Spring 2007
1. a. Your demand for drinks is given by Q = 20 – ½ P. The current price of drinks is $10. What is the maximum cover charge that you would be willing to pay to get into a bar that would sell you drinks for $5?
(Note: it would be difficult to answer this question without a graph.)
Q = 20 – ½ (10) = 15
Q = 20 – ½ (5) = 17.5
Original CS = $225
New CS = $306
Entry fee = $81 b. Now suppose that there are 100 customers with the demand curve shown above, and 200 customers with demand given by Q = 10 – ½ P. The bar estimates that its marginal cost per drink is $1. Find the combination of cover charge and drink price that maximizes profit. How many people will come to the bar, and what will profit be?
(Note: don't expect the cover charges to be anything that you'd reasonably pay to go to a bar; it would take me too long to work that out!)
At a price of $1/drink, the first group will buy 19.5 drinks, and the second group will buy 9.5 drinks. (You should probably round these to the nearest whole number, but I carried it out.)
CS for first group= ½ (40-1)(19.5) =$380
CS for second group = ½ (20-1)(9.5) = $90.
If you charge a $90 entry fee, ALL consumers will come, and profit will be (300)(90) = $27,000
If you charge a $380 entry fee, the second group will not come. Thus you will have 100 customers, and your profit will be (380)(100) = $38,000.
In this case, it is better to charge the higher fee and exclude the low-demand consumers.
2. There are two consumer groups, students and non-students.
Demand for students: Q = 1000 – 2P
Demand for non-students: Q = 1500 – 2P
MC = AC = 100 a. Find the profit-maximizing price/quantity combination in each market if the groups can be separated.
Calculate CS, PS, and DWL.
Students: Q = 400, P = $300
CS = 40,000
PS = 80,000
DWL = 40,000
Nonstudents: Q = 650, P = $425
CS = 105,625
PS = 211,250
DWL = 105,625

b. Find the profit-maximizing price/quantity combination if the groups cannot be separated. Calculate CS,
PS, and DWL.
(Hint: to do this, you have to add up the demand curves above, as we discussed in class. Remember that when you add demand curves, you have to be sure to add quantities, not prices. Then DRAW the demand curve and think about what it would really look like, since no one in the student market will buy anything at all unless the price is less than $500.)
Q = 1050, P = $362.50
CS = 169, 062.50
PS = 275,625
DWL = 137,812.50 c. Carefully explain why your results are different and who wins and who loses from the price discrimination scheme, and WHY the outcomes are different.
Society as a whole loses from the price discrimination scheme as opposed to the single-price monopolist.
We know this because deadweight loss is higher for the price discrimination outcome. If you think about the reason why, that’s because less is sold to the higher-value consumers and more to the lower value consumers. This is what we would call a Pareto-inferior result, because social welfare could obviously be increased if some students trade their units to the non-students (who would be willing to pay more for them than the students paid, and thus both groups are better off).