Autumn 2011

Dr. Mani Problem Set 2 Due Date: Oct31, Monday – between 9 & 11 AM in room S 2.132

Please keep a copy of your assignment and show all your work clearly.

(1) Mr. J. Bond, a retired movie actor, consumes only grapes and the composite good Y (i.e. price of Y is £1). His income consists of £10000 a year from his investment fund plus the proceeds of whatever he sells of the 2000 bushels of grapes he harvests annually from his vineyard in Tuscany. Last year, grapes sold at £2 per bushel and Bond consumed all 2000 bushels of his grapes, in addition to 10,000 units of Y. This year, the price of grapes is £3 per bushel (and the price of the composite good Y is the same as before). If Bond

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Shirley thinks a 16-ounce can of beer is just as good as two 8-ounce cans. Lorraine only drinks 8 ounces at a time and hates stale beer, so she thinks a 16-ounce can is no better or worse than an 8-ounce can.

(a) Write a utility function that represents Shirley's preferences between commodity bundles comprised of 8-ounce cans and 16-ounce cans of beer. Let X stand for the number of 8-ounce cans and Y stand for the number of 16-ounce cans. (b) Write down a utility function to represent Lorraine’s preferences. (c) Would the function utility U(X, Y ) = 100X+200Y represent Shirley's preferences? How about U(X,Y) = X + 3Y?

(6) Suppose that a typical research student at the University of Warwick lives in a two good world, books ( x ) and beer ( y ), with utility function u(x, y) = x1/5 y4/5 . The price of book and beer are £50 and £10, respectively. (d) If a research student gets £1000 as a scholarship, then find his demand for book and beer. (e) Show that the expenditure on beer is 4 times as much as that on