## 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. *