Problem1 (Substitution and Income effect, Slutsky method) A rational consumer has preferences for x and y summarized by the utility function U(x,y) = x!/3y?/3, 1. Find the consumer's demand for X and demand for Y. Show your work or explain your reasoning. Suppose the consumer starts with a budget M= 60 and faces prices px = py = 1. 2. 3. What is the consumer's optimal bundle? Show your work or explain your reasoning. At new ptices with a budget of M = 60, what bundle would the consumer buy? If the price of X increases to p'x = 4, 4. 5. 6. 7. What is the 'Slutsky' compensation? After receiving this compensation, at new prices, what bundle would the consumer purchase? Using the Slutsky method, what are the substitution and the income effects of the higher price of X on the consumer's purchases of X and Y? Mlustrate in an X/Y diagram. Make sure yout graph includes all budget lines and indifference cutves needed to illustrate the otiginal optimal bundle, the new optimal bundle, and the 'Slutsky' compensated bundle