Question

Jane receives utility from days spent traveling on va- cation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the util- ity 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.

a. Illustrate the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200.

Answer 1

Step-by-step explanation:

A point on U=800 is (5, 16)

From BL:

400*F+100D =4000

400*5+100*16 =3600<4000

Therefore u = 800 affordable.

U= 1200

F = 1200/10D

If D = 20

F = 1200/200

=6

Now from BL:

400*6+100*20= 2400+2000=4400>4000

Not affordable.

Maximization:

L = 10DF+ʎ[100*D+400*F – 4000]

Differentiating wrt D and F:

dL/dD = 10F + ʎ*100

dL/dF = 10D +ʎ*400

equating to zero;

ʎ= -F/10

ʎ=-D/40

equating the two:

F/10=D/40

D = 4F

From BL:

400*F+100*D = 4000

400F+100*4F = 4000

800F = 4000

F = 5

D = 4*5=20