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.

A. (4 points) Set up the Lagrangian for Jane's constrained utility maximization problem.

B. (12 points) Using differential calculus and algebra and your answer to A, find how much of each good he should buy if he wishes to maximize his utility subject to the constraints on his purchasing power.

C. (4 points) What is the value and interpretation of the Lagrange multiplier for this problem?

D. (4 points) How much utility is attained with the original utility maximizing amounts of foreign and domestic travel?

E. (8 points) Suppose that the price of domestic travel now increases to $200 per day with the price of foreign travel and income constant. Find the new utility maximizing amounts of foreign and domestic travel. (You need not use the Lagrangian method)

F. (10 points) Determine the decomposition basket for the substitution effect due to the change in the price of domestic travel.

G. (6 points) Find the numerical values of the income and substitution effects of the change in the price of domestic travel measure in days of domestic travel.