Question

The director of the local Arts Council in a college town has hired a consultant to help her price theater tickets so as to maximize revenues. The consultant begins by classifying all theater patrons into two groups: Students (S) and the General Public (GP). She assesses their respective demand functions. They are: Q students (S)=200−4P Q gen-public (GP)=500−5P

(i) If the current price of a theater ticket is $35, calculate how many theater tickets are demanded by each group at equilibrium. (ii) What is the price elasticity of demand for each group at the current price and quantity demanded? Whose demand is more elastic? (iii) To maximize revenues the consultant advises the Arts Council to charge two different prices - one for the students and one for the general public. Specifically, she advises the Council to raise the price for the general public to $50 per ticket and lower the price for students to $25. Drawing on what you know about the relationship between elasticity and revenue, state whether you agree or disagree with the consultant's recommendation. Why? (Tip: It is NOT necessary to calculate the revenue-maximizing fares.)

Answer 1

At the current price of $35, 60 theater tickets are demanded by students and 325 theater tickets are demanded by the general public. Both groups have inelastic demand with a price elasticity of 0. The consultant's recommendation to charge two different prices based on the groups' demand is correct as it can help maximize revenue.

Step-by-step explanation:

(i) To find the equilibrium quantity demanded by each group, we need to set the demand functions equal to the given price and solve for quantity:

For students: Qstudents = 200 - 4P = 200 - 4(35) = 200 - 140 = 60

For the general public: Qgen-public = 500 - 5P = 500 - 5(35) = 500 - 175 = 325

So, at the current price of $35, 60 theater tickets are demanded by students and 325 theater tickets are demanded by the general public.

(ii) The price elasticity of demand (PED) can be calculated using the formula: PED = (% change in quantity demanded) / (% change in price).

For students: PEDstudents = (ΔQstudents / Qstudents) / (ΔP / P) = (60 / 60) / (0 / 35) = 0 / 35 = 0 (inelastic)

For the general public: PEDgen-public = (ΔQgen-public / Qgen-public) / (ΔP / P) = (325 / 325) / (0 / 35) = 0 / 35 = 0 (inelastic)

Both groups have inelastic demand, as the price elasticity of demand is 0 for both groups at the current price and quantity demanded. Therefore, the demand of both groups is equally inelastic.

(iii) Based on the concept of price elasticity and revenue maximization, the consultant's recommendation to charge two different prices is correct. Since both groups have inelastic demand, the Arts Council can charge a higher price to the general public and a lower price to students without significantly affecting the quantity demanded. This pricing strategy can help maximize the revenue for the theater.