1. Suppose a consumer's utility function is given by U(X,Y) = X^1/2*Y^1/2.Also, the consumer has $72 to spend, the price of Good X, P_X = $1, and the price of Good Y, P_Y = $1.

a) (4 points) How much X and Y should the consumer purchase in order to maximize her utility?

b) (4 points) How much total utility does the consumer receive?

c) (4 points) Now suppose P_X increases to $9.What is the new bundle of X and Y that the consumer will demand?

d) (4 points) Of the total change in the quantity demanded of Good X, how much is due to the substitution effect and how much is due to the income effect? (Note: since there is an increase in the price of Good X, these values will be negative).

f) (14 points) On the following page, draw on a graph the

original budget constraint (draw this in black)

new budget constraint (draw this in green)

compensated budget constraint (draw this in red)

Also, on your graph, indicate the optimal bundle on each budget constraint.

Label the optimal bundle on the original budget constraint X* and Y*

Label the optimal bundle on the new budget constraint X** and Y**

Label the optimal bundle on the compensated budget constraint X^C and Y^C

2. Suppose that Lynn enjoys sugar in her coffee.She has very particular preferences, and she must have exactly three spoonfuls of sugar for each cup of coffee.Let C be the number of cups of coffee, and S be the number of spoonfuls of sugar.Also, let P_C be the price of a cup of coffee.Suppose Lynn has $12 to spend on Coffee and Sugar.Also, the price of Sugar is $.20 per spoonful.

Graph Lynn's Price consumption curve for prices, P_C = $.60, P_C = $.90, and P_C = $1.80.Please put the number of cups of coffee (C) on the horizontal axis, and the number of spoonfuls of Sugar (S) on the vertical axis.Be sure to graph each budget constraint associated with each price of Coffee, identify Lynn's optimal bundle on each budget constraint, and make sure your graph is labeled carefully and accurately.