Answer to Question #219960 in Economics for Spencer

Question

Q1. A consumer has a utility function given by
ln U = 5 ln x + 3 ln y
if the budget constraint is given by
10x + 14y= 124, find
a. the optimal quantities of the two goods that the consumer should purchase in order to maximize utility, subject to the budget constraint.

b. the value of the consumer’s marginal utility of money at the optimum.

c. the marginal rate of substitution (MRS) of x for y and determine its direction at the optimum

Q2. Assume the logarithmic transformation of a utility function, for the consumption of two commodities is given by
ln U = ln4 + 0.5ln X + 0.25lnY

(a) if the price of X is $2.50 and that of Y is $4.00, calculate the optimal combination for an income of $50.00.

b) Determine and interpret the value of the Lagrange multiplier.

Answer 1

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