## Simple Economics Problems.

1. Using graphical analysis, show the optimal choice between two goods for a
consumer interested in maximizing utility subject to a budget constraint
when the indifference curves are concave to the origin. Be sure to explain
in your own words why the consumer chooses where she does.

Figure 1: Concave Indifference Curves

2. A consumer purchases two goods, $x_1$ and $x_2$. The utility function is
$U (x_1, x_2) = x_1x_2$. The marginal utilities are $MUx_1 = x_2$ and $MUx_2 =
x_1$
. The prices are $Px_1$ and $Px_2$and income is $I$.

Given this information, show that the equation for the demand curve
for $x_1$ is $x_1 = I/2Px_1$.