E (Ipts) Consider a consumer with the utility function U(X,Y} = Inl'Jf +11?) and suppose that the prices of goods and income level are given by p: = $2, pf = $4 and the income of consumer is I = $120. a} Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. In) Now, consider another consumer with utility U(X,l") = v? + VT, facing d) the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. Finally, considera different consumer with utility U(X.l'} = 3N)? + if?) facing the same prices and income level. Compute this consumer's optimal consumption levels of goods X and Y and the maximum utility level that she can attain. Compare your ndings in parts (a),(b) and {c}. 1What difference does having the "In" in the utility function make? How does multiplying a utility function with a constant affect the solution of the utility maximization