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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.
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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