Question 3 Randy has the utility function U (I. y) = 3(y + 1}- The price of a: is $2 and the price of y is $1. Income is $10. a. How much :1: does Randy demand? How much y? b. If his income doubles and prices stay unchanged? will Randy's demand for both goods double? c. If Randy chooses the bundle (I. y} = (3.4}. what level of utility does he get? Answer To set his MRS equal to the price ratio: Randy sets (MU/1 = 2. His budget constraint is 2:: + y = 10. (a) Solve these two equations to nd that .r = 11/4 and y = 9/2. {b} If his income doubles and prices stay unchanged1 his demand for both goods does not double. A quick way to see this is to note that if quantities of both goods doubled, the MRS would not stay the same and hence would not equal the price ratio! which has stayed constant. (c) The level of utility obtained is U(3.4) = 3(4 + l) = 15