1. Customers to Live Theaters, Inc. can be divided into two groups: seniors and
ID: 1178410 • Letter: 1
Question
1. Customers to Live Theaters, Inc. can be divided into two groups: seniors and everyone else. The inverse demand curves for each of the two groups are given below. The marginal cost (which equals the average variable cost) of serving an additional patron, either senior or everyone else, is equal to $4. Fixed costs are equal to $1000.
Ps = 80 %u2013 Qs
Pe = 100 %u2013 2Qe
Where Ps and Pe denote, respectively, the prices charged to seniors and everyone else and Qs and Qe denote the number of seniors and the number of all other customers served.
a. What is Live Theaters%u2019 total revenue function? What is its total cost function? Its total profits function? For the total revenue use Total Revenue=Ps*Qs + Pe*Qe
b. What are the profit maximizing levels of price and output if Live Theaters, Inc. engages in third degree price discrimination? Show that MRe = MRs = MC. Use MRe = d/dQ(Pe*Qe), MRs = d/dQ(Ps*Qs), and MC = d/dQ (TC)
c. What are profits associated with this option?
d. If Live Theaters charges one price to all patrons, what would it be? How many customers would it serve? What would be its profits?
Customers to Live Theaters, Inc. can be divided into two groups: seniors and everyone else. The inverse demand curves for each of the two groups are given below. The marginal cost (which equals the average variable cost) of serving an additional patron, either senior or everyone else, is equal to $4. Fixed costs are equal to $1000. Ps = 80 %u2013 Qs Pe = 100 %u2013 2Qe Where Ps and Pe denote, respectively, the prices charged to seniors and everyone else and Qs and Qe denote the number of seniors and the number of all other customers served. What is Live Theaters%u2019 total revenue function? What is its total cost function? Its total profits function? For the total revenue use Total Revenue=Ps*Qs + Pe*Qe What is Live Theaters%u2019 total revenue function? What is its total cost function? Its total profits function? For the total revenue use Total Revenue=Ps*Qs + Pe*Qe What are profits associated with this option? If Live Theaters charges one price to all patrons, what would it be? How many customers would it serve? What would be its profits?Explanation / Answer
P=80-Qs
P=100-2Qe
Qs=80-P
Qe=50-0.5P
Qs+ Qe=130-1.5P
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TOTAL OUTPUT=P=130/1.5-Q/1.5
TR=PQ
TC==Y(Q)+1000
TI =TR-TC=PQ-4Q-1000
=130/1.5 %u2013Q/1.5)Q-4Q-1000
=130/1.5-2Q/1.5-4
=130-2Q=6
2Q=124=
Q=62
P=130/1.5-62/1.5=45.333
PROFIT= (130/1.5-62/1.5).62-4.63-1000
=2810.66-1248=1562.66
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