Suppose that the average daily demand for dinners at Paradise Grille is as follows:

Demand for dinners by senior citizens: P = 50 – 0.5Q

Demand for dinners by others: P = 100 – Q

Marginal cost of a dinner: MC = 10 in both cases

1. What is the equation for marginal revenue from the sale of a dinner to a senior citizen?

2. What is the equation for marginal revenue from the sale of a dinner to others?

3. How many dinners should be sold to senior citizens to maximize profit?

4. How many dinners should be sold to other to maximize profit?

5. What is the profit-maximizing price for a dinner sold to a senior citizen?

6. What is the profit-maximizing price for a dinner sold to others?

7. Translate these answers into real-world business terms: If you owned this restaurant, what “senior citizen discount” would you be offering, in percent?

8. Ignoring fixed costs, what would be the total profit earned by this restaurant per day?

9. If it became illegal to discriminate on the basis of age, the owner of the restaurant would face a single demand curve: P = 67 – (1/3)Q with MR = 67 – (2/3)Q.

a. How many dinners should be sold in this single market to maximize profit? Round to the nearest whole number.

b. What would be the profit-maximizing price charged for a dinner in this single market?

c. What would the restaurant’s daily profit be in this single market?