Consider a consumer whose utility function is u(x,y) = √xy MRS(x,y) = xy (a) Assume the consumer has income $120 and initially faces the prices px = $1 and py = $1. How much x and y would they buy? Draw the budget constraint and the demands. (b) Next, suppose the price of x were to increase to $2. How much would they buy now? Draw this in the same figure. (c) Decompose the total effect of the price change on demand for x into the substitution effect and the income effect. That is, determine precisely how much of the change is due to each of the component effects. (Hint: See the lecture notes for the two properties that determine the location of "z", the reference point for distinguishing the income and substitution effects.) 1
