Answer to Question #73779 in Macroeconomics for Paddy

Question

Mark’s preferences over two goods are given by the following utility function
U(x1,x2) = x1x2 + 2x1
and his financial resources are unlimited. The prices in the market are P1 = €4 and P2 = €2.
a) Does one observe that “more is better” in the case of each good?
b) In the case of each good, how does marginal utility behave as consumption increases?
c) What are the optimal quantities that Mark should consume? Comment.
d) If one were to limit Mark’s financial resources to income I (a finite amount), how much
would he spend in total?

Answer 1

U(x1,x2) = x1x2 + 2x1, P1 = €4 and P2 = €2.
a) Mark observes that “more is better” in the case of each good, as total utility increases according to increase in consumption.
b) In the case of each good marginal utility decreases as consumption increases.
c) The optimal quantities that Mark should consume can be found at point, for which MU1/P1 = MU2/P2.
d) If one were to limit Mark’s financial resources to income I (a finite amount), then the optimal quantities that Mark should consume can be found at point, for which MU1/P1 = MU2/P2 and P1*Q1 + P2*Q2 = I, where I is income and Q1, Q2 are optimal quantities.