Usher Political Economy (Blackwell, 2003)

The demand curve is based on an ordering of projects, programs, and activities, from best to worst, according to their benefit per dollar of public expenditure, where “benefit” refers to the sum of all benefits to whomsoever they may accrue. For any given expenditure, E, the height of the demand curve is the highest attainable benefit per dollar of expenditure among all projects, programs, or activities that remain when E has already been spent on other more advantageous projects. The demand curve is downward sloping by construction. It cannot be otherwise when projects, programs, and activities are ordered by their benefit per dollar of expenditure.

The supply curve shows the full cost to the tax payer per dollar of additional public expenditure as an increasing function of total public expenditure. For any expenditure, E, the height of the supply curve is ( R + L)/ R as defined in equation (17) of chapter 4 where R is the extra revenue acquired, where L is the additional excess burden of taxation and where public revenue and expenditure are necessarily the same. Such a supply curve has already been developed in two different contexts. In chapter 4, the height of the supply curve of public expenditure was reflection of the loss of surplus associated with the tax-induced shift in consumption from taxed cheese to untaxed bread. The extra bread consumed was worth less to the tax payer than the cheese he might have consumed instead, the tax each person saved by switching from cheese to bread had to be paid by somebody else, the required tax rate was slightly higher than it would otherwise have been, and there was a less than optimal mix of bread and cheese consumed. In chapter 9, the deadweight loss in taxation was a reflection of the reduction in total output from the tax-induced switch from paid work to untaxable do-it-yourself activities. Since do-it-yourself activities were exempted from tax, each person was inclined, in his own interest to do less work for pay and more do-it-yourself activities than would be appropriate if all sources of income could be taxed.

The switch in consumption from more taxed to less taxed goods and the switch from paid work to do-it-yourself activities are not the only sources of the excess burden of taxation. As mentioned in chapter 4, the income tax entails a double taxation of saving, inducing a switch from investment to consumption not unlike the switch from cheese to bread. Taxation also provokes a diversion of private resources from the production of goods to legal tax avoidance and illegal tax evasion, together with a diversion of public expenditure from the provision of benefits like roads, schools, and hospitals to the detection and punishment of tax evasion. There is a compounding of the different sources of the excess burden of taxation. As shown in equation (27) of chapter 4, the marginal cost of public funds is a reflection of the shrinkage of the tax base in response to an increase in the tax rate. Demonstrated for a bread and cheese economy, this remains true of any and every source of the tax-induced shrinkage of the tax base.

The supply curve begins at a height of 1 because, when public expenditure is tiny, the required tax rate is tiny as well, and there is virtually no excess burden per dollar of public revenue. The supply curve rises steadily as additional public expenditure requires ever-higher tax rates and generates an ever-increasing excess burden of taxation. Along the supply curve for the bread and cheese economy in table 4.1, the full cost to the tax payer per additional dollar of public expenditure rose steadily from 1.07 when public revenue is $3.50 per person per week, to 1.3 when public revenue is $6.00 dollars per person per week, to $1.83 when public revenue is $7.50 per person per week. A similar story could be told about the choice in chapter 9 between paid labor and

do-it-yourself activities. In general, the supply curve would reflect a compounding of all sources of the excess burden of taxation.

The economy-wide marginal cost of public funds (indicated as mcpf on figure 10.1) identifies the cut-off for public projects, programs, and policies. Those with benefit–cost ratios above the marginal cost of public funds are undertaken. Those with benefit–cost ratios below the marginal cost of public funds are not. In practice, the economy-wide marginal cost of public funds varies from time to time and from place to place in accordance with the characteristics of the economy and the share of the government in the national income. The determination of the marginal cost of public funds is complex and judgmental because every facet of taxation must be taken into account. Estimates at various times and places suggest that the marginal cost of public funds might be in the order of 1.5, and we shall suppose that to be so. A marginal cost of public funds of 1.5 means that the cost to the tax payer of any program or project is $1.50 per extra dollar of tax revenue acquired. Table 10.3 above shows the costs and benefits of the five roads as they appear to the accountant in the Ministry of Transport. To say that the marginal cost of public funds is 1.5 is to say that all costs should be marked up by 50 percent to account for the excess burden of taxation. With this rule in place, the recalculation of costs and benefits of the five roads is as shown in table 10.4.

Ignoring deadweight loss and postulating a market-wide rate of interest of 8 percent, we tentatively inferred from the information in table 10.3 that roads A, C, E, and F are worth building while roads B and D are not. A marginal cost of public funds of 1.5 raises all costs accordingly. Now, of the six roads, only roads E and F yield more than the required 8 percent, though a third road, A, is just on the margin.

The simultaneous determination in figure 10.1 of total public expenditure and the marginal cost of public funds is based on the assumptions that society’s only concern in choosing projects, programs, and policies is to ensure that the benefit exceeds the full cost inclusive of the deadweight loss in taxation, and that the allocation of cost and benefit among people can be safely ignored. The analysis suggests a simple rule of thumb for the government to follow. Undertake projects, programs, and activities if

and only if the benefit–cost ratio (where cost is measured net of the deadweight loss in taxation) exceeds the marginal cost of public funds. Admittedly, projects, programs, and policies are not neutral in their impacts on different people. One project is especially beneficial to the rich. Another is especially beneficial to the poor. Another is especially beneficial to people in the east. Another is especially beneficial to people in the west. The rationale for this rule of thumb is that it makes most people better off in the long run than any other procedure the government might adopt.

The rule requires justification. To argue that the rule is appropriate, one would need, at a minimum, to identify simple cases where it is unambiguously right. Two such cases are especially interesting. The first is where people are identical in every respect, so that everybody’s benefit and cost from any given project are the same. The rule is clearly appropriate in this case as long as projects are financed by ordinary taxation, but it is open to the objection that, if people really were identical, projects would be financed by lump sum taxes instead. Consider the derivation of the full cost of additional public expenditure in chapter 4. If people really were identical, it would be silly for the government to raise public revenue, denominated in bread, by a tax on cheese. Far better to impose a uniform head tax of a certain number of loaves of bread, eliminating all deadweight loss because the tax-induced wedge between the demand price and the supply price of cheese would be removed. To look upon the rule of thumb as being strictly correct for a society of identical people, it would be necessary to forbid lump sum taxation, recognizing by the back door that people are not really identical at all.

Another simple interpretation of the rule of thumb links the discussion of costs and benefits of projects in this section with the discussion in the last chapter of the determination by the median voter of the rate of the negative income tax. The rule of thumb is strictly valid for a community of people whose incomes differ but whose benefits and costs of each and every project are proportional to their incomes. The assumption is that if a project costs $100 per head and yields benefits of $200 per head, the benefit and cost to a person with the average income are $200 and $100, the benefit and cost to a person with twice the average income are $400 and $200, the benefit and cost to a person with half the average income are $100 and $50, and so on.

Generalizing, the simplification is that a project yielding total benefits of $B in an economy with N people would yield an average benefit per person of $(B/N), but its benefit to person i with income yi becomes $(yi/yav )(B/N) where yav is the average income per person. Similarly, a project with a total cost of $C, inclusive of the excess burden of taxation, would entail an average cost of $(C/N), but its cost to person i becomes $(yi/yav )(C/N). This is obviously so for the proportional income tax. Assume this allocation holds for the additional excess burden as well. Think of the allocation of benefits and cost in accordance with people’s incomes as a paradigm case, against which other possibilities may be compared. Wealthier people are assumed to place higher valuations on the benefits of public undertakings, but to bear proportionately more of the tax and the associated deadweight loss.

This assumption eliminates all conflict of interest in the choice of public projects, programs and activities, for, if one of two projects has the higher benefit–cost ratio for me, it must have the higher benefit–cost ratio for you as well. The assumption has an important bearing on the meaning of the scale of the vertical axis for the demand

and supply curves in figure 10.1. Now, the height of the demand curve is not just the benefit per dollar of additional public expenditure. It is the benefit per dollar of additional public expenditure on the understanding that benefit is allocated among people in proportion to their incomes. The height of the supply curve is not just the full cost to the tax payer per additional dollar of public revenue. It is the full cost to the taxpayer on the understanding that taxes and the excess burden of taxation are borne by different people in proportion to their incomes. For any particular person, a benefit or cost is higher or lower than indicated by the demand and supply curves of figure 10.1 depending on whether his income is greater or less than the average.

This restriction on the allocation among people of the benefits and costs of projects permits a sharp distinction to be drawn between “ordinary” taxation and expenditure with costs and benefits accruing to people in proportion to their incomes and “lump sum” taxation and transfers with costs and benefits that are always the same for everybody. A lump sum tax is a fixed dollar value of tax per person, rich or poor. A lump sum transfer is a fixed payment by the government to every person, rich or poor. The lump sum transfer was exemplified by the demogrant in the negative income tax discussed in the last chapter. Of course, these instruments cannot be employed simultaneously because they would cancel out.

The new, more structured scaling of the vertical axis allows lump sum taxes and transfers to be linked to ordinary expenditure, but the equivalence varies from one person to the next in accordance with one’s income. For example, for a person whose income is twice the national average, a lump sum tax of $1.00 per head is equivalent to only 50¢ per head of ordinary taxation because the cost to that person of 50¢ per head of ordinary taxation is a full dollar. When 50¢ per head is raised by ordinary taxation and when each person’s burden of taxation is proportional to his income, that person’s burden of taxation must be a full dollar which is equivalent in his assessment to a lump sum tax of $1.00. Similarly, for a person whose income is half the national average, a lump sum tax of $1.00 per head is linked on the vertical axis of figure 10.1 to ordinary taxation of $2.00 per head because that person’s share of $2.00 of ordinary taxation is only $1.00.

Now consider the median voter whose preferences are assumed to determine all expenditure and taxation. In this analysis, two cases must be carefully distinguished. In the first case, the government can raise a lump sum tax or supply a lump sum subsidy to each and every person, without exception, and the median voter is utterly self-interested in his choice of public revenue and taxation. In the second case, poverty limits the scope of lump sum taxation and the median voter may be somewhat altruistic. Begin with the first case.

The median voter is considering whether to allocate an extra dollar of public expenditure per person to increasing the demogrant or to undertaking an ordinary public expenditure yielding a benefit per person of b dollars where, as we have assumed, the benefit is allocated among people in accordance with their incomes. Ignoring any extra administrative cost of taxation, an extra dollar per person spent to increase the demogrant provides the median voter with exactly $1. An extra dollar per person spent on the additional project yields an average benefit of $b but a benefit to the median voter of only $b(ymed/yav ). The median voter is indifferent between an addition to the demogrant and equally costly additional provision of ordinary public services – extra

The equilibrium marginal cost of public funds cannot be less than yav /ymed because, if it were, the median voter would favor an increase in the demogrant, and the equilibrium marginal cost of public funds cannot be more than yav /ymed because, if it were, the median voter would favor a decrease in the lump tax. If public expenditure lifts the marginal cost of public funds substantially as indicated by the supply curve S , the crossing of the demand and supply curves occurs above the flat line at a height representing the cost or benefit to the median voter per dollar of head tax or demogrant. In that event, the median voter wants the government to undertake E dollars of public expenditure financed by E dollars of ordinary taxation and a head tax of E − E dollars. If public expenditure lifts the marginal cost of public funds moderately as indicated by the supply curve S , the crossing of the demand and supply curves occurs below the flat line at a height representing the cost or benefit to the median voter per dollar of head tax or demogrant. In that event, the median voter would want the government to raise E dollars of revenue by ordinary taxation, to undertake E dollars of ordinary public expenditure and to supply a demogrant of E − E dollars. In either case, the equilibrium marginal cost of public funds must be yav /ymed.2

For Canada in the year 1998, the ratio of average family income to median family income was about 1.2 [all family units, 1998]. If the marginal cost of public funds would exceed 1.2 in the absence of a lump sum tax, the median voter would favor the introduction of a lump sum tax. If the marginal cost of public funds would be less than 1.2 in the absence of a lump sum transfer, the median voter would favor the introduction of a lump sum transfer. In either case the marginal cost of public funds settles down at 1.2.

This explanation of how lump sum taxes or transfers constrain the marginal cost of public funds depends critically on the assumption that each and every person, without exception, can be subsidized or taxed alike. Drop that assumption and the clean results of the preceding paragraph begin to disintegrate. As the assumption is not unreasonable for a lump sum transfer, the estimate in the preceding paragraph may be reasonable as a lower limit to the marginal cost of public funds when the supply curve in figure 10.2 rises slowly enough that a lump sum transfer is warranted. Lump sum taxation is different because some people are deemed too poor to pay the tax. This constraint may raise the marginal cost of public funds considerably. For example, if 25 percent of the population were deemed too poor to pay the lump sum tax, then the cost to the median voter per dollar of tax revenue (per person) raised by the lump sum taxation must rise from $1 (which is what the median voter actually pays) to $1.33 (equal to 1/(0.75) which is what the median voter must pay to increase the revenue from the lump sum tax by $1 per person in the population as a whole). Furthermore, since the median voter pays only 83¢ (1/1.2) per dollar of ordinary tax revenue, the full cost per dollar of additional public revenue must rise to $1.60 (1.33 × 1.2) before it becomes in the interest of the median voter to raise additional public revenue by a head tax instead. The exemption from the head tax of 25 percent of the population raises the marginal cost of public funds from $1.20 per dollar of public expenditure to $1.60. Generalizing, it may be said that the median voter is only content with the mix of ordinary taxation and lump sum taxation once the marginal cost of public funds has

risen not to yav /ymed but to (yav /ymed)/s where s is the proportion of the population paying the head tax.

That is not the end of our difficulties. The exemption from the head tax must be based on some minimal income. Suppose the minimal income is $20,000 and the head tax is $1,000 per person. In these circumstances, anybody who, in the absence of the head tax, would have a taxable income between $20,000 and $21,000 is provided by the tax with an incentive to lower his declared taxable income – working less or evading more – below the critical threshold at which the exemption takes effect. Even people whose incomes are somewhat higher than $21,000 might be inclined to take steps to drive taxable income below $20,000 to avoid the head tax. This contraction of taxable income is a kind of deadweight loss that must be taken into account when assessing the effect of lump sum taxation, and the equilibrium marginal cost of public funds must rise accordingly. The flat line in figure 10.2 begins to curve upward soon after the transition from lump sum transfer to lump sum tax. The ratio of median to average income becomes a lower bound to the marginal cost of public funds, effective in the event that the supply curve of public funds is low enough for a lump sum subsidy to be warranted, but not binding when a lump sum tax is imposed. These difficulties would normally rule out the lump sum tax as a practical proposition. The simple story in figure 10.1 may be essentially right except when the supply curve of public funds is low enough to warrant a lump sum subsidy.

There is also a political reason why it is neither possible nor desirable for the government to trace the beneficiaries of each and every project. An omniscient, omnipotent, and benevolent planner would maximize the value of some social welfare function by weighing the benefits of all projects according to the incomes of the people to whom those benefits accrue. A democratic society must eschew such fine computations. A great virtue of benefit–cost analysis is that it is blind. Costs are weighed against benefits, to whomsoever the benefits accrue. A simple rule suppresses conflict among potential recipients, avoiding the scramble for public largess and the vast potential conflict among would-be beneficiaries that would otherwise occur. The best rule in the circumstances is whatever is likely to benefit most people in the long run. The question is how and to what extent, in forming such a rule, the marginal cost of public funds should be taken into account. The “right” marginal cost of public funds is the most appropriate mark-up cost in this context. Even so, the weighing of benefits might be slanted to take account of their apportionment among people and of the incentives they generate. Other things being equal, a project favoring the poor might be preferred over a project favoring the rich, or, where the excess burden of taxation arises from the diversion of effort from labour to leisure, a project, such as a training school, that encourages people to work might be favored over a project, such as a park, that encourages people to take more leisure.

Finally, it should be stressed that the excess burden of taxation only arises because, and only because, of people’s individually advantageous but socially disadvantageous maneuvers to reduce the amount of tax they pay. There could be no excess burden if each person’s tax assessment could be set independently of his behavior. A head tax would do, but that would impose a very great burden upon the poor. A skill tax would do as well. There could be no maneuvering to reduce one’s tax bill if the government could observe each person’s ability and impose taxes accordingly. That will not do, in practice, because skill cannot be observed or assessed objectively as a tax base.

The closest observable counterpart to skill is income which can be influenced by working less, by diverting labor time from taxable work for pay to untaxable do-it-yourself activities or by diverting effort from production of goods to tax avoidance or tax evasion. Starting from any tax system whatsoever, all deadweight loss could be eliminated by an agreement or contract among tax payers to abolish the system by which each person’s tax is determined but to continue paying the same tax as before. Such an agreement would allow each person to make the best use of his resources without at the same time reducing total public revenue. The excess burden arises because no such agreement could be enforced.

THE EVALUATION OF PERSONAL GOODS

Most goods – like bread and cheese in the models of the economy in chapters 3 and 4 – have market prices which are the same for everybody, but there are exceptions. Some goods cannot be traded between people at uniform market-wide prices because they are attached to their users. Eggs are ordinary goods because everybody, old and young, rich and poor, pays the same price for a dozen eggs at the grocery store. Leisure is a personal good because people place different values on an hour of leisure. A highly skilled person who earns $300 per hour and who may work as many or as few hours as he pleases places a value of $300 on an hour of leisure because, if his value of leisure were less than $300, he would work more, and, if his value of leisure were more than $300, he would work less. An unskilled person who earns a minimum wage of $6 an hour and who can also work as many or as few hours as he pleases places a value of about $6 on an hour of leisure. There can be no uniform economy-wide price of leisure because there is no mechanism enabling people with low valuations of leisure relative to goods to sell leisure at a uniform market-wide price to people with high valuations of leisure relative to goods. Mortality rates are also personal goods because people differ in their willingness to pay for small reductions in their mortality rates. Typically, a rich person is willing to pay a relatively high price for a given reduction in his mortality rate, as, for instance, when he buys a safe but expensive car that the poor cannot afford.

Personal goods create two sorts of problems for cost–benefit analysis: (1) how to value personal goods, such as time saved or lives saved due to improvements in transport, when people may or may not differ in their valuations of personal goods, but decision-makers have no information whatsoever about whether or to what extent beneficiaries’ valuations differ from one project to the next, and, (2) how to compare projects when the beneficiaries of one project are known to place higher values on personal goods than the beneficiaries of another project. The latter question is whether a higher value should be placed on an hour of time saved or a life saved in the avoidance of road accidents in a project where the beneficiaries are rich (and therefore likely to place high valuations on time saved and lives saved) than in another project where the beneficiaries are poor. We shall discuss these matters in turn, with special reference not to leisure, but to the value of life. The remainder of this section is about the choice of a value of life for cost–benefit analysis on the working assumption that everybody’s

value of life is the same. Differences among beneficiaries of projects will be discussed in the following section.

The Ministry of Transport is contemplating a number of projects to improve the safety of roads. Eight projects are under consideration. Their costs in millions of dollars and their expected numbers of lives saved are as shown in table 10.5. (Assume for convenience that the projects have no benefits other than lives saved, and that the saving of lives occurs over a short enough period of time that the discounting of costs and benefits accruing at different times can be ignored.)

What ought the Ministry of Transport to do? We cannot slough off the problem with platitudes about the pricelessness of life because the trade-off between money and life is inescapable. We routinely trade money for lives in decisions about medical care when, for instance, we decide whether or not to adopt expensive but potentially life-saving procedures, or whether or not to undertake expensive research which may in time give rise to live-saving discoveries. We could spend the entire national income on medical care before exhausting all the opportunities to save lives at a price. If lives were priceless, we would never build tall buildings, send sailors to sea or collect ore in mines. Implicitly or explicitly, we must place a value on life, saying, in effect, that a life is worth saving if it can be saved for less than some dollar amount, but not otherwise. We must do so because the alternative is to throw lives away, for instance, in spending ten million dollars to save a life in one highly visible project but refusing to spend five million dollars to save two other lives elsewhere.

A distinction must be drawn in this context between an actual life and a statistical life. To say that one’s value of life is, for instance, five million dollars is not to say that one would voluntarily give up one’s life for five million dollars. That is not what the statement means. To say that one’s value of life is five million dollars is to say how much he would be prepared to spend to avoid a small risk of losing his life. It is to say one would spend up to $100 to avoid a one in 50,000 chance of losing his life, or would spend up to $1,000 to avoid a one in 5,000 chance of losing his life, or that 1,000 people just like him would together pay $5,000,000 to save one randomly chosen life among them. We make such calculations all the time in deciding when to use a