Question

The Perch is a pub that has two types of potential customers: legal and underage drinkers.

It is illegal to allow entry to underage drinkers, but there is no way to perfectly identify

underage drinkers (fake IDs, etc.). Assume that Perch ’s marginal cost is $3.00 per drink.

The drink demand for a representative customer in each of the two groups is given by:

PL= 6- QL (legal drinkers)

PU= 4 -QU (underage drinkers)

(1) If the price per drink is $3, how many drinks does each type of drinkers have?

(2) What is a pricing policy that will extract all of the profit from the legal drinkers?

(3) How many drinks do legal drinkers have under this pricing policy?

(4) Do underage drinkers have incentives to go to the bar under this pricing policy? Why?

Answer 1

(1) If the price per drink is $3, how many drinks does each type of drinkers have?

Legal drinkers have a demand curve:

$$PL= 6- QL$$

And underage drinkers have a demand curve:

$$PU= 4 -QU$$

If the price is $3, legal drinkers will demand:

$$3 = 6 - QL\\[0.3cm] \color{red}{QL = 3}$$

And underage drinkers will demand:

$$3 = 4 - QU\\[0.3cm] \color{red}{QU = 1}$$

(2) What is a pricing policy that will extract all of the profit from the legal drinkers?

The price policy to extract all the profit from the legal drinkers is setting a price equal to their willingness to pay.

(3) How many drinks do legal drinkers have under this pricing policy?

When each buyer is charged a price equal to the willingness to pay, the seller will sell up to the point where the last buyer pays a price equal to the marginal cos. Therefore:

$$3 = 6 - QL\\[0.3cm] QL^* = 3$$

Legal drinkers will have 3 drinks.

(4) Do underage drinkers have incentives to go to the bar under this pricing policy? Why?

Under this pricing strategy, the underage drinkers will have the incentive to go to the bar since they can also get a drink by paying a price equal to the seller's marginal cost, which is one drink.