Item 3 is worth 20 points. Show and explain your work. If you need more space, u
ID: 1120423 • Letter: I
Question
Item 3 is worth 20 points. Show and explain your work. If you need more space, use the back. 3. A minor league baseball team called the Eugene Emeralds attracts both students and non- students during the tans. The Emeralds have estimated that, among students, the weekly demand for tickets to Emerald home games varies according to the equation Q 3250-250P, where Q is the quantity of tickets sold and P is the ticket price in dollars. Among non-students, weekly demand is given by the equation Q 3000-200P. The Emeralds earn marginal revenue from students according to the equation MR 13-0.008Q and from non-students according to the equation MR 15-0.01Q. The Emeralds incur marginal cost of $9 among all fans. a. How many tickets would the Emeralds sell to students, to maximize profit? What price would the team charge students? it? What b. How many tickets would the Emeralds sell to non-students, to maximize prof price would the team charge non-students? c. We can calculate price elasticity of demand (E,) at any point on a demand function using the formula E, (slope)/(P/Q), where slope refers to the (negative) slope of the demand function ( lies on the demand curve. Use this the profit-maximizing price for students and for non-students. Which group exhibits greater elasticity of demand for Emeralds tickets? O/dP) and P and Q represent a price and quantity combination that formula to calculate the price elasticity of demand at d. The Emeralds organization incurs total costs according to the equation TC 400 9Q. If the Emeralds succeed at price discrimination, how much economic profit (or loss) will the team earn selling tickets to students? How much will it earn selling tickets to non- students? How much total economic profit will the team earn from ticket sales?Explanation / Answer
a) The Emerald profit maximizing pice and output is the level where its marginal revenue equal to marginal cost.
13-0.008Q=9
.008Q = 4
Q = 500
and P = 13-.004*500 = 13-2 = $ 9
b) MR=MC
15-0.01Q=9
.01Q=6
Q = 600
P = 15-.005*600 = 15-3 = $12
c) Demand funtion for student. Q = 3250-250P
DQ /Dp= -250
Ed = -250 * 9/500 = -4.5
demand for non-students , Q = 3000-200P
Dq/Dp = -200
Ed = -200 * 12/600 = -4
SO, Studen group exhibits the greater elasticity of demand becasue their ed is -4.5 > -4.0 ed of non student.
d)TC = 400 +9Q
profit from sales = TR-TC => 500 * 9) - ( 400 + 9 *500)
profit = 4500 -4900 ,= -400
profit fro, non students= 600*12 ) - ( 400 +600*12)
profit = 7200 - 400 - 7200 = - 400
so total economic loss = $800
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