4. Sheila and Bruce are going backpacking. Sheila and Bruce each have 24 power bars (x) and 24 ounces of water (y). Their preferences can be represented by: US(x,y)=lax +lays and UB(x,y³) = 3ln x³ +lny a) Find Sheila and Bruce's MRS at endowment. Illustrate in an Edgeworth box diagram, the endowment point and the indifference curves through that point. b) What is the pattern of trade associated with mutually beneficial trades? Find one mutually beneficial trade where the terms of trade are 2 ounces of water (y) per 1 power bar (x). c)
4. Sheila and Bruce are going backpacking. Sheila and Bruce each have 24 power bars (x) and 24 ounces of water (y). Their preferences can be represented by: US(x,y)=lax +lays and UB(x,y³) = 3ln x³ +lny a) Find Sheila and Bruce's MRS at endowment. Illustrate in an Edgeworth box diagram, the endowment point and the indifference curves through that point. b) What is the pattern of trade associated with mutually beneficial trades? Find one mutually beneficial trade where the terms of trade are 2 ounces of water (y) per 1 power bar (x). c)
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.7P
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Transcribed Image Text:4. Sheila and Bruce are going backpacking. Sheila and Bruce each have 24 power bars
(x) and 24 ounces of water (y). Their preferences can be represented by:
U*(x°,y°) = la xS + la y and U(x",y) = 3lm x# + la y"
a) Find Sheila and Bruce's MRS at endowment. Illustrate in an Edgeworth box
diagram, the endowment point and the indifference curves through that point.
b) What is the pattern of trade associated with mutually beneficial trades?
c) Find one mutually beneficial trade where the terms of trade are 2 ounces of water
(y) per 1 power bar (x).
Instead of trading directly, Sheila and Bruce trade in a market. Sheila and Bruce are price
takers on both the power bar and water markets. Each can buy and sell goods at the same
price. Let P, be the price of a power bar and P, be the price of an ounce of water.
d) Are the prices Px = 4 and Py-1 General Equilibrium prices? Briefly explain. You
do NOT need to find the GE prices to answer this question. Do use the MRS at
%3D
endowment.
e) Write the two equations that define the best bundle for Bruce at prices P and Py.
f) Find Bruce's best bundle as a function of prices. Write Bruce's net
demand/supply for each good as a function of the prices.
Sheila's net demand/net supply functions are x = 122
Px
12 and y = 12 - 12
%3D
%3D
Suppose that P.=2 and Py= 1.
!!
g) At these prices, who is a net demander of power bars (x)? Who is a net supplier of
water (y)?
h) Is the vector (2,1) a general equilibrium price vector? Briefly explain.
i) Illustrate the budget line associated with the price vector (2,1) in your diagram
above. Indicate on the budget line Sheila and Bruce's best bundles.
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