2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current income is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope.. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint.

2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current income is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope.. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.7P

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2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
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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*