Barry runs the only bar in town, Barry’s Bar. An individual consumer’s demand fo

Question

Barry runs the only bar in town, Barry’s Bar. An individual consumer’s demand for bar drinks is Q = 8 – P. The bar’s marginal cost is $2 per drink.

a. Compute the profit-maximising monopoly quantity, price, and profit from serving this single consumer if Barry’s Bar charges a constant price per drink rather than using some other 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 Barry moves to a pricing scheme involving an admission fee to the bar but lowers the price per drink to marginal cost. How should the admission fee be set to maximise profit? How many drinks would the bar sell and how much profit would it earn from this pricing scheme on a typical night when 100 identical customers enter the bar? What type of pricing scheme have you developed?

c. Now suppose that, in addition to the 100 consumers mentioned in part (b), 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 Barry’s Bar earn if it continued to use the pricing scheme from part (b)? Show that the bar could earn more profit by moving to a scheme with a $3 price per drink.

Explanation / Answer

A) Price = X Q = 8-X Marginal Profit = Marginal Revenue (Price) minus Marginal Cost (2) Total Profit per Customer = Quantity Sold times Marginal Profit Profit per Customer = (8-X)(X-2) or -(X^2) + 10X - 16 Total Profit per Night = Profit per Customer * Number of Customers Profit per Night = 9 * 100

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