[Economies with indivisible commodities admit allocations that are nearly price equilibria, provided that the number of agents is large relative to the number of commodities. In the course of the proof, it is shown that a similar result is valid if agents are insensitive to small price changes.]
[Programming theory is treated initially without any assumptions about the functions and with interpretation for production and activity analysis. By proof of a general theorem about optimal and support solutions and subsequent introduction of convexity assumptions, a new method for obtaining standard propositions and an amplification of their content becomes possible. Properties entirely peculiar to linear problems are noted. Two "shadow price" interpretations are discussed, one being the standard one in which support solutions appear as prices in a fictitious market. Consideration is also given to the law of diminishing returns. Finally, vector output, with emphasis on a concept of irreducible limit output, is treated.]
[This paper is a natural outgrowth of recent studies in markets with a "continuum" of traders. An equivalence theorem for the core of such economies was obtained, under the assumption that the measure space of economic agents is atomless. We introduce a sufficient condition under which the preceding result can be extended to economies containing "atomic" traders. The condition bears on the measure of the atoms.]
This paper develops approximations of the Gram-Charlier type to the cumulative distribution function of the instrumental variables estimator on classical assumptions. In the special case where there are only two endogenous variables in the estimated equation, exact values of the cumulative distribution function are computed by numerical integration and compared with the approximations. Although the error in the approximation depends critically on the parameters of the stochastic model, the approximation is good for the special case even for small sample size over a wide range of values of the parameters. THIS PAPER was originally conceived as a study of the finite sample distribution of two stage least squares estimates. Since it was found that the distribution of a more general class of instrumental variables estimates can be discussed in the same way with a trifling complication of the algebra, the paper was modified to cover these estimates. The basic approach is somewhat similar to that of Nagar [15], since it involves expanding the formulae for the estimator as a series of terms of 0(1), O(T-+), O(T- 1), O(T- 1+), etc., and from this a similar expansion is found for the cumulative probability of the form
TO AN ECONOMIST the study of economic development is in large part an investigation into the mechanics of capital formation. At least in theory, the output options open to a developing economy are more restricted in the case where possibilities for obtaining foreign exchange via trade or aid are relatively limited. Society's menu of choices is even easier to enumerate if it is further assumed that labor is surplus in the sense that labor supply is a non-binding constraint on economic development now and for some time to come. These conditions are roughly descriptive of the historical situation confronting some large underdeveloped nations wishing to industrialize rapidly; the U.S.S.R. in the thirties is a classic example. In such situations the key to economic growth is the capacity of the domestic capital goods sector. Increasing that capacity by ploughing back a high proportion of investment goods for purposes of self-reproduction will permit high consumption levels eventually, but not just in the near future. The reverse is true if, by bolting down a substantial percentage of investment goods there, the consumer goods sector is presently expanded. These thoughts underlie a very interesting model of economic development first propounded by the Soviet engineering economist G. A. Fel'dman in 1928 [7] 2 We are indebted to Professor Domar [6] for pointing out the significance of this model and for relating it to current growth theory as well as to the Soviet industrialization debate of the twenties. The same model has been independently formulated by the Indian statistician P. C. Mahalanobis [9] who places somewhat greater emphasis on making it operational enough to serve as a rough guide of sorts for Indian long term planning.3 In its simplest form this model splits an economy into two departments, investment and consumption. Investment goods are general ex ante and can be used to increase the capacity of either sector. But ex post, capital is specific to the