# Mary's Utility function is given by U(X,Y)=X^a Y^(1-a) , the price of X and Y are given by px and py,

respectively, and total income is equal to I.

a) Write down Mary's budget constraint.

For the rest of the question, consider the case in which a = 0.5.

b) Find the consumption bundle Lisa will optimally choose.

c) Calculate Mary's total expenditure on good X. Compute the share of income spent on the

good X?

d) Suppose now that the price of X doubles. Recalculate the share of income spent on the

good X by Mary. What is the interpretation of the parameter a?

e) Now suppose that Mary's utility function is U(X,Y)=Xa+0.3Y1-a-0.3 and that the price of X goes back to px. Without solving the maximization problem, how many unit of X will Lisa buy now?

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