Example problem

Suppose you have income $y=5$ the following utility function over consumption (c):

$u(c) = \sqrt c$

Suppose you have the opportunity to take a gamble where you can win $x=4$ with 50% probability or lose $x=4$ with 50% probability.

Show that you will prefer not to take this gamble.

Try this example problem yourself to check your understanding. Once you've given it a try, watch the video to see me walk through it.

Note: There is a mistake in the following video at 0:57. The mistake is explained in the text after the video.

At around 0:57, the video above states "with 50% probability we have the utility of losing. We started with 5 but now we lose 1." This is a mistake. The video should have stated "with 50% probability we have the utility of losing. We started with 5 but now we lose 4." The video is correct thereafter though, and correctly writes that the utility of losing is equal to 1.

Example Problem

Suppose an individual lives for two periods. Their income in periods 1 and 2 is $y_1$ and $y_2$ respectively. Consumption in periods 1 and 2, is denoted $c_1$ and $c_2$ respectively, and prices are also denoted $p_1$ and $p_2$. The interest rate is $r$.

Consider the following diagram of an indifference curve and intertemporal budget constraint.

Draw (or imagine) what happens to the intertemporal budget constraint under each condition:

    1. The price $p_1$ falls.

    2. Income $y_2$ increases.

    3. The interest rate $r$ falls.

Try this example problem yourself to check your understanding. Once you've given it a try, watch the video to see me walk through it.

Did you feel like any of the videos above were confusing, or could use more detail? If you're a student at Iowa State University, send me a quick note at mclancy@iastate.edu, referencing the video number and your issue, if applicable.