4.The utility function is U(x, y) = x²y.

a) Derive the Marshallian demand for x and y.

b) Derive the Compensated demand for x and y.

c) What is the substitution effect of a price change in P_x?

d) Suppose initially, the consumer has income I = 240 and faces prices P_x= $8 and P_y= $2. If the price of y increases to $8 and income is unchanged, what must the price of x fall in order for the consumer to be exactly as well off as before the change in P_y?