Question 5. Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 30 units of good X and 10 units of good Y. Consumer B is given an initial endowment of 60 units of good X and 10 units of good Y. Consumer A's utility function is given by: UA(X,Y)= X1/⁹*Y8/⁹, And consumer B's utility function is given by UB(X,Y)=X2/3y1/3 a) (8 points) Suppose the price of good Y is equal to 1 (Py=$1). Calculate the price of good X that will lead to a competitive equilibrium. b) (2 points) How much of each good does consumer A demand in equilibrium? Good X: Good Y: c) (2 points) How much of each good does consumer B demand in equilibrium? Good X: Good Y:

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Question 5. Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A
is given an initial endowment of 30 units of good X and 10 units of good Y. Consumer B is
given an initial endowment of 60 units of good X and 10 units of good Y. Consumer A's utility
function is given by:
UA(X,Y)= X1/⁹*Y8/9,
And consumer B's utility function is given by
UB(X,Y)= X2/3*Y1/3
a) (8 points) Suppose the price of good Y is equal to 1 (Py = $1). Calculate the price of good X
that will lead to a competitive equilibrium.
b) (2 points) How much of each good does consumer A demand in equilibrium?
Good X:
Good Y:
c) (2 points) How much of each good does consumer B demand in equilibrium?
Good X:
Good Y:
Transcribed Image Text:Question 5. Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 30 units of good X and 10 units of good Y. Consumer B is given an initial endowment of 60 units of good X and 10 units of good Y. Consumer A's utility function is given by: UA(X,Y)= X1/⁹*Y8/9, And consumer B's utility function is given by UB(X,Y)= X2/3*Y1/3 a) (8 points) Suppose the price of good Y is equal to 1 (Py = $1). Calculate the price of good X that will lead to a competitive equilibrium. b) (2 points) How much of each good does consumer A demand in equilibrium? Good X: Good Y: c) (2 points) How much of each good does consumer B demand in equilibrium? Good X: Good Y:
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