Knowledge that Transforms

This paper explores the profit-maximizing strategy for a monopolistic firm selling to two national markets simultaneously. The choice of how much to produce and sell in each country, how much to export between the two, and what transfer price to put on intrafirm exports is shown to depend heavily on two considerations: (1) whether the marginal costs of production are rising or falling, and (2) whether tariffs are high enough for the firm to discriminate perfectly between its two national markets. After showing how the firm reacts to a given set of tariffs on imports and taxes on profits, the impact of a change in any policy variable is assessed.

Discrimination concentrates Negroes into certain occupations while virtually excluding them from others. In the occupations to which Negroes are relegated, marginal productivity may be lowered by the enforced abundance of supply. A model embodying this "crowding" hypothesis is used to estimate the effects on white incomes of a reduction in discrimination. Whites with only an elementary education might have a once-for-all loss on the order of 10 percent; on all other whites and on national income the effect is estimated to be trivial. Formulations by Becker and Thurow concerning Negro marginal productivity and wages are criticized.

None of the existing methods of evaluating loss or saving life, or assessing an increase or reduction in accidents resulting from investment projects, is satisfactory for a number of reasons. This is so chiefly because they are all inconsistent with the Pareto base of existing allocation theory and benefit-cost analysis. Strict application of the Pareto principle to changes in accidents and fatalities involves a calculation of the compensating variation associated with the changes in risk bearing regarded as external effects. Several of these external effects are discussed at length.

This article uses linear programming techniques to "estimate" a frontier Cobb-Douglas production function for U.S. agriculture from 1960 to 1967, using the "average farm" in each state in each year as an observation. Both deterministic and probabilistic frontiers are generated and the results compared with ordinary least-squares and analysis of covariance estimates of the production function. Technical inefficiency is defined relative to the probabilistic frontier function and the extent of any inefficiency calculated for each state. Little technical inefficiency exists across states when the production function includes intermediate inputs as well as land, labor, and capital.

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The paper indicates how the Shephard duality theorem may be utilized in order to obtain a system of derived demand equations which are linear in the technological parameters, thus facilitating econometric estimation. This theorem states that technology may be equivalently represented by either a production function or a cost function, and a proof of the theorem is given. The chosen functional form is a quadratic form in the square roots of input prices and is a generalization of the Leontief cost function. The generalization has the property that it can attain any set of partial elasticities of substitution using a minimal number of parameters.