Question

Suppose that you are a monopolist who produces yachts, Z, with the total cost function C(Z) = F + 50Z, where F represents the firm’s fixed cost. Your marginal cost is MC = 50. Suppose now that there are 32 consumers in the market for yachts, each with the individual demand function P = 60 - Z. How large can the fixed costs F be for you to still earn positive profits if you use the a nonlinear pricing strategy with a usage fee of $50 per unit and a subscription fee of $50?

Answer 1

C(Z)=TC=F+50Z

Let us calculate the quantity demanded at P=50

P=60-Z

50=60-Z

Z=10

Total Revenue=TR=Fixed fee+Usage fee=32*(50+50*10)=$17600

Total output of firm=number of customers*quantity demanded by each customer

Total output of firm=32*10=320

Total Cost=TC=F+50Z=F+50*320=F+16000

Profit=TR-TC=17600-F-16000=1600-F

Profit should be positive, it means

1600-F0

F1600

So, maximum value of F=$1600

(At F being $1600, economic profit is zero. If you want strictly positive profit, it should be less than $1600 say $1599.99)