Question

5. A small community theater is trying to determine a price to maximize profits. They have collected the following data. If they set one price to maximize profit, what should it be and how many customers would they serve? If the firm wants to further increase their profits through price discrimination, upon what would they split the customers into groups? What are the two prices they would set to maximize their profits? How many customers would fall into each group? What is the difference in profits between one price and two prices? Customer Maximum willingness to pay Age Emily Dennis Gina Marsha Wendy Eric Anna 14 25 36 23 17 10

Answer 1

Answer:

5.

While setting one price, the monopolist would want to maximize his profits.

This can be done by using the method of hit and trial.

The two prices they would set to maximize their profits are:

If the firm sets price equal to 8, 4 units would be sold for a profit of 32.

If the firm sets price equal to 7, 5 units would be sold for a profit of 35.

If the firm sets price equal to 6, 7 units would be sold for a profit of 42.

Hence, the firm would set price equal to 6 per unit.

While price discriminating,

the firm would divide the consumers on the basis of their maximum willingness to pay.

customers that fall under the group of price 9 per unit:

Hence, for Dennis, Eric, Anna, and Emily, price will be 9 per unit.

customers that fall under the group of price 6  per unit:

For Gina, Marsha, and Wendy price will be 6 per unit for a total profit of 54.

difference in profits between one price and two prices:

The profit under price discrimination is greater than the profit under one price by 12.