Answer to Question #171604 in Microeconomics for Christiana Ise

Question

Question 1: Given the utility function u = Ax^ay^b subject to the budget constraint P_xx + P_yy = B, prove that at the point of constrained utility maximization the ratio of prices Px / Py must equal the ratio of marginal utilities MU_x/MU_y.

Question 2: Consider the utility surface for two goods A and B: U = AB - 2A² - B² + 14B

What is the maximum utility level achieved?

Answer 1

Question 1

To obtain the greatest utility the consumer should allocate money income so that the last dollar spent on each good or service yields the same marginal utility.

So, Px / Py = MU_x/MU_y or MUx/Px = MUy/Py.

Question 2

If U = AB - 2A2 - B2 + 14B, then the utility is maximized when MUa/Pa = MUb/Pb.