5. Sheila and Bruce are taking a canoe trip. Sheila brought 10 boxes of peanuts (x) and 15 bags of chips (y). Sheila's utility function is US(x,y) = Inxs+ Invys. Bruce also brought 20 boxes of peanuts and 5 bags of chips. Bruce's utility function is UB(x,y) = min[x³, y³]. a) Illustrate the endowment point and draw a sample set of indifference curves through the endowment point. b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade? c) If the terms of trade are the number of bags of chips (y) per box of peanuts (x) then what is the largest value that these terms can be for a mutually beneficial trade in this economy? d) Find one mutually beneficial trade where the terms of trade are 1 bag of chips (y) per 2 boxes of peanuts (x). Suppose that Sheila and Bruce set up two competitive markets for peanuts and chips. Below you will show that if the price of peanuts (x) is $1 and the price of chips (y) is $2 then the markets for both peanuts and chips will clear. e) Write the two equations that define Bruce's best bundle. Write the two equations that define Sheila's best bundle. Write the remaining 2 market clearing equations that define the General Equilibrium. f) Show that Px=1 and Py=2 is a General Equilibrium price vector. g) Illustrate the General Equilibrium allocation and price ratio in your Edgeworth box diagram. Include a pair of indifference curves through the GE allocation.
5. Sheila and Bruce are taking a canoe trip. Sheila brought 10 boxes of peanuts (x) and 15 bags of chips (y). Sheila's utility function is US(x,y) = Inxs+ Invys. Bruce also brought 20 boxes of peanuts and 5 bags of chips. Bruce's utility function is UB(x,y) = min[x³, y³]. a) Illustrate the endowment point and draw a sample set of indifference curves through the endowment point. b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade? c) If the terms of trade are the number of bags of chips (y) per box of peanuts (x) then what is the largest value that these terms can be for a mutually beneficial trade in this economy? d) Find one mutually beneficial trade where the terms of trade are 1 bag of chips (y) per 2 boxes of peanuts (x). Suppose that Sheila and Bruce set up two competitive markets for peanuts and chips. Below you will show that if the price of peanuts (x) is $1 and the price of chips (y) is $2 then the markets for both peanuts and chips will clear. e) Write the two equations that define Bruce's best bundle. Write the two equations that define Sheila's best bundle. Write the remaining 2 market clearing equations that define the General Equilibrium. f) Show that Px=1 and Py=2 is a General Equilibrium price vector. g) Illustrate the General Equilibrium allocation and price ratio in your Edgeworth box diagram. Include a pair of indifference curves through the GE allocation.
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 9P
Related questions
Question
Transcribed Image Text:5. Sheila and Bruce are taking a canoe trip. Sheila brought 10 boxes of peanuts (x) and 15
bags of chips (y). Sheila's utility function is U*(x,y) = lnvx*+ Invy°. Bruce also brought
20 boxes of peanuts and 5 bags of chips. Bruce's utility function is UB(x.y) = min[x', y'I.
a) Illustrate the endowment point and draw a sample set of indifference curves
through the endowment point.
b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade?
c) If the terms of trade are the number of bags of chips (y) per box of peanuts (x) then
what is the largest value that these terms can be for a mutually beneficial trade in
this economy?
d) Find one mutually beneficial trade where the terms of trade are 1 bag of chips (y)
per 2 boxes of peanuts (x).
Suppose that Sheila and Bruce set up two competitive markets for peanuts and chips.
Below
you
will show that if the price of peanuts (x) is $1 and the price of chips (y) is $2
then the markets for both peanuts and chips will clear.
e) Write the two equations that define Bruce's best bundle. Write the two equations
that define Sheila's best bundle. Write the remaining 2 market clearing equations
that define the General Equilibrium.
f) Show that P,-1 and Py-2 is a General Equilibrium price vector.
g) Illustrate the General Equilibrium allocation and price ratio in your Edgeworth box
diagram. Include a pair of indifference curves through the GE allocation.
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Step 1: State the given information
VIEWStep 2: Draw these indifference curves through the endowment point in the Edgeworth box
VIEWStep 3: Find the pattern of mutually beneficial trade
VIEWStep 4: Find the largest value of these terms of trade
VIEWStep 5: Find mutually beneficial trade with specific terms
VIEWStep 6: Find competitive market equations for best bundles
VIEWStep 7: Analyze the general equilibrium price vector
VIEWStep 8: Illustrate general equilibrium in the Edgeworth box
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