Calculate the own-price elasticity of X

Reference no: EM132157553

Questions -

Q1. True or False. Explain your answer.

a) Utility function U = f(x, y) has the property that it's marginal utility of Y (MUY) is constant. Therefore, MRS for this utility function does not diminish.

b) When the price of X decreases, the substitution and income effects will both act to increase X consumption.

c) In a two-good world, the price of X (a normal good) decreases. If Y consumption decreases, then Y cannot be a normal good.

Q2. New York, Boston, or Chicago? Josie's utility function: U = 10√x + y

a) Show that the Marshall demand functions are

x_M = 5(P_y/P_x)², y_M = I/P_y - 25(P_y/P_x)

b) Show that the indirect utility function is V = 1/P_y + 25(P_y/P_x).

c) Josie currently works in New York, where P_x = 10 and P_y = 8 and I = 1,000. She receives a job offer from a company in Boston, where P_x = 5 and P_y = 10. What minimum income offer would make Josie indifferent between the 2 jobs?

d) There is also a job offer from a company in Chicago, where P_x = P_y = 10. Chicago can only offer I = 750 but they can include an award of units of X as part of her total compensation package.

These award units of X cannot be traded or sold, so they must be consumed. Does the Chicago company need to make the award of X part of the offer?

If so, how many units of X must Chicago include so that Josie is indifferent between New York and Chicago?

Q3. Consider this demand function: x = P_y√I (1 - ½P_x)

Assume P_x = ½, P_y = 1 and I = 1

a) Calculate the own-price elasticity of X.

b) Calculate the income elasticity of X.

c) Calculate the income elasticity of Y.

Reference no: EM132157553

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