Question

2) Assume that utility is given by Utility-U(X,Y)-X03yo7 a) Calculate the ordinary demand functions, indirect utility function, and expenditure function. b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good X. Use the results from part (b) together with the ordinary demand function for good X to show that the Slutsky equation holds for this case. c) d) Prove that the expenditure function calculated in part (a) is homogeneous of degree 1 in prices. Give an intuitive description of what this means. e) Suppose that the utility function given in this problem represents your preferences for the monthly rental of xylophones (X) and yaks (Y). The government, out of their belief that yaks are essential for the basic happiness and welfare of every American, has decided to subsidize yak rentals. Suppose the monthly rental price of X is $10, the monthly rental price of Y is $10, and your monthly income is $100. If the government pays 50 percent of the monthly rental price for yaks, how many yaks and xylophones will you rent? How much money will the government have to spend subsidizing your yak consumption? Is there a less expensive way for the government to increase your welfare to the level obtained with the subsidy? Explain and show mathematically.

Answer 1

03.0. uつ a) MRSP condition at 0-3 0-3了 indirect-utality function i。UR49 0.