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Suppose you have a total income of I to spend on two goods x1 and x2, with unit prices p1 and p2 respectively. Your taste can be represented by the utility function u left parenthesis x subscript 1 co...

Suppose you have a total income of I to spend on two goods x1 and x2, with unit prices p1 and p2 respectively. Your taste can be represented by the utility function u left parenthesis x subscript 1 comma x subscript 2 right parenthesis equals x subscript 1 cubed x subscript 2 squared (a) What is your optimal choice for x1 and x2 (as functions of p1 and p2 and I) ? Use the Lagrange Method. (b) Given prices p1 and p2, what is the maximum utility you can attain with an income I? What do we call this function? (c) Given prices p1 and p2, what is the minimum expenditure you need to attain a utility level u? What do we call this function? (Hint: use your result in b) (d) Using your result in (c), derive the compensated demand functions h1 and h2 using the Shephard's Lemma. (e) Set up the expenditure minimization problem to find the compensated demand functions. Verify that your answers are the same as in (d).

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Griven that A total income ta o Spend on tw o or) 1+x, my左 9 px,下 2f

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