Avi (A) and Brad (B) live in an exchange economy where they consume cakes, z, and litres of beer, y. Both of their preferences are given by: u=aln(x) + (1-a) In(y) where 0< a < 1. There are a total of n cakes and 3n litres of beer in the economy, where 3 > 0. a. Assuming Py = 1 and letting pe=p, show that there will be a constant equilibrium price, p* (a, 3), regardless of the initial distribution of a and y between Avi and Brad. What is this price? b. Consider a beer-heavy economy in which n = 10, a = 0.2 and 3= 8. Suppose Avi starts with all the beer, and Brad starts with all the cake. What will be the post-trade equilibrium? Who trades how much for what? Show the situation on an Edgeworth-box diagram with post-trade indifference curves. (Your diagram. does not have to be 'to scale'.)
Avi (A) and Brad (B) live in an exchange economy where they consume cakes, z, and litres of beer, y. Both of their preferences are given by: u=aln(x) + (1-a) In(y) where 0< a < 1. There are a total of n cakes and 3n litres of beer in the economy, where 3 > 0. a. Assuming Py = 1 and letting pe=p, show that there will be a constant equilibrium price, p* (a, 3), regardless of the initial distribution of a and y between Avi and Brad. What is this price? b. Consider a beer-heavy economy in which n = 10, a = 0.2 and 3= 8. Suppose Avi starts with all the beer, and Brad starts with all the cake. What will be the post-trade equilibrium? Who trades how much for what? Show the situation on an Edgeworth-box diagram with post-trade indifference curves. (Your diagram. does not have to be 'to scale'.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Avi (A) and Brad (B) live in an exchange economy where they consume
cakes, r, and litres of beer, y. Both of their preferences are given by:
u = a ln(x) + (1 – a) In(z)
where 0 < a < 1. There are a total of n cakes and Bn litres of beer in the economy,
where 3 > 0.
a. Assuming Py =1 and letting p = p, show that there will be a constant equilibrium
price, p"(a, 3), regardless of the initial distribution of r and y between Avi and
Brad. What is this price?
b. Consider a beer-heavy economy in which n 10, a = 0.2 and B = 8. Suppose
Avi starts with all the beer, and Brad starts with all the cake. What will be the
post-trade equilibrium? Who trades how much for what? Show the situation on
an Edgeworth-box diagram with post-trade indifference curves. (Your diagram
does not have to be 'to scale'.)
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