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, $\displaystyle x_1$ and $\displaystyle x_2$. The utility function is

$\displaystyle U (x_1, x_2) = x_1x_2$. The marginal utilities are $\displaystyle MUx_1 = x_2$ and $\displaystyle MUx_2 =

x_1$. The prices are $\displaystyle Px_1$ and $\displaystyle Px_2 $and income is $\displaystyle I$.

Given this information, show that the equation for the demand curve

for $\displaystyle x_1$ is $\displaystyle x_1 = I/2Px_1$.