1. Consider the utility functions of the form . Show that the implied
demand curves are
(see attached file for equations)
2. Suppose a consumer will have income this year and next year. He or she consumes this year and next year, being able to borrow and lend at interest rate . Assume the consumer maximizes the utility of consumption over these two years.
a. Derive the comparative statics for this problem. Will an increase in this year's income necessarily lead to an increase in consumption this year?
b. Prove that the consumer will be better off or worse off if the interest rate rises if he/she was net saver or dissever this year.
Using Lagrangian technique, maximize utility subject to the budget constraint.