Question

In: Economics

A monopolist has the cost function C(Q) = 30*Q, and faces two types of consumers, A...

A monopolist has the cost function C(Q) = 30*Q, and faces two types of consumers, A and B, with the following demand curves for its product:

PA = 60 – 3*QA

PB = 80 – 2*QB

  1. (4 points) What price will the monopolist charge under uniform pricing?
  2. (3 points) What prices will the monopolist charge if it can price discriminate?
  3. (3 points) How much higher is the monopolist’s profit in (b) than in (a)?

Solutions

Expert Solution

Given, C = 30Q

Differentiating TC wrt Q we get

MC = 30

and

A. When the firm charges uniform price then Pa = Pb and Qa + Qb = Q

Add the two equation we get

After simplifying we get the inverse demand function. As shown above. Now, calculate TR

Differentiate the TR wrt Q we get

Equate MR to MC

72 - 2.4Q = 30

=> 2.4Q = 72 - 30

=> Q = 42 / 2.4

=> Q = 17.5 units

P = 72 - 2.4 × 17.5 = $ 51

Profit = 51 × 17.5 - 30 × 17.5 = $ 367.50

b. The inverse demand function of A is

Equate it to MC

Now, calculating price

Revenue consumer A = 45 × 5 = $ 225

Now, calculating the quantity and price of consumer B

Equate MR to MC

Quantity consumer B = 12.5

Price = $ 55

Revenue from consumer B = 55 × 12.5 = $ 687.50

Profit from price discrimination

= TRa + TRb - TC

= 225 + 687.50 - 30 × 17.5

= $ 387.50

C. Difference in profit = 387.50 - 367.50 = $ 20.

Please contact if having any query will be obliged to you for your generous support. Your help mean a lot to me please help. Thank you

Rahul Sunny answered 1 year ago
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