3. A natural monopoly exists in an industry with a demand schedule P 100 - Q. Th

Question

3. A natural monopoly exists in an industry with a demand schedule P 100 - Q. The marginal revenue schedule is then MR = 100-20. The monopolist operates with a fixed cost F, and a total variable cost IvC 20O. The corresponding marginal cost is thus constant and equal to 20. a) Suppose the firm sets a uniform price to maximize profit. What is the largest value of F for which the firm could b) Suppose the firm is able to engage in perfect first-degree price discrimination. What is the largest value of F for which the firm could earn zero profit?

Explanation / Answer

1- here we are calculating normal monopoly profits

So MR= MC

100-2Q= 20

Thus Q = 40 and P= 60

Now profits =tr-tc

So (60-20)(40)-F= 0 SO F= 1600

2- now in case of perfect price discrimination the output produced is where p= mc

Thus Q=80 AND P= 20

Profits in first degree price disrcimination is equal to the consumer surplus

So c.s here is

0.5(100-20)(80)= 3200

So F must be 3200

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