Question

12. Consider a bar whose owner plans to set profit-maximizing two-part tariff (entry fee and per-drink price) on two types of customers. The owner would like to welcome both types into hi bar, meaning that he will not charge an entry fee that is too high.

There are 20 people of the X-type whose individual demand is given by P = 10 – Qx. There are 30 people of the Y-type whose individual demand is given by P = 10 – 2Qy. The MC = AC = $2 per drink.

Find the optimal entry fee and per-drink price. Also, calculate the profit the bar can make from these 50 customers.

Answer 1

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12.

Ans:

Rational firm will set that tariff and price such that both type of customers stay in the market.

Tariff will be equal to consumer surplus of one type which is lower such that type with higher consumer surplus stays in the market.

Since consumer surplus is maximized at Price = MC,

Quantity purchased by X-type customer each = 10 - P = 10 - 2 = 8

Quantity purchased by Y-type customer each = (10 - P) / 2 = 8 / 2 = 4

Consumer surplus of X-type customer = 0.5(10 - 2)(8) = 32

Consumer surplus of Y-type = 0.5(10 - 2)(4) = 16.

So, we have:

Optimal entry fee = 16

Price = MC = 2

Profit = 16(50) + (2 - 2)Q = 16(50) = 800.

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