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3. Given the following information; solve the consumer's problem by finding the optimal demand functions for X and Y:
U(X, Y) = X ^ (1/3) * Y ^ (2/3)
Also, you are given the following initial market conditions:
Px =\$6
Py =\$4
M =\$360
a. Setup the Optimization Problem
b. Find the First Order Conditions of Optimization
c. Find X ^ * and Y ^ *
d. Graph the solution and explain the economic intuition behind the graph: i.e. What are the conditions met at the optimal bundle? Introduce another consumption bundle and explain why it is NOT the optimal.
e. If income doubles, what will the new x ^ * and Y ^ * be?
f. If your preferences change and you prefer X and Y equally; illustrate how the consumer's optimization problem might change and solve for the new X ^ * and Y ^ * under your new model.
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