Doreen has preferences represented by the utility function U(x, y)  10x  5y.She consumes 10 units of good x and 9 units of good y.If her consumption of good x is lowered to 1, how many units of y must she have in order to be exactly as well off as before?

A) 20
B) 30
C) 27
D) 18
E) None of the above.

Question

Bushra Chaudhry · Accepted Answer

Final Answer : C, Explanation :  To find out how many units of good y Doreen needs to have in order to be as well off as before, we need to find the utility she derives from (1, y) and then solve for y.U(1, y) = 10(1) + 10(5y)U(1, y) = 50y + 10We want to find y such that the utility from (1, y) is the same as the utility from (10, 9).U(10, 9) = 10(10) + 10(5(9))U(10, 9) = 460So we want to solve for y in the equation:50y + 10 = 46050y = 450y = 9Therefore, Doreen must have 9 units of good y when her consumption of good x is lowered to 1 in order to be as well off as before.

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