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(a) Write an equation for Clara's indifference curve that goes through the point (X,Y) = (2,8). (b) What is Clara's marginal rate of substitution (MRS)? (c) Suppose that the price of each good is 1 and that Clara has an income of 11. Write down Clara's budget line. Now write down an equation the sets the absolute value of the MRS equal to the price ratio. With these two equations, find Clara's optimal choices of X and Y.

(a) Write an equation for Clara's indifference curve that goes through the point (X,Y) = (2,8). (b) What is Clara's marginal rate of substitution (MRS)? (c) Suppose that the price of each good is 1 and that Clara has an income of 11. Write down Clara's budget line. Now write down an equation the sets the absolute value of the MRS equal to the price ratio. With these two equations, find Clara's optimal choices of X and Y.

Micro Economics For Today
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 11SQ
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Clara's utility function is U(X, Y) = (X + 2)(Y + 1), where X is her consumption of good X and Y is her consumption of good Y. (a) Write an equation for Clara's indifference curve that goes through the point (X,Y)= (2,8). What is Clara's marginal rate of substitution (MRS)? Suppose that the price of each good is 1 and that Clara has an income of 11. Write down Clara's budget line. Now write down an equation the sets the absolute value of the MRS equal to the price ratio. With these two equations, find Clara's optimal choices of X and Y. (b) (c) Solution: a) Utility at (2,8) is 4*9=36 ⇒ Y = c)X = 1 and X + Y = 11 ⇒ X = 5, Y = 6. Y+1 X+2 36 X+2 1. b) d = Y+1 X+2*
Transcribed Image Text:Clara's utility function is U(X, Y) = (X + 2)(Y + 1), where X is her consumption of good X and Y is her consumption of good Y. (a) Write an equation for Clara's indifference curve that goes through the point (X,Y)= (2,8). What is Clara's marginal rate of substitution (MRS)? Suppose that the price of each good is 1 and that Clara has an income of 11. Write down Clara's budget line. Now write down an equation the sets the absolute value of the MRS equal to the price ratio. With these two equations, find Clara's optimal choices of X and Y. (b) (c) Solution: a) Utility at (2,8) is 4*9=36 ⇒ Y = c)X = 1 and X + Y = 11 ⇒ X = 5, Y = 6. Y+1 X+2 36 X+2 1. b) d = Y+1 X+2*
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