1. (26 Total Points) Suppose a consumer's utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $48 to spend, and the price of Good X, PX = $1. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X.

a) (2 points) How much X and Y should the consumer purchase in order to maximize her utility? X* = __________________ Y* = __________________

b) (2 points) How much total utility does the consumer receive? U(X*,Y*) = _________________

c) (2 points) Now suppose PX increases to $4. What is the new bundle of X and Y that the consumer will demand? X** = __________________ Y** = __________________

d) (2 points) How much additional money would the consumer need in order to have the same utility level after the price change as before the price change? (Note: this amount of additional money is called the Compensating Variation.) Compensating Variation = ________________________

e) (2 points) How much money would the consumer be willing to pay to avoid the increase in the price of Good X from PX = $1 to PX = $4? (Note: the amount of money the consumer is willing to pay to avoid the price increase is called the Equivalent Variation.) Equivalent Variation = ________________________

f) (2 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). SE = __________________ IE = __________________

f) (14 points) In the space below, 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 XC and YC Do not scale your axes above 100. In order to receive full credit, your graph must be neat, accurate, and fully labeled