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11. (25 points) Lochlyn\'s Orchids has two types of customers. One type consists

ID: 1130355 • Letter: 1

Question

11. (25 points) Lochlyn's Orchids has two types of customers. One type consists of tourists who have little knowledge of orchids or the orchid market, and are only in S. Florida for a short period of time. Their demand Lochlyn's Orchids is given by the following: Pr=90-QT/25 where Q, is the number of orchids purchased by tourists, and Pr is the price they pay The second type of customers consist of locals who know about orchids and the orchid market. Their demand curve is Pc = 40-30L/1000 where Q is the number of orchids purchased by locals, and p, the price they pay Lochlyn sells her orchids at two locations Bayside and the Redland (that's an agricultural area in far south Miami-Dade County). Bayside caters only to tourists because tourists are not aware of the Redland location where prices are lower. Locals buy only at the Redland location because prices are lower there. Lochlyn's a) Show that the quantities Lochlyn's Orchids sells to tourists at Bayside and to the locals at the Redland, respectively, are (1,000 orchids, 5,000 orchids). b) Show that the prices Lochlyn's Orchids charges to tourists at Bayside and to the locals at the Redland, respectively, are ($50/orchid, $25/ orchid) Explain why Lochlyn's Orchids charges tourists a higher price. c)

Explanation / Answer

PT = 90 - QT/25

PL = 40 - 3QL/1000

MC = AC = 10

a)

PT = 90 - QT/25

MRT = 90 - 2QT/25

Profit maximization at

MRT = MC

90 - 2QT/25 = 10  

90 -10 = 2QT/25

80 = 2QT/25

QT = 80(25)/2

= 1000

PL = 40 - 3QL/1000

MRL = 40 - 6QL/1000

MRL = MC

40 - 6QL/1000 = 10

40 - 10 =   6QL/1000

30 = 6QL/1000  

QL = 30(1000)/6

= 5000

b)

PT = 90 - QT/25

= 90 - 1000/25

= 90 - 40

= 50

PL = 40 - 3QL/1000

= 40 - 3(5000)/1000

= 40 -15

= 25

c)

PL = 40 - 3QL/1000

dPL/dQL = - 3/1000

so dQL/dPL = - 1000/3

EdL = - (dQL/dPL)(PL/QL)

= - (-1000/3)(25/5000)

= 1.67  

PT = 90 - QT/25

EdT = -(dQT/dPT)(PT/QT)

PT = 90 - QT/25  

dPT/dQT = - 1/25

so dQT/dPT  = - 25

EdT = -(dQT/dPT)(PT/QT)

= -(-25)(50/1000)

= 1.25

since EdT < EdL implies PT > PL

therefore he will charge tourists a higher price