Jamal only consumes two things: lift tickets at the local ski hill (S), and a composite good (Y). The composite good costs $1 per unit. He has an annual income of $55,000, and his utility function and associated marginal utilities are as follows: U = 10s0.lY MUS = S-09y MUy = 1051 %3D The local ski hill offers the following three pricing options: (i) Pay-as-you-go: In this option, each lift ticket costs Jamal $100. (ii) Member discount: In this option, Jamal pays a $540 membership fee at the start of the year, then each lift ticket costs $90. (iii) Season Pass: In this option, Jamal pays $9000 membership fee at the start of the year, then each lift ticket costs $0. Note that, given the length of the ski season, the maximum number of lift tickets Jamal can consume per year is 100. For each option, find Jamal's optimal consumption bundle and its associated utility. Which option should Jamal pick?
Jamal only consumes two things: lift tickets at the local ski hill (S), and a composite good (Y). The composite good costs $1 per unit. He has an annual income of $55,000, and his utility function and associated marginal utilities are as follows: U = 10s0.lY MUS = S-09y MUy = 1051 %3D The local ski hill offers the following three pricing options: (i) Pay-as-you-go: In this option, each lift ticket costs Jamal $100. (ii) Member discount: In this option, Jamal pays a $540 membership fee at the start of the year, then each lift ticket costs $90. (iii) Season Pass: In this option, Jamal pays $9000 membership fee at the start of the year, then each lift ticket costs $0. Note that, given the length of the ski season, the maximum number of lift tickets Jamal can consume per year is 100. For each option, find Jamal's optimal consumption bundle and its associated utility. Which option should Jamal pick?
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 8P
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Transcribed Image Text:Jamal only consumes two things: lift tickets at the local ski hill (S), and a composite
good (Y). The composite good costs $1 per unit. He has an annual income of $55,000,
and his utility function and associated marginal utilities are as follows:
U = 10s0lY
MUS = S-0.9Y
MUy = 10S1
%3D
The local ski hill offers the following three pricing options:
(i) Pay-as-you-go: In this option, each lift ticket costs Jamal $100.
(ii) Member discount: In this option, Jamal pays a $540 membership fee at the start
of the year, then each lift ticket costs $90.
(iii) Season Pass: In this option, Jamal pays $9000 membership fee at the start of the
year, then each lift ticket costs $0.
Note that, given the length of the ski season, the maximum mumber of lift tickets
Jamal can consume per year is 100.
For each option, find Jamal's optimal consumption bundle and its associated utility.
Which option should Jamal pick?
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