7. Sheila and Bruce are going tubing. They brought with them boxes of cereal (x) and bags of pretzels (y). Their utility functions and endowments are given in the table: Sheila Bruce Utility Function Inxs+ in ys 0.5lnxB+ InyB Endowment (20, 10) (15,45) Suppose that Sheila and Bruce set up competitive markets for cereal (x) and pretzels (y). Let Px be the price of cereal and Py the price of pretzels. a) Write the two equations that define Bruce's best bundle of cereal and pretzels. Solve for his best bundle (i.e. his Marshallian Demands) b) Use his Marshallian Demands to write Bruce's net demands for cereal (x) and pretzels (y). c) Do the same for Sheila (find her Marshallian Demands and her net demands for cereal and pretzels)

7. Sheila and Bruce are going tubing. They brought with them boxes of cereal (x) and bags of pretzels (y). Their utility functions and endowments are given in the table: Sheila Bruce Utility Function Inxs+ in ys 0.5lnxB+ InyB Endowment (20, 10) (15,45) Suppose that Sheila and Bruce set up competitive markets for cereal (x) and pretzels (y). Let Px be the price of cereal and Py the price of pretzels. a) Write the two equations that define Bruce's best bundle of cereal and pretzels. Solve for his best bundle (i.e. his Marshallian Demands) b) Use his Marshallian Demands to write Bruce's net demands for cereal (x) and pretzels (y). c) Do the same for Sheila (find her Marshallian Demands and her net demands for cereal and pretzels)

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

7. Sheila and Bruce are going tubing. They brought with them boxes of cereal (x) and bags
of pretzels (y). Their utility functions and endowments are given in the table:
Sheila
Bruce
Utility Function
In xs+ in ys
0.5ln x³+ ln y
Endowment
(20, 10)
(15,45)
Suppose that Sheila and Bruce set up competitive markets for cereal (x) and pretzels (y).
Let Px be the price of cereal and Py the price of pretzels.
a) Write the two equations that define Bruce's best bundle of cereal and pretzels. Solve
for his best bundle (i.e. his Marshallian Demands)
b)
Use his Marshallian Demands to write Bruce's net demands for cereal (x) and
pretzels (y).
c) Do the same for Sheila (find her Marshallian Demands and her net demands for
cereal and pretzels)
d) Use Sheila and Bruce's net demand for cereal (x) to find the price ratio that clears
the market for cereal. Show that this same price ratio clears the pretzels market.
e) The price ratio represents the number of units of the y good that an individual
must give up in order to get an additional unit of the x good. What is the
relationship between the GE price ratio and the terms of trade implied by the
mutually beneficial trade of part (e)?
f) Illustrate the General Equilibrium allocation and price ratio in an Edgeworth box
diagram. Include a pair of indifference curves through the GE allocation.

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