Recently, there have been several proposals to encourage conservation of oil. One proposal from Robert Frank increases the tax on gasoline, then rebates the tax revenue to consumers through a payroll tax reduction or some other means. As he states:
In my Feb. 16 column, I suggested an additional gasoline tax of $2 a gallon. All revenue would ... be returned on an approximately equal per capita basis
To look at the economics of this proposal, I decided to examine a fairly standard textbook treatment of the topic where a tax on each gallon of gas consumed is imposed along with a lump-sum tax rebate to consumers on an equal per capita basis. (I hope the microeconomists won't mind a macro guy stumbling around in their territory. This proposal is discussed in Pindyck and Rubinfeld 5th ed., pgs. 114-115.)
Here's a graph of what happens before and after the tax, and after both the tax and the rebate.
Click on figure to enlarge
The consumer starts out at point A consuming QA gallons of gasoline and has a utility level of U2. After the tax, which rotates the budget line downward as shown by the dashed budget constraint, the consumer moves to point B which is on a lower indifference curve U1, and consumption falls to QB. Finally, after the rebate which shifts the budget line outward, the consumer moves to point C and consumption increases to QC (the tangent indifference curve at point C is omitted for clarity).
Overall, the consumption of gasoline has fallen, as intended, and the consumer is worse off because the level of utility attainable at point C is below the level U2 at point A. Even though the money comes back to consumers in the form of a rebate, the reason consumption falls from A to C is because the income elasticity of demand for gasoline is relatively low (around .3 by some estimates) so that the substitution effect dominates the income effect.
In this example, a low-income household would be made worse off by the tax and rebate proposal (because indifference curve U2 is no longer attainable), but it's still possible for some low-income individuals, those who consume less gas than the value of the lump-sum rebate, to benefit. However, the substitution effect induced by the tax makes the average household worse off. To aid low income individuals, other proposals such as linking the size of the rebate to income could be examined as well.
Finally, this highlights the costs to households, but there are also potential benefits. To assess the proposal, the costs must be compared to the benefits from reduced dependence on foreign oil and the additional security that brings about, and the environmental and other benefits from lower consumption of gasoline.