Allocation of Time and Hateful Behavior: A Theoretical and Positive Analysis Of Hate and Hate Crimes - Statistical Data Included

American Journal of Economics and Sociology, The,  Oct, 1999  by Marshall H. Medoff

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For simplicity, it is assumed that an individual's utility (U) depends on the consumption of antisocial hateful behavior (H) and all other commodities which are combined into an aggregate good (Z). [2] The utility function becomes

U=U(H,Z). [1]

Goods H and Z are not perfect substitutes for each other in consumption and H is a more time-intensive consumption activity than Z Hateful activity cannot be purchased in the market, but is self-produced using market goods and services and one's own time. Both commodities Hand Z are produced using a vector of market goods [x.sub.i] and a vector of its own time [t.sub.t] within the context of a vector of environmental variables E in which production takes place. [3]

H = h([x.sub.h], [t.sub.h]; E), Z = z([x.sub.z], [t.sub.z]; E). [2]

An individual's available time T is given by the time spent working, [t.sub.w] the time spent in producing H, [t.sub.h], and the time spent in producing Z, [t.sub.z] given by the constraint

T = [t.sub.w] + [t.sub.h] + [t.sub.z]. [3]

An individual's income constraint is given by the equation

[Wt.sub.h] + [Wt.sub.z] + [P.sub.h] [x.sub.h] + [P.sub.z] [x.sub.z] = M, [4]

where w is the market wage rate, [P.sub.h] and [p.sub.z] are the price of the respective market-good input used in producing H and Z, and M is the individual's potential full income.

Maximizing the utility function (1) subject to the production function (2) and income (4) constraints yields the first-order condition.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the numerator (denominator) of the right-hand side of (5) represents the marginal cost (MC) of commodity H (commodity Z) given by the sum of the opportunity cost of time plus the cost of producing a unit of commodity H (commodity Z).

An increase in the value of an individual's time (W) would increase the marginal cost of both H and Z, but especially H which is relatively more time-intensive, leading to a decrease in its consumption. Thus, equation (5) implies an increase in an individual's market wage will lead to a decrease in hateful activity.

The value of market time in equation (5) changes at various points in a person's life cycle and these changes should induce substitution towards cheaper methods of production. At an early stage in the life cycle an individual's value of time is relatively low and the value of goods high. This suggests that one should observe relatively more consumption of time-intensive modes such as hate activity when individuals are young. [4]

A change in an environmental variable is represented by E in equation (2). A change in E changes the amounts of goods and time required to produce a given amount of either H or Z. The effect of a change in E on [MC.sub.H] is given by

dM[C.sub.H]/dE = d[t.sub.t]/dH dw/dH + w [d.sup.2][t.sub.h]/dEdH + [[[p.sub.h].sup.[d.sup.2][x.sub.h]]/dEdH.] [6]

An increase in an environmental variable, such as education, in equation (6) will raise (i) the market value of time (dw/dE [greater than] 0) and (ii) the productivity of non-market consumption activity ([d.sup.2][t.sub.h]/dEdH [less than ] 0, [d.sup.2][x.sub.h]/dEDH [less than] 0) because education reduces the cost of producing H. Thus, the impact of an increase in education on the marginal cost of hateful behavior depends on whether the magnitude of the substitution effect away from hateful behavior is greater than, equal to, or less than the productivity effect towards more hateful activity.