¹ It is important to note that an investment in fencing may also increase household welfare by producing aesthetic pleasure. When a single input, fencing, is used to produce two outputs, legal welfare and aesthetic pleasure, joint production is said to occur. This paper abstracts from the problems associated with jointly produced outputs.

² Service flows are benefits (objective or subjective) per unit of time which increase overall household well-being.

³ We do not model the household's problem as a question of bilateral monopoly or oligopoly. These refinements would take the paper into the field of multiplayer games, an interesting field for further research.

⁴ A planning horizon is some length of time (e.g., one, two, or three years) for which a household makes a resource allocation plan.

⁵ Just as firms invest in machines, buildings, and other types of physical assets, a household makes decisions which can be treated analytically as investments in its own human assets (human capital). The value of these assets is enhanced by formal education, on-the-job experience, etc. These actions are costly, and the analytic treatment of costly decisions which yield returns over time is an important topic considered by capital theory.

⁶ The utility function represented in equation (1) does not assume that preferences for conventional goods (X _i) or leisure (T_i) are independent of preferences for legal welfare (h_i). Stated formally, the utility function (1) does not maintain that conventional economic goods and leisure are separable from the service flows of legal welfare. The composition of the household's consumption of conventional goods and leisure may be quite different if the household chooses to invest only modestly rather than intensively in legal welfare.

⁷ It is important to emphasize that households may retain lawyers for purposes other than resolving disputes. Households may consult lawyers regarding estate planning and tax matters. Expenditures like these do not enter the investment equations (3), but are represented in the vector of ordinary consumption goods X appearing in equation (1).

⁸ Note the assumption that the household controls its lawyers. This assumption might be relaxed by positing an objective function for lawyers and then modeling the interaction between lawyers and the household.

⁹ In the context of traditional economic theory, investments in capital goods (e.g., buildings and equipment) are assumed to wear out or depreciate over time. The legal welfare model similarly allows for the possibility that investments which increase legal welfare may depreciate over time. The value of lawyers' services received in the past, for example, can depreciate as new precedents or statutes affect the usefulness of the legal advice received in the past.

¹⁰ This requirement is imposed on the model for simplicity. The model could be analyzed if equation (7) were written as an inequality. The budget constraint also assumes that the household does not want to leave a bequest to succeeding generations. Such a bequest could be incorporated into the model if desired, but would not affect the substantive conclusions of the paper.

¹¹ Note suppression of the time subscript for simplicity.

¹² Note that both the discount rate β and the depreciation rates η and δ appear in (10c) through (10f). The marginal utility of a present investment in any future period is not only discounted back to the present but is also depreciated as smaller and smaller proportions of the economic value of the initial investment survive over time.

¹³ See note 6.

¹⁴ See, for example, the applied model suggested in Marquardt (1980).

For references cited in this article, see p. 883.