Continuing on with demand theory. Previously we discussed the Cobb Douglas function, now we move into perfect substitutes and the corner solution. Here are some factors to keep in mind.

1. Indifference curves must interest one of the axis (not necessity or essential good)
2. Budget constraint line is such that the slope is greater than the MRS (marginal rate of substitution) (MRS x1, x2) good 2 for good 1 at the intercept (M/p2).

For example: Perfect substitutes: the solution –> spend your entire budget on the cheaper of any two goods to maximize utility. This is mathematically express like:


X1 * = M/P1 ; X2* = 0 if P1 < P2 or X1 * = 0 ; X2* = M/P2 if P1 > P2

Graphically:
corner solution graph

In an example using excises taxes, we can apply budget constraints to determine the maximum in excise taxes and lump sum taxes. An excise tax increases the relative pricing of the taxes good. Lump sum taxes alter the budget you have available.

Expressed graphically in conditions P1X1 + P2X2 = M ; MRS <> P1/P2

composite good

Given a choice between two taxes, a “representative consumer” would choose the lump sum option.