10. Suppose that a small market Major League Baseball team currently charges $15
ID: 1153297 • Letter: 1
Question
10. Suppose that a small market Major League Baseball team currently charges $15 for a ticket. At this price, they are able to sell 11,500 tickets to each game. If they raise ticket prices to $20, they would sell 10,000 tickets to each game. What is the arc price elasticity estimated from this change? If the demand curve is linear, what is the algebraic expression for demand?
11. The demand curve for the new computer game, Rock and Roll Trivia, is given as follows: Q = 200 - 5P - .1Pc - .5Pd + .2A – 0.5I where P is the price of the game Pc is the price of a computer Pd is the price of a diskette A is the level of advertising I is the level of income Suppose P = 10, Pc = 100, Pd = 2, A = 5, and I = 50. What is the income elasticity of demand?
Explanation / Answer
(10)
Linear demand function: P = a - bQ
When P = $15, Q = 11,500
15 = a - 11,500b..........(1)
When P = $20, Q = 10,000
20 = a - 10,000b.........(2)
(2) - (1) yields: 5 = 1,500b
b = 5/1,500 = 1/300 = 0.0033
a = 20 + 10,000b [From (2)] = 20 + 10,000 x 0.0033 = 20 + 33.33 = 53.33
Therefore, linear demnd function:
P = 53.33 - 0.0033Q
(11)
Q = 200 - 5P - 0.1Pc - 0.5Pd + 0.2A - 0.5I
Plugging in given values,
Q = 200 - (5 x 10) - (0.1 x 100) - (0.5 x 2) + (0.2 x 5) - (0.5 x 50)
Q = 200 - 50 - 10 - 1 - 25
Q = 114
Income elasticity = (dQ/dI) x (I/Q)= - 0.5 x (50/114) = - 0.22
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