The director of a theatre company in a small college town is considering chargin
ID: 1192886 • Letter: T
Question
The director of a theatre company in a small college town is considering charging the way he prices tickets. He has hired an economic consulting firm to estimate the demand for tickets. The firm has classified people who go to the theatre in to two groups and has come up with two demand functions. The demand curves for the general public and students are given below:
General Public: QGP = 500 - 5p
Students: QS = 200 - 4p
The tickets are currently sold at $35.
a) Find the price elasticity of demand for each group at the current price.
b) Is the director maximizing the revenue he collects from ticket sales by charging $35 to both groups? Explain.
c) What price should he charge each group if he wants to maximize revenue collected from ticket sales?
Explanation / Answer
General Public: QGP = 500 - 5p
Students: QS = 200 - 4p
At p=35,
QGP = 500 - 5p= 500 – 5.35= 325
QS = 200 - 4p= 200 – 4.35 =60
Elasticity= dQ/dp*(p/Q)
Elasticity of demand for GP = -5*(35/325)= -0.54
Elasticity of demand for Students = -4*(35/60)= -2.91
Thus the elasticity of demand for students is much higher.
Here the profit is definitely not maximized if we charge a single price to cater to the 2 groups with varying elasticities of demand. The ideal strategy should be perfect price discrimination such that a higher price is charged for the relatively more inelastic population. Thus price is set for each by equating MC to the two MR. And in this case the entire consumer surplus of the two groups can be taken over by the producer.