Question

MC=5 4. (51 points) The inverse demand function a monopoly faces is P = 100 – Q. The firm's cost curve is TC(Q) = 10 +5Q (a) (3 points) What is the monopolist's marginal revenue curve? TR=(P)(Q) TR=(100-Q)(Q) MR=100-2Q (b) (3 points) What is the monopolist’s marginal cost curve? (c) (3 points) What level of output maximizes the monopolist's profits? MR=MC -> 100-2Q=5 –> Q=47.5 Units (d) (4 points) What is the price charged by a profit maximizing monopolist? P=100-47.5 = $52.5 (e) (3 points) How would your answers to parts (a)- (d) change if TC(Q) = 100+5Q? They wouldn't (f) (4 points) For what value of fixed costs, does the monopolist break even? (g) (4 points) For what value of fixed costs, would be monopolist find it optimal to shut down in the short-run? (h) (3 points) For what value of fixed costs, would be monopolist find it optimal to shut down in the long-run? (i) (4 points) What is the value of Lerner Index at the profit maximizing level of output?

Please answer parts F, G, H, I.

Thank you in advance

Answer 1

f)

Total Revenue at optimal output=P*Q=52.5*47.5=$2493.75

Let F be the fixed cost.

Total Cost at optimal output=TC=F+5Q=F+5*47.5=237.50

Profit=TR-TC=2493.75-F-237.50=$2256.25-F

In case of break even, profit is equal to zero. So,

2256.25-F=0

or F=$2256.25

g)

In short run, a firm will shut down if Price is less than variable cost per unit. This decision does not depend upon the value of fixed cost.

Any amount of fixed cost would not affect the decision to shut down in short run.

h)

In long run, a monopolist will shut down if economic profit is less than zero.

We have seen that a fixed cost of $2256.25 gives an economic profit of zero. We can say that a monopolist will shut down in long run if fixed cost is higher than $2256.25

i)

Lerner index=(P-MC)/P=(52.5-5)/52.50=0.90