Answer to Question #4512 in Microeconomics for Marie Maloney

Question

Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F) = 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $4000. Suppose F is on the horizontal axis and D is on the vertical axis. Jane's marginal rate of substitution between F and D is equal to

Answer 1

U(D,F) = 10DF. P(d)= $100, P(F)= $400& Budget= $4000.

The marginal rate of substitution(MRS) of good or service X for good or service Y (MRSxy) is equivalent to the marginal utility of X over the marginal utility of Y. Formally,

MRSxy=MUx/MUy

When consumers maximize utility with respect to a budget constraint, the indifference curve is tangent to the budget line, so MRSxy=Px/Py. Or in our case MRS=4 (where instead of X-F, instead of Y-D).

Let’s check it:

MRSfd=MUf/MUd=10D/10F=D/F

To find the equilibrium we should solve the system of these two equations:

MUf/MUd=Pf/Pd

and& PfF+PdD=B

D/F=400/100 => D=4F

100*4F+400F=4000

where& F=5, D=20 => MRSfd=4