Suppose you own a super fancy restaurant in Wailea, Hawaii, called the Ocean Paradise Grille. You suspect that the demand for your dinners is different for senior citizens compared to everyone else, and so you are considering price discriminating by offering a senior citizen discount. You estimate that for the two groups the average daily demand for your dinners is as follows:

Group 1 - non-senior citizens: 1 = 330 21 Group 2 - senior citizens: 2 = 510 42

Where 1 is the quantity demanded for Group 1 when it faces price 1 and 2 is the quantity demanded by Group 2 when it faces price 2. This implies that the marginal revenue for each group is:

1 = 165 1 2 = 127.5 1 22

You have the following total and marginal costs: = 1,000 + 2 1 = 2 = 2 Where is your total quantity produced (i.e. = 1 + 2). Notice here, that marginal cost is the same whether you're producing in Market 1 or in Market 2, and that marginal cost is increasing - which means that when you produce more in Market 1, your cost of producing an additional unit in market 2 also increases. Finally, assume that the two markets are distinct, so arbitrage is not possible.

A) If you price discriminate, what is the profit maximizing price for each group?

B)Translate this into real world jargon: what "senior citizen discount" would you offer, in percent (round to the nearest percent)?

C )How much profit would you make if you price discriminated?

D)If it became illegal to discriminate on the basis of age, you would face only one demand curve. Aggregating the two demand curves yields:

= 840 6 & = 140 1 3

What are the optimal price and quantity in this unified market ( still equals 2)?

E)What is the profit in this discrimination-free market? Keeping in mind that these are average daily demands, and assuming that you're open 365 days a year, how much profit per year do you lose by not discriminating (compare your answer here with the profit calculated in part c)?