Answer to Question #37611 in Microeconomics for Zach Sonenblum

Question

Anna consumes only two commodities, x1 and x2, and her preferences are such that her utility function over these two commodities is given by:
U(x1,x2)=4x1ax21-a,
where 0<a<1.
Part (i): Identify the marginal utility that Anna receives from an additional unit of x1 and of x2. That is, find MU1(x1,x2) and MU2(x1,x2).
Part (ii): Using your answer to part (i), derive Anna’s demand function for x1, x1*(p1,p2,M). Part (iii): Using your answer to part (i), derive Anna’s demand function for x2, x2*(p1,p2,M).
Part (iv): Initially, Anna had an income of M=$60 and faced prices p1=$5 and p2=$4. Identify Anna’s initial bundle (x1*, x2*). Hint: Your answers should be in terms of a, as you have not been given an explicit value.
Part (v): After a sudden price change, Anna had an income of M=$60 and faced prices p1=$5 and p2=$2. Identify Anna’s new bundle (x1*, x2*). Hint: Your answers should be in terms of a, as you have not been given an explicit value.

Answer 1

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