When demand is estimated to be p = 50 – 0.5q, calculate the loss in consumer surplus when a tax drives price from £1 to £5.
Profit Maximisation Question 3
A monopolist's cost function is
TC(q) =0 if q = 0
100q + F if q > 0.
It faces the demand function p = 300 - 5q. How much does the monopolist produce (as a function of F )? What is the price? What is the monopolist's profit?
Now suppose the firm has to pay a lump sum tax of T.
What would be the impact on the monopolist's profit maximising output?
Would your answer change if it was a % tax?
PROFIT MAXIMISATION QUESTION 2
A monopolist's cost function is TC(q) = (q/2500)(q - 100)2 + y, so that MC(q) = 3q2/2500 4q/25 + 5. It faces the inverse demand function P(q) = 4 4q/100. Find its output, the associated price, and its profit.
Profit maximisation question 1
A monopolist has the cost function TC(q) = 200q + 15q2 and faces the demand function given by p = 1200 10y.
What output maximizes its profit? What is the profit-maximizing price? What is its maximum profit?