Question

Suppose that a small market Major League Baseball team currently charges $12 for a ticket. At this price, they are able to sell 12,000 tickets to each game. If they raise ticket prices to $15, they would sell 11,052 tickets to each game.  
a) Assuming the demand curve is linear, what is the algebraic expression for demand?
b) What is the price elasticity of demand at $12?
c) What is the price elasticity of demand at $15?
d) Suppose that the supply curve can be described by the following equation: Qs = 15,002. What will the equilibrium price of tickets be?
e) What is the effect on revenue of charging $12 per ticket instead of the equilibrium price?

Answer 1

a. Q = a + bP
b = inverse of slope = Change in Q/Change in P = (11052-12000)/(15-12) = -948/3 = -316
So, Q = a - 316P
When when Q =12,000 and P = 12
12,000 = a - 316(12) = a - 3792
So, a = 12000 + 3792 = 15,792

So, Qd = 15,792 - 316P

b. (dQ/dP) = -316
Ed = (dQ/dP)*(P/Q) = -316*(12/12000) = -0.316

c. Ed = (dQ/dP)*(P/Q) = -316*(15/11,052) = -0.43

d. At equilibrium, Qd = Qs
So, 15,792 - 316P = 15,002
So, 316P = 15,792 - 15,002 = 790
So, P = 790/316
So, P = 2.5

e) At P = 2.5, TR = P*Q = 2.5(15,002) = 37,505
At P = 12; TR = 12*(12,000) = 144,000

So, revenue increases by 144,000 - 37505 = 106,495