Slutsky Ecuacion

148 SLUTSKY EQUATION (Ch. 8)

x2

Indifference
curves

Original budget line

Final budget line Shift Pivot x1 Income effect = total effect

Figure 8.4

Perfect complements. complements.

Slutsky decomposition with perfect

As a third example, let us consider the case of quasilinear preferences. This situation is somewhat peculiar. We have already seen that a shift in incomecauses no change in demand for good 1 when preferences are quasilinear. This means that the entire change in demand for good 1 is due to the substitution effect, and that the income effect is zero, as illustrated in Figure 8.6.

EXAMPLE: Rebating a Tax
In 1974 the Organization of Petroleum Exporting Countries (OPEC) instituted an oil embargo against the United States. OPEC was able to stop oilshipments to U.S. ports for several weeks. The vulnerability of the United States to such disruptions was very disturbing to Congress and the president, and there were many plans proposed to reduce the United States’s dependence on foreign oil. One such plan involved increasing the gasoline tax. Increasing the cost of gasoline to the consumers would make them reduce their consumption of gasoline, and thereduced demand for gasoline would in turn reduce the demand for foreign oil. But a straight increase in the tax on gasoline would hit consumers where it hurts—in the pocketbook—and by itself such a plan would be politically

EXAMPLES OF INCOME AND SUBSTITUTION EFFECTS

149

x2 Indifference curves

Original choice

Final budget line

Original budget line

Final choice

x1Substitution effect = total effect

Perfect substitutes. Slutsky decomposition with perfect substitutes.

Figure 8.5

infeasible. So it was suggested that the revenues raised from consumers by this tax would be returned to the consumers in the form of direct money payments, or via the reduction of some other tax. Critics of this proposal argued that paying the revenue raised by the tax back to theconsumers would have no effect on demand since they could just use the rebated money to purchase more gasoline. What does economic analysis say about this plan? Let us suppose, for simplicity, that the tax on gasoline would end up being passed along entirely to the consumers of gasoline so that the price of gasoline will go up by exactly the amount of the tax. (In general, only part of the tax wouldbe passed along, but we will ignore that complication here.) Suppose that the tax would raise the price of gasoline from p to p = p + t, and that the average consumer would respond by reducing his demand from x to x . The average consumer is paying t dollars more for gasoline, and he is consuming x gallons of gasoline after the tax is imposed, so the amount of revenue raised by the tax from theaverage consumer would be R = tx = (p − p)x . Note that the revenue raised by the tax will depend on how much gasoline the consumer ends up consuming, x , not how much he was initially

150 SLUTSKY EQUATION (Ch. 8)

x2 Indifference curves Final budget line

Original budget line

Pivot x1

Substitution effect = total effect

Figure 8.6

Quasilinear preferences. In the case ofquasilinear preferences, the entire change in demand is due to the substitution effect. consuming, x. If we let y be the expenditure on all other goods and set its price to be 1, then the original budget constraint is px + y = m, and the budget constraint in the presence of the tax-rebate plan is (p + t)x + y = m + tx . (8.5) (8.4)

In budget constraint (8.5) the average consumer is choosing theleft-hand side variables—the consumption of each good—but the right-hand side— his income and the rebate from the government—are taken as fixed. The rebate depends on what all consumers do, not what the average consumer does. In this case, the rebate turns out to be the taxes collected from the average consumer—but that’s because he is average, not because of any causal connection. If we cancel tx from...