Knowledge that Transforms

While contemporary rhetoric often highlights differences between races, the data show that blacks are becoming less distinguishable from whites in at least one relevant index of performance-market earnings. Relative to white males, black male earnings have gradually increased, and the rise during the 1960's and the early 1970's is larger than that observed earlier. (See Table 1.) Yet, it is clearly the contrast between white and black females that is extraordinary. Twenty years ago the average black woman employed full time was earning approximately half the wage of a similarly employed white woman. By 1975, almost complete racial parity among women had been achieved. In a recent article (1977), Finis Welch and I argued that the advance in the relative income of black males between 1960 and 1970 was due mainly to converging educational distributions by race and a narrowing in wage differentials between regions. Skill levels were relatively constant within cohorts and convergence was accomplished as increasingly similar racial cohorts entered labor markets while other less similar cohorts retired. Finally our test of affirmative action pressures indicated that before 1970 they had little impact. My first objective is to update our previous research to determine if the events of the last decade for males have continued unabated into the mid1970's. Since a complete understanding of the dynamics of blackwhite changes necessitates explaining the patterns for females, my second goal is to expand the wage comparisons to include women. The major explanations for narrowing in racial wage differences can be placed under four general categories. The central idea of the vintage hypothesis is that more recent black cohorts begin their job experiences with larger initial stocks of human capital, relative to whites, than previous cohorts. The second explanation involves migration. The rural-South to urban-North migration has partly been superceded by southern blacks moving to what are by now economically vibrant southern cities. The third category involves the effects of government affirmative action. Since 1970, it is alleged that a series of court cases imposing severe financial penalties on firms for noncompliance with affirmative action goals have added sharp teeth to government jaw boning. Finally, changes in other aspects of market work may be important in narrowing relative wages. This factor is more relevant for women than men and includes the choice of partor full-time work, unique characteristics of certain occupations, and biases due to limiting comparisons solely to working women.

In a recent article in this Review, David lIevhari and Don Patinkin (hereafter noted L-P) develop an equilibrium growth model for a simple economy in which money is treated as a productive factor, entering an aggregate production function. In their policy section, they are unable to determine the effects of an increase in the exogenously determined rate of inflation on the equilibrium capital and real-balance intensities. They are also unable to establish whether or not steady-state equilibrium is stable. The purpose of this note is to extend their dynamic analysis and to show that 1) the effects of a change in the rate of inflation are more or less predictable, and 2) steady-state equilibrium can be expected to be stable. The L-P model can be briefly summarized. Assume a growing neoclassical economy where Y = G(K, M/P, N), and where Y, K, M/P, and N represent real output, the stock of physical capital, the real money stock, and the labor force, respectively. Assume further that G is linear homogeneous and twice continuously differentiable. The function can therefore be written y = g(k, m), where y, k, and m are Y/N, K/N, and M/PN, respectively. Assume g is wellbehaved such that gi > 0, gii 0. Let the labor force grow at some exogenously determined exponential rate n. Money is costlessly produced by the government and injected into the economy via transfer payments to the public. In order to avoid stability problems noted by Miguel Sidrauski, it is assumed that the rate of nominal expansion is altered by the government in order to maintain a constant target rate of inflation.' The rate of nominal expansion is u = DM/M, where D denotes the time derivative of the variable which follows it. The rate of inflation is p = DP/P. It follows that D(M/P) = (u p)M/P. From this and the labor force growth assumption, it follows that the rate of growth of the real per capita money stock is

It is often true that a manager's opinions about events relevant to production are valued but are not fully known by others. This note suggests that in such circumstances there may be a problem with production. Consider a competitive equilibrium in a standard Arrow-Debreu model of an economy. In such an equilibrium production decisions are guided by prices and, in particular, by contingent commodity prices (which in fact may be implicit in stock market prices). Moreover, in such an equilibrium the managers of production processes play a strictly passive role since complete instructions for production are implicit in the criterion of profit maximization.' However, if the probabilistic beliefs of the managers are valued but are not fully known by the other agents in the economy, then it seems that these agents might well prefer to have the managers play an active role in making production decisions. In other words, it seems that profit maximization with respect to contingent commodity prices may encourage managers to act contrary to what would be the best wish of others, and consequently that the absence of markets in certain contingent commodities might not be undesirable.2 Our discussion of this issue will make reference to a simple example. An economy with many identical individuals and few identical managers uses seed to produce wheat which may be grown in two regions, A and B. Managers decide where to plant the seed. The wheat harvest is uncertainit is either positive or zero-depending on which of the two possible states of nature, a and ,B, occurs. This is described in Table 1, where si is the amount of seed planted in region i and f is the usual type of production function (f' > 0, f < 0). Let us suppose for simplicity that consumers alone determine prices in competitive equilibrium, that is, the few managers have only a negligible impact on the prices. Assume initially that consumers have fixed beliefs, independent of those which the managers might have. Specifically, assume that consumers believe the state a will occur with probability a. Then, since a competitive equilibrium in which there are markets for contingent wheat is Pareto efficient, it must in this case maximize expected utility of consumers. Consequently, if each consumer's endowment consists of one unit of seed and his von Neumann-Morgenstern concave utility function U(.) depends only on consumption of wheat, the problem solved by the market is to maximize expected utility: