For each of the following situations, find the consumer’s optimal bundle. Be sure to show your work. Also, for each case, draw the consumer’s budget constraint, indicate the optimal bundle on the graph, and accurately draw the indifference curve that runs through the consumer’s optimal bundle.

a) U(X, Y) = XY2. The consumer has $24 to spend and the prices of the goods are PX = $2 and PY = $4.

Note that the MUX = Y2 and the MUY = 2XY.

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

In equilibrium X= 3Y

c) U(X, Y) = 3X + Y. The consumer has $60 to spend and the prices of the goods are PX = $4 and PY = $1.