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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 show all work a) Suppose the price 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: c)What is the marginal rate of substitution for consumer A at the 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 show all work a) Suppose the price 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: c)What is the marginal rate of substitution for consumer A at the competitive equilibrium?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
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

show all work

a) Suppose the price 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:

c)What is the marginal rate of substitution for consumer A at the competitive equilibrium? 

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