Suppose Elizabeth’s preferences can be described by the Cobb-Douglas utility function, u(x_1, x_2 ). She consumes two goods only. The price of good 1 is p1 and price of good 2 is p2. Her budget is M. It is known that Elizabeth’s optimal consumption bundle is (7,7), which gives her utility Ubar. If we plot the indifference curve U(x_1, x_2 ) = Ubar on the diagram, where consumption of good 1 is on the horizontal axis and the consumption of good 2 is on the vertical axis, what can we tell about the absolute value of the MRS at the point (6, x_2^* ) which belongs to this indifference curve? a) It is below the price ratio p1/p2. b) It is above the price ratio p1/p2. c) It is above 1. d) It is below 1. e) We can’t make any conclusion because we don’t know the exact value of x_2*

Microeconomic Theory
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ISBN:9781337517942
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Chapter3: Preferences And Utility
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Problem 3.2P
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2. Suppose Elizabeth’s preferences can be described by the Cobb-Douglas utility function, u(x_1, x_2 ). She consumes two goods only. The price of good 1 is p1 and price of good 2 is p2. Her budget is M. It is known that Elizabeth’s optimal consumption bundle is (7,7), which gives her utility Ubar. If we plot the indifference curve U(x_1, x_2 ) = Ubar on the diagram, where consumption of good 1 is on the horizontal axis and the consumption of good 2 is on the vertical axis, what can we tell about the absolute value of the MRS at the point (6, x_2^* ) which belongs to this indifference curve?

a) It is below the price ratio p1/p2.

b) It is above the price ratio p1/p2.

c) It is above 1.

d) It is below 1.

e) We can’t make any conclusion because we don’t know the exact value of x_2*

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