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 =<br />
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.