Question

Market perfectly competitive

1. Current market equilibrium price = $15

Short run total cost of TC= 0.5q^2

1. Profit maximization?
2. Total revenue?

2. TC= aQ^2-bQ+c where, a,b,c are positive constants. For this cost function AC is minimum at the output level where, AC=MC

3. Monopolist seller faces an inverse demand curve P=40-0.5Q and the monopolist can produce at a constant marginal cost of $5

1. How many units will an unregulated profit maximization monopolist sell?
2. If the government imposes a price ceiling of $6, how many units, will the monopolist sell and at what price?

Thanks, please show all steps and graphs!

Answer 1

As per HomeworkLib guidelines in case of multiple questions only the first question is to be answered

Kindly ask rest of the questions in a separate post

1.

In perfectly competitive markets, profit is maximized at the point P = MC

A) Given TC, we can calculate MC = dTC/dQ = Q

Now, setting P = MC gives P = 15 = Q

This means P* = $15 and Q* = 15 units

B) Total revenue = PQ = 15x15 = $225

Profits = TR - TC = 225 - 0.5(15)² = $112.50