Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 2

Bruce runs the only bar in town. An individual consumer's demand for bar drinks is Q = 8 - P. The associated marginal revenue curve for this consumer is MR = 8 - 2Q. The bar's marginal cost is $2 per drink.
a. Compute the profit-maximizing monopoly quantity, price, and profit from serving this single consumer if Bruce's Bar charges a constant price per drink rather than using some nonlinear pricing scheme. What would the quantity and profit be if the bar serves 100 consumers identical to this one on a typical night?
b. Suppose Bruce moves to pricing scheme involving an admission fee to the bar but lowers the price per drink to marginal cost (which we showed in the text is the best per-unit price with identical consumers). How should the admission fee be set to maximize profit? How many drinks would the bar sell and how much profit would it earn from this two-part scheme on a typical night when 100 identical consumers show up?
c. Now suppose that, in addition to the 100 consumers mentioned above, an additional 15 show up whose demand for drinks is twice as high as the original consumers (so each has demand Q =16 - P). What profit would Bruce's Bar earn if it continued to use the two-part scheme from b? Show that the bar could earn more profit by moving to a scheme with a $3 price per drink. (Hint: as a preliminary step, compute the highest admission fee it can charge and still retain the 100 original consumers after increasing the per-drink price to $3. Then compute profits from both this admission fee charged to all 115 plus the variable sales of drinks to the 100 original and 15 new consumers at a price of $3 per drink.)