Daily demand for ski lift tickets is Qdt = 1200 - 5Pt for out-of-town tourists Q
ID: 1189845 • Letter: D
Question
Daily demand for ski lift tickets is Qdt = 1200 - 5Pt for out-of-town tourists Qdl = 900 – 10 Pl for locals There is only one ski run permitted by zoning in this market area, so it operates as a monopolist.
a. Derive the firm's total demand function, and graph it.
b. Find the monopolist's optimal output, and profit or loss, if a single lift ticket price is charged to all consumers. Assume the firm's cost function is TC = 20,000 + 20 q. (Hint: there are 2 possible solutions, check both)
c. If the firm could price-discriminate between these 2 types of customers, what would be the optimal lift ticket price for each type now? What would profit or loss be in this case?
Explanation / Answer
Q =1200-5P
P = 240-0.2Q
Q*=900-10P*
P*=90-0.1Q*
(a) Total demand=240-0.2Q+90-0.1Q*
Total demand = 330-0.3Q
When Q = 0, P=300
When P=0 Q =1100
(b) Monopolist produces where MR = MC
TC = 20000+20q
MC = 20
TR = 330Q-03Q2
MR = 330-0.6Q
MR = MC
330-0.6Q =20
310 = 0.6Q
Q = 516.66
P = 175
P=$175
Profit = TR-TC
Profit = 175 x 516.66 -20000-20x516.66
Profit = $60083.85
(c) MR=MC for out of twon
P = 240-0.2Q
PT=TR = 240Q-0.2Q2
MR = 240-0.4Q
240-0.4Q=20
Q=2200/4 = 550
P=$130
SImialrly for locls
MR = MC
90-0.2Q=20
Q =700/2 = 350
P= $55
Total profit = 55x350+550x130-20000-20x(350+550)
Total profit = $52750
The prfoits are lower with price discrimination
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