Question #37611

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.

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