1. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y)=X*Y UB(X,Y)=X*Y³ Therefore: For consumer A: MUX-Y; MUY-X For consumer B: MUX-Y³; MUY = 3XY² The initial endowments are: A: X= 10; Y = 6 B: X= 14; Y = 19 Suppose the price of Y, PY=1. Calculate the price of X, Px that will lead competitive equilibrium.
1. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y)=X*Y UB(X,Y)=X*Y³ Therefore: For consumer A: MUX-Y; MUY-X For consumer B: MUX-Y³; MUY = 3XY² The initial endowments are: A: X= 10; Y = 6 B: X= 14; Y = 19 Suppose the price of Y, PY=1. Calculate the price of X, Px that will lead competitive equilibrium.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![1. Suppose there are two consumers, A and B.
The utility functions of each consumer are given by:
UA(X,Y)=X*Y
UB(X,Y)=X*Y³
Therefore:
For consumer A: MUX-Y; MUY-X
For consumer B: MUX-Y³; MUY-3XY²
The initial endowments are:
A: X= 10; Y = 6
B: X-14; Y = 19
a)
Suppose the price of Y, Py = 1. Calculate the price of X, Px that will lead to a
competitive equilibrium.
b)
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
What is the marginal rate of substitution for consumer A at the competitive
c)
equilibrium?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cbb3a16-d911-4d4e-ac4a-559489c6b9b1%2F8985792b-aaf1-4cb1-a446-4febd325bdbd%2F4bmtrdt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose there are two consumers, A and B.
The utility functions of each consumer are given by:
UA(X,Y)=X*Y
UB(X,Y)=X*Y³
Therefore:
For consumer A: MUX-Y; MUY-X
For consumer B: MUX-Y³; MUY-3XY²
The initial endowments are:
A: X= 10; Y = 6
B: X-14; Y = 19
a)
Suppose the price of Y, Py = 1. Calculate the price of X, Px that will lead to a
competitive equilibrium.
b)
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
What is the marginal rate of substitution for consumer A at the competitive
c)
equilibrium?
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