2) (24 points) For each of the following situations, draw the consumer's budget constraint and indicate the consumer's optimal bundle on the budget constraint. Make sure your graph is accurate and clearly labeled. a) U(X,Y) = X1/3Y2/3. The consumer has $36 to spend and the prices of the goods are PX = $2 and PY = $1. Note that the MUX = (1/3)X-2/3Y2/3 and the MUY = (2/3)X1/3Y-1/3.

b) U(X,Y) = MIN(2X,Y). The consumer has $40 to spend and the prices of the goods are PX = $3 and PY = $1.

c) U(X,Y) = 2X + 3Y. The consumer has $30 to spend and the prices of the goods are PX = $2 and PY = $5.