Question

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:

P_A = 60 – 3*Q_A

P_B = 80 – 2*Q_B

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)?

Answer 1

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.

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