Section 0 Study Problems

These four study problems are to be completed in advance of the first day of the course.  Working these problems will provide some basic but important background to the lectures of week 1.

More generally, study problems play a key role in the class, helping students learn the core material. For each study problem, a list of the objectives is provided.

Problem	Core ideas
Problem 1: Optimal consumption over time in a simple two period setting, with income in each period. Answer as PDF	Intertemporal decision problems for households are similar to the static decision encountered in EC701. The intertemporal problem with time-varying income is similar to the static problem with endowments of goods However, in an intertemporal setting, there are particular forms of utility used and particular normalizations of prices (choices of numeraire). For some such decision problems, there are analytical solutions that can be worked out. A higher interest rate leads to a higher growth rate of consumption, in a manner originally described by Irving Fisher
Problem 2: Optimal labor supply in a static setting Answer as PDF	Optimal labor supply can be viewed as the optimal "demand for leisure" in a manner originally suggested by John Hicks. The wage is then the price of leisure. Since the individual has an endowment of time, a change in the wage rate has an important positive income effect on leisure demand as well as a negative substitution effect. For some utility and endowment specifications, these two effects exactly cancel out. Sometimes, an analytical solution obtains with a specified utility. Other times, the method of comparative statics must be employed, as developed in EC701
Problem 3: An asset accumulation difference equation Answer as PDF	Assets accumulate over time, given saving and the return on assets. This leads to a difference equation for assets in a simple setting. Solving the asset difference equation forward provides a link between the time series of interest rates and the present value price of future consumption
Problem 4: Optimal consumption over time with many periods Answer as PDF	Intertemporal consumption choice with many periods can be modeled as a generalization of the two period analysis of problem 1, using the asset accumulation results of problem 3. A particular example with an analytical solution is considered.