) = N 's“, where 0 < a <1 and N > 0. The price of jam is pj, the price of sandwiches is Ps, and Joey monthly budget Y to spend on lunch. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. Transform V (j, s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the (1-a)Y formulas j* aY and s* = Ps Pj
) = N 's“, where 0 < a <1 and N > 0. The price of jam is pj, the price of sandwiches is Ps, and Joey monthly budget Y to spend on lunch. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. Transform V (j, s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the (1-a)Y formulas j* aY and s* = Ps Pj
Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter6: Consumer Choice And Demand
Section: Chapter Questions
Problem 2QFR
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Question
Answer Subpart D
Transcribed Image Text:1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function
U(j, s) = Nj1-asª, where 0 < a <1 and N > 0. The price of jam is pj, the price of sandwiches is Ps, and Joey
has a monthly budget Y to spend on lunch.
a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's
preferences, which is the same as U(j, s) except for replacing N with 1.
b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this
for a Cobb-Douglas utility function, but not for a quasi-linear utility function.
Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*,
and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the
С.
(1-a)Y
aY
formulas j* =
and s*
Ps
d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?
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