Exercise 1 A monopolist has an inverse demand curve given ... - IDEA

) Joan’s nephew courses ADE/ECO at UPF and argues that given their
different demands, the two groups should be charged different prices. In this
case, what prices would he charge for men and women How many hours
would be demanded by each group What would BCN Sports’profits be
c) Joan’s niece also courses ADE/ECO at UP and she suggests him to
charge an entry fee in addition to the charge per hour. What prices would
he charge as entry and per hour for each group How many hours would be
demanded in each group What would BCN Sports’ profit would be
d) What option (among a), b) and c)) would Joan prefer What about
the men What about the women Explain.
Answers
a) q M = 16 − p M and q W = 20 − 2p W
q M + q W = q = 36 − 3p ⇒ p = 12 − q 3
π = 10q − 1 3 q2
∆π
∆q = 10 − 2 3 q = 0 ⇒ q = 15
p = 12 − 1 3 q ⇒ p = 7
π = pq − cq = 75
b) π M = p M q M − 2q M = (16 − q M )q M − 2q M = 14q M − q 2 M
∆π M
∆q M
= 14 − 2q M = 0 ⇒ q M = 7
p M = 16 − 7 = 9
π W = p W q W − 2q W = 8q W − 1 2 q2 W
∆π W
∆q W
= 8 − q W = 0 ⇒ q W = 8
p W = 10 − 4 = 6
π = π M + π W = 9 ∗ 7 − 2 ∗ 7 + 6 ∗ 8 − 2 ∗ 8 = 81
c) p∗ = MC = 2
q M = 16 − 2 = 14 ⇒ F M = 1 (16 − 2) ∗ 14 = 98 (surface of a triangle
2
= 1 × height × base)
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q W = 10 − 2 = 8 ⇒ F W = 1 (10 − 2) ∗ 16 = 64
2
Profits=consumers’surplus + profits per hour. But profits per hour=0
(since p = MC). Therefore:
π M = 98
π W = 64
π = π M + π W = 98 + 64 = 162
d) which is the best option
From the table, it is straightforward to see that the option c) is the best
for the firm. For the men, it is a) and for the women it is b).
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