Question

Q2. MC versus AC pricing

Suppose that inverse demand facing a monopolist is given by P=100-10Q. Suppose further that TC can be approximated by TC=10Q+140. It should be clear that AC is falling in output. This gives the regulator a dilemma. They can set prices=ac (to insure the firm is viable) or they can set prices=mc and subsidize the firm to make sure it is viable. For a and, graph the result.

a. What are market outcomes (P, Q) if a regulator sets price=AC? (you will need use the quadratic formula, you will get two solutions, and you must pick 1).

b. What are market outcomes (P, Q) if prices are set to MC? How much will you need to subsidize the firm.

Answer 1

Ans

a) AC = TC/Q = 10 +140/Q

When price is set equalt to AC,

Then, AC = 100 - 10Q

=> 10 + 140/Q = 100 - 10Q

=> Q2 -9Q + 14 = 0

=> Q = 7 units or Q = 2 units

To maximize wefare, firm will produce 7 units of output at price of $30

b) MC = dTC/dQ = 10

Using MC pricing,

MC = 100 - 10Q

=> 10 = 100 - 10Q

=> Q = 9 units and P = $10

At this price, loss per unit = P - AC = 10 - (10 + 140/9) = - $15.55

Thus, subsidy per unit sold = $15.55

Therefore, total subsidy = 15.55*9 = $140

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