Answer to Question #169490 in Microeconomics for Hassan

Question

Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling in a foreign country (F) as given by the utility U(D, F) = DF. The price of a day spent traveling domestically is $160 and in a foreign country $200. Jane’s annual budget for traveling is $8,000 a) Find Jane’s utility maximizing choice of days traveling domestically and in a foreign country. Find also her utility level from consuming that bundle. b) Suppose that the price of domestic traveling increases to $250 per day. Calling her budget for traveling $ x, (suppose now it is unknown) find the demand for D and F under the new prices as a function of x. c) Compute the quantities demanded with the new prices and the original income. d) Find the income necessary to make Jane reach the same utility level as before the price change as in part (a).

Answer 1

U(D,F) = 10DF. P(d)= $160, P(F)= $200& Budget= $8000.

The marginal rate of substitution(MRS) of good or service X for good or service Y $(MRS_{xy} )$ is equivalent to the marginal utility of X over the marginal utility of Y. Formally,

$MRS_{xy} =\frac{MU_x} {MU_y}$

When consumers maximize utility with respect to a budget constraint, the indifference curve is tangent to the budget line, so $MRS_{xy} =\frac{Px} {Py}$ . Or in our case MRS=5 (where instead of X-F, instead of Y-D).

$MRS_{fd} =\frac{MU_f} {MU_d} =\frac{10D} {10F} =\frac{D} {F}$

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

$\frac{MU_f} {MU_d} =\frac{Pf} {Pd}$

$\frac{D} {F} =\frac{200} {160} = 1.25 and D=5F$

$160 ×5F+200F=8000$

where F=8, D=40; $MRS_{fd}$ =5