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 $50, the price of a day spent traveling in a foreign country is $300, and Jane’s annual travel budget is $1000. a) Illustrate the indifference curve associated with a utility of 400 and the indifference curve associated with a utility of 1000. b) Graph Jane’s budget line on the same graph. c) Can Jane afford any of the bundles that give her a utility of 400? What about a utility of 1000? d) What is the optimal bundle for Jane, what is the maximum utility? e) If there is a special rate for travelling in a foreign country, the price decreases to $200 per day, graph the new budget line. What is the optimal bundle for her now?

Answer 1

U = 10 DF

Pd = $50 and Pf = $300.

Income (M) = $1000.

(a) Total utiltiy =400.

10 DF = 400

DF = 40

D = 40/F

It implies that when D=4 then F= 10 or D=10 then F=4.

By plotting these we get the indifference curves.

Now, when utility = 1000

10 DF = 1000

DF = 100

D= 100/F

It implies that when D=10 ,F= 10 or When D= 20 then F=5 or when D=5 then F=20.

By plotting these points we can get the indifference curve.

(b) Budget constraint :

Pd (D) + Pf(F) = M

50 D + 300 F = 1000

When D=0, then F=3.33

When F=0, then D=20.

By plotting these points we get the budget line, where horizontal axis denote the quantity of D and vetical axis denote the quantity of F.

(c) NO, Jane cannot afford any of the bundles tht give her a utility of 400 or utiltiy of 1000. Because these indifference curves lies outside the budget constraint and consumer is not able to afford these.

(d) To calculate the otimal bundle equate MRS with price ratio,

MRS = MUd /MUf

MUd = 10F

MUf = 10D

MRS = 10F/10D = F/D

MRS = F/D

And Pd= 50

Pf = 300,

MRS = F/D = 50/300

D= 6F

Now, put this into budget constraint . we get

50(6F) + 300F = 1000

600 F = 1000

F = 1.66

D = 6(1.66) = 9.96

D= 9.96.

(e) When Pf decreases to $200.

MRS = F/D = 50/200

D= 4F

Now, putting this into budget constraint , we get:

50 D + 200 F = 1000

50 (4F) + 200F = 1000

400 F = 1000

F = 2.5

D = 4(2.5)

D=10.