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Problem: Summer break is approaching! Suppose you derive utility from days spent traveling on vacation domestically, D, and days spent traveling on vacation in a foreign country, F. Your utility function over these two "goods" is U(D,F) 4D^0.25 F^0.75. Let your budget constraint be I(D,F)=PdD+pfF where I is income, Pdis the price of domestic travel per day, and Pf is the price of foreign travel per day.
Required:
a. Determine the demand functions for domestic travel and foreign travel. Make sure you show your work - show the steps used.
b. Suppose that you've saved $800 for your summer travel, the price of domestic travel per day is $25 and the price of foreign travel per day is $100. How many days of each type of travel will you embark on?
c. Illustrate the utility function, budget constraint, and the utility-maximizing bundle associated with (b). Make sure you show the level of utility, the budget constraint intercepts, and the optimizing equilibrium.
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