# Calculation of the Dependency Rate in Fatal Accident Actions

This article first appeared in the winter 1996 issue of the Expert Witness.

In a fatal accident action, the surviving spouse is entitled to claim for any loss of pecuniary advantage which would have been derived from the deceased. There is considerable uncertainty, however, concerning the manner in which this loss of dependency is to be calculated. The purpose of this paper is to discuss three alternative approaches to the calculation of the dependency and to argue that selection among them depends upon the nature of the couple’s marriage. The three approaches are defined in the first part of the paper. In the second, three types of marriage are defined and each type is matched with an associated method of calculating the dependency.

## Theoretical Approaches to Calculation of Dependency

Assume that the husband of a childless couple has been killed. The husband was earning \$30,000 per year (after taxes) and the wife \$20,000 per year. Assume also that the wife’s dependency on family income has been found to be 70 percent – composed of 30 percent of family income spent on items which benefitted the wife alone and 40 percent spent on items which benefitted the husband and wife equally. Three different approaches to the calculation of the wife’s loss can be identified.

### a) The sole dependency method

In this approach, the wife receives 70 percent of her husband’s projected income.

### b) The “traditional” cross-dependency method

In this approach, the wife receives 70 percent of the family’s income net of her earnings:

(0.70 x \$50,000) – \$20,000 = \$15,000 (2)

The source of the difference between these approaches can readily be seen if the cross-dependency equation is rewritten in a form which makes it equivalent to that used in the sole dependency method. In doing this, it is first necessary to recognise that the family income figure, here \$50,000, is composed of the sum of the wife’s and husband’s incomes, that is, \$30,000 + \$20,000. Thus, the equation for the wife’s dependency in the cross-dependency approach, (equation (2)), may be rewritten:

0.70 x (\$30,000 + \$20,000) – \$20,000 = \$15,000 (3)

Furthermore, with rearrangement, equation (3) can be represented as:

(0.70 x \$30,000) + (0.70 x \$20,000 – \$20,000) = \$15,000 (4)

or as:

(0.70 x \$30,000) – (0.30 x \$20,000) = \$15,000 (5)

That is, the difference between the sole dependency approach and the cross-dependency approach is that in the latter, the element (0.30 x \$20,000), which is the portion of the wife’s income which had previously been devoted to the husband, is deducted from her loss of dependency.

### c) A “revised” cross-dependency method

In this approach, the wife receives the husband’s total income net of the total amount devoted to his personal expenditures. Thus, as it has been assumed that the husband’s personal expenditures accounted for 30 percent of family income (and family income is \$50,000), the wife would receive:

\$30,000 – (0.30 x \$50,000) = \$15,000 (6)

Recognising, again, that the \$50,000 family income figure in this equation is the sum of the husband’s and wife’s incomes, equation (6) can be rewritten:

\$30,000 – (0.30 x (\$30,000 + \$20,000)) = \$15,000 (7)

or:

\$30,000 – (0.30 x \$30,000) – (0.30 x \$20,000) = \$15,000 (8)

which, with simplification, becomes:

(0.70 x \$30,000) – (0.30 x \$20,000) = \$15,000 (9)

Equation (9), however, can be seen to be identical to equation (5), the method for calculating a “traditional” cross-dependency. Hence, although the rationale for using equation (9) is different from that for equation (5), the two approaches yield the same result. It is for this reason that I used the term “revised” cross-dependency to describe the approach which was used to derive equation (9)

## Three Types of Marriages

In this section, I discuss three types, or “styles,” of marriage and identify the appropriate dependency approach associated with each.

a) The idealised marriage. In what might be called an “idealised view of marriage”, the couple marries for love and shares all family income (approximately) equally. That 30 percent of family income is spent on items which benefit the husband alone implies that 30 percent of each of the husband’s and wife’s income is devoted to those expenditures. (And, conversely, 30 percent of each spouse’s income is devoted to items which benefit the wife alone.) The wife is assumed to spend 30 percent of her income on her husband because she loves him and, hence, derives pleasure from expenditures which benefit him.

In such a marriage, the pecuniary impact of the husband’s death is as follows: First, the wife has lost the 70 percent of the husband’s income (0.70 x \$30,000 = \$21,000) which he had spent on joint, family expenditures and on her personal consumption. Second, the wife now “saves” the 30 percent of her income, here \$6,000 (= 0.30 x \$20,000), which she had previously been spending on her husband’s personal consumption. However, it is not correct to say that she is “better off” by that \$6,000. In the “idealised” marriage, her “gift” of \$6,000 to her husband was voluntarily made because that use of her money gave her greater pleasure than any other use available to her. Thus, when the death of her husband “freed” her to spend the \$6,000 on herself, she was not made better off. The “freeing” of the \$6,000 forces her to purchase something – goods and services for herself – which she values less than the items she was purchasing before – goods and services for her husband.

A less emotion-laden example might help to explain this point. Assume that individual A has been leasing a car for \$500 per month. The tortious intervention of individual B has destroyed the car and \$1,500 of contents belonging to A. Although two months had remained on the lease, A has been excused from further payment (perhaps on the ground that the contract was frustrated). B admits that he owes \$1,500 to A, to compensate him for the loss of his personal belongings, but argues that this should be offset in part by the \$1,000 A has “saved” because he no longer has to make two months of lease payments. B’s argument is wrong. Although A now has \$1,000 which he did not have before; he has been deprived of the use of a car, a use on which he had placed a value of at least \$1,000. Instead of being made better off by the “gain” of that \$1,000, he will actually be made worse off by the difference between the value of the car and the value of the “next best” set of goods and services which he can now purchase. Similarly, the wife who was previously devoting some of her income to her husband is not better off when she is prevented, by the tortious action of some third party, from spending that money. Rather, like the individual deprived of his car, she is worse off. Hence, in the idealised form of marriage, it is the sole dependency approach which is justified.

b) The marriage of convenience. The couple may not have married for reasons of love, but for reasons of financial gain. From a purely financial perspective, the marriage described above cost the wife \$6,000 – the amount which she spent on items which benefitted her husband alone. In return, however, she received the benefit of the expenditures her husband made on her – 70 percent of his income, or \$21,000. That is, she may be thought of as having “paid” \$6,000 in order to receive \$21,000. In such a marriage of convenience, the wife loses only the difference between these two figures – \$15,000 – when her husband dies. (Note: the husband has also gained from this marriage, as he has “paid” 30 percent of his income, or \$9,000, in order to obtain the benefit of 70 percent of his wife’s income, \$14,000.)

In such a marriage, it is the “traditional” cross-dependency approach which is justified – subject to the following caveat: The 30 percent of the wife’s income which benefitted the husband alone must have been less than the 70 percent of the husband’s income which benefitted the wife, (and vice versa), otherwise the marriage would not have provided a financial gain to the wife. For example, if the wife’s income had been \$50,000 and the husband’s \$20,000, the wife would have spent (0.30 x \$50,000 =) \$15,000 on the husband in return for only (0.70 x \$20,000 =) \$14,000. Such an outcome would have been possible in an “idealised” marriage, but not in one which had been entered for financial gain.

c) A marital partnership. Although the couple may have married for love, they may have agreed to maintain separate bank accounts, with each spouse paying for those items which benefitted him/her alone. In this case, it is only that portion of the deceased’s income which was spent on joint household expenditures which the surviving spouse will have lost. In the example developed above, the husband was assumed to have earned \$30,000 and the wife \$20,000. Thirty percent of total family income, or (0.30 x \$50,000 =) \$15,000, was for the husband’s benefit alone. In the “marital partnership” model, the husband is assumed to have paid for all of the latter expenditures. What remained of his \$30,000 income, after deduction of this figure, was the husband’s expenditure on items which benefitted the couple jointly. That amount is also \$15,000 (= \$30,000 – \$15,000). It is the “revised” cross-dependency approach which would compensate the wife for the loss of this amount.

It will be noted that the loss of dependency calculated on this basis, \$15,000, is identical to that calculated according to the “traditional” cross-dependency approach. This is not a coincidence. Mathematically, the two can be shown to be identical to one another. Hence, the use of the cross-dependency approach can be justified on the basis of either the “marriage of convenience” or the “marital partnership” model. It should be cautioned that both suffer from the reductio ad absurdum that individuals earning relatively high incomes will be found to be “better off” when their spouses are killed.

## Conclusion

It is now seen that there is not a unique approach which can be applied to all marriages. Rather, one must consider the nature of the relationship which had been shared between the deceased and the plaintiff. Two types of evidence can be led: subjective and objective.

a) Subjective evidence. Subjective evidence concerns the nature of the personal relationship which had existed between the husband and wife. If evidence is led to indicate that the marriage in question had been based on love and mutual respect, a prima facie case would appear to have been made for use of the sole dependency approach. Only if it could be shown that the marriage was one of “convenience” would it be appropriate to employ the traditional cross-dependency approach.

b) Objective evidence. Objective evidence concerns the extent to which the couple had intermingled their incomes and paid for personal and household items jointly. Even when the court is reluctant to rule on the basis of the presence or absence of a “loving” relationship, use of the sole dependency approach can be justified on the pragmatic ground that many couples combine their incomes in a single pool, within which it is impossible to distinguish one individual’s contribution from the other’s. Hence, if 30 percent of the (family) income in this pool is spent on the husband, for example, it would not make sense to argue that 30 percent came entirely from his income. Rather, the more reasonable conclusion would have to be that 30 percent derived from his contributions to family income and 30 percent from his wife’s contributions – that is, that the sole dependency approach should be employed.

On the other hand, if the couple had carefully kept their accounts separate from one another, a strong presumption would appear to have been made for use of the “revised” cross-dependency approach – unless the individuals had markedly different incomes. (If the wife’s income was \$10,000 per year and her husband’s \$50,000, for example, it would be extremely unusual to find that the husband had spent 60 percent of “his” \$50,000 income on items specific to himself; while only 60 percent of the wife’s \$10,000 income had been spent on items specific to her.)

Christopher Bruce is the President of Economica and a Professor of Economics at the University of Calgary. He is also the author of Assessment of Personal Injury Damages (Butterworths, 2004).