Question

buestion 3 A night club owner has both student and adult customers. The demand for drinks by a typical student is Q. 18-3P. The demand for drinks by a typical adult is QA-10-2P. There are an equal number of adults and students. The marginal cost of each drink is $2. 6 18 Q 10 Part 1: a) What price will the club owner set if she cannot discriminate between the two groups? What will total profit be at this price? b) If the club owner could separate the groups and practice 3rd-degree price discrimination what price per drink would be charged to members of each group? What would be the club owner's profit? Part 2: a) If the club owner in problem 4 can card patrons and determine who among them is a student and who is not and in turn can serve each group by offering a cover charge and a number of drink tokens to each group ( 2-part pricing what will the cover charge and number of tokens to students be? what will the cover charge and number of tokens to adults be? What is the club-owners profit under this regime b) Is total welfare higher with the 2-part pricing plan than with 3rd degree price discrimination (in part 1b above)? Explain your answer

Answer 1

The demand of a typical student for drinks is, Of = 18-3P The demand of a typical adult for drinks is, Q+ = 10-2P The marginal cost is constant at $2. Part 1: a. If club owner cannot discriminate between two group of customers, she will consider combine demand. So, combine demand is, Q=Q + = 18-3P+10-2P = 28 - 5P P=28 5 g 5 Compute MR as follows to determine equilibrium price, TR =PxQ -28_2 At equilibrium, equate MR and MC and solve as follows:

MR = MC 28-20 =10 Q=9 II i II P=3.8 Hence, the club owner will charge price of $3.5 when she cannot discriminate. The total profit will be, profits =(P-MC) = (3.8-219 profits = $16.2 b. If club owner practice 3rd degree price discrimination, she will charge different price to both groups. Students The inverse demand of a typical student for drinks is, Oʻ =18-3P The MR is,

MRⓇ =6=.3 At equilibrium MR = MC O Q* = 6 wla A P=$4 Hence, she will charge $4 per drink to students. Adults The inverse demand of a typical adult for drinks is, Q4 =10-2P The MR is, =594_1001) MR* = 5-04 At equilibrium,

MR = MC 5-4 = 2 Q4 = 3 P=s- P=$3.5 Hence, she will charge $3.5 per drink to adults. The profit of club owner will be Profit = profit from students + profits from adults = (4-2)6+(3.5-2)3 = 12 +4.5 = 16.5 Hence, the profit of club owner is $16.5. Part 2: a. If club owner practice 2-part pricing, the number of tokens will be equal to the quantity demanded at marginal cost of $2. Number of tokens for students will be, Tokens = 18-3P =18-3(2) = 12 Number of tokens for adults will be, Token = 10-2P =10-2(2) = 6 Hence, the number of tokens for students is 12 and for adults is 6 Next, the cover charge for each group will be equal to their total willingness to pay. The cover charge for students will be

Cover charge = -(6-2)(12)+2(12) = 24+24 = 48 The cover charge for adults will be, Cover charge* = =(5-2)6)+2(6) =9+12 = 21 Hence, the cover charge for students is S48 and for adults is $21. The total profit of the club is, Profit=TR-TC = (48 +21)-(2(12+6)) = 69-36 = 33 Hence, the profit of club owner under 2-part pricing is $33 b. Under 2-part pricing, profit is $33 and under 3rd degree price discrimination, profit is $16.5. Hence, club owner is better off with 2-part pricing.