## Question from Past Microeconomics Qualifying Exam

Spring 2001 - Section II, Question four, George Mason University Give complete answers to three of the following four questions (about 25percent each) Write clear concise and legible answers.:

Construct an intertemporal model of an individual who has both productive and exchange oportunities between two periods. He has an interior initial endowment that consists mostly of present goods.

• a. Show the individual's productive ${\displaystyle (Q~1) }$ and consumptive ${\displaystyle (C~1) }$ optima at an interest rate ${\displaystyle (i~1) }$.
• b. Imagine that there is a fall in the interest rate, denoted ${\displaystyle (i~0) }$. Show what happens (graphically) to this individual's consumptive optima (C*) and productive optima (Q*) and his savings, borrowing, investment, and wealth. Give brief explanations for the changes you show.
• c. In the model you have constructed, and in general, is it at all conceivable that an individual can be worse off as a result of a fall in the interest rate? Why?
• d. "Saving need not equal investment for any individual but they must equal for the market as a whole." Comment briefly.

• a.

The interest rate is given by the slope of the budget line, i.e. -Δc1/Δc0 = 1 + r.

• b. A decrease in the interest rate will change the slope of the budget line to be flatter. This leads to greater wealth, W*0, and to the individual ending up on a higher indifference curve. Consumption in period 0 will rise. But consumption in period 1 might be lower. Depending on the shape of the indifference curves this can vary however, i.e. more will be consumed in both periods. Savings will usually decrease because the interest rate is lower and individualy will borrow more. Investment should increase.
• c. Yes. If an agents preferences are biased towards future consumption, i.e. corner solution or near corner solution, the agent might be worse off, i.e. end up on a lower indifference curve than before.
• d. True. For an individual agent in an exchange economy at a certain point in time savings don't have to equal investment. Investment might be greater than saving indicating that the agent is borrowing some of the savings of other individuals to be repaid out of her future investment yield.
For the overall economy however the rate of interest will equilibrate the aggregate demand for investment and supply of savings.