Perfect substitutes almost always have boundary solutions, which are found in a different way than interior optima. The demand functions from perfect substitutes are contingent; specifically, they depend on the slopes of the indifference curves and the budget line. Consider a utility function u(x1,x2)=ax1+bx2 and a general-form budget line p1x1+p2x2=m.

If the absolute value of the slope of the indifference curve, a/b, is greater than the absolute value of the slope of the budget line, p1/p2, the consumer will find it optimal to consume.

1. Choose one:

a. any combination of goods 1 and 2 she can afford.
b. all of good 2 she can afford and none of good 1.
c. a combination of goods 1 and 2 such that exactly half her income is spent on each good.
d. all of good 1 she can afford and none of good 2.

2. In such a case, demand for good 1 is x∗1(p1,p2,m)=x1∗(p1,p2,m)=

a. m/p2
b. m/2p2
c. 0
d. m/p1
e. m/2p1