in MR =MC, q=1.5 and p=4.5. Now if consumer are charged fee Price equal to monopoly price i.e 4.5, so fees will be equal to 4.5 per unit and quantity will be equal to 3. So monopolist will offer 3 packages to consumer 1 and fees it will take is 4.5.

For consumer 2, p2 = 8 - 5q2, TR = p2*q2 = 8q2 - 5q22 , MR = 8 - 10q2. Now according to P=MC , 8-5q2=0, therefore q2 = 1.6, so quantity will be 1.6 and price or here monopoly fees would be i.e p2 =8 - 5*0.8 =4. So the monopolist will sell 1.6 packages to consumer2. The fees will be charged to consumer 2 is 4.

From consumer 1 monopoly will earn profit equal to 3*4.5 = $13.5 and from consumer 2 monopoly will earn the profit equal to 4*1.6 = 6.4.

Rahul Sunny answered 2 years ago
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