Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y)=X³ Y UB(X,Y)=X*Y Therefore: • For consumer A: MUx= 3X2Y; MUY = X³ . For consumer B: MUX = Y; MUY = X The initial endowments are: A: X= 30; Y = 90 B: X= 50; Y 60 a) (16 points) Suppose the price of Y, Py = 1. Calculate the price of X, Px that will lead to a competitive equilibrium. b) (8 points) How much of each good does each consumer demand in equilibrium? Consumer A's demand for X: Consumer A's demand for Y: Consumer B's demand for X: Consumer B's demand for Y: c) (4 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium?
Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y)=X³ Y UB(X,Y)=X*Y Therefore: • For consumer A: MUx= 3X2Y; MUY = X³ . For consumer B: MUX = Y; MUY = X The initial endowments are: A: X= 30; Y = 90 B: X= 50; Y 60 a) (16 points) Suppose the price of Y, Py = 1. Calculate the price of X, Px that will lead to a competitive equilibrium. b) (8 points) How much of each good does each consumer demand in equilibrium? Consumer A's demand for X: Consumer A's demand for Y: Consumer B's demand for X: Consumer B's demand for Y: c) (4 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Suppose there are two consumers, A and B. The utility functions of each consumer are
given by:
UA(X,Y)= X³ Y
UB(X,Y)= X Y
Therefore:
• For consumer A: MUx = 3X2Y; MUY = X³
. For consumer B: MUX = Y; MUY = X
The initial endowments are:
A: X= 30; Y = 90
B: X= 50; Y = 60
a) (16 points) Suppose the price of Y, Py = 1. Calculate the price of X, Px that will lead to
a competitive equilibrium.
b) (8 points) How much of each good does each consumer demand in equilibrium?
Consumer A's demand for X:
Consumer A's demand for Y:
Consumer B's demand for X:
Consumer B's demand for Y:
c) (4 points) What is the marginal rate of substitution for consumer A at the competitive
equilibrium?
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