Question

You have a monopoly on ice cream in a town. It costs you an average of $2 to produce each ice cream cone. Suppose you know that a certain percentage of your customers are willing to pay $4 for a cone and the rest are willing to pay $3. Does it seem reasonable for you to charge $3.50? Briefly explain why or why not.

Answer 1

The monopolist sets its own price as they have full market power. The price it will set will be uncontested. Then the monopoly pricing should be such that it can rip the maximum profit. In this light, $3.5 is not a profit-maximizing option. The monopolist should charge either $4 or $3. The marginal revenue for demand between $4 and $3 is discontinuous or undefined. Then for MC=$2, it is profit-maximizing to charge either $4 or $3. The maximizing price depends on the fraction of people who wants to pay $4.

This is because at $4 the profit of the firm is (assuming α is the fraction wants to pay $4)

The profit with price of $3, (note at $3 everyone will buy the ice cream)

The monopolist will charge $4 as long as

The monopolist will charge $3 if the fraction of people want to pay $4 decreases below 50% of the market.