John C. Harsanyi, Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen's, Hicks', and Nash's Theories, Econometrica, Vol. 24, No. 2 (Apr., 1956), pp. 144-157

A study of the efficient allocation problem in production by the evaluation of the merits of private or corporate enterprise versus a centrally directed economy. Presented before a joint meeting of the American Statistical Association, the American Economic Association, and the Econometric Society in New York City, December 29, 1949.

Given a sufficient number of instrumental variables significantly correlated with the investigational variables, consistent estimates of the coefficients of the linear relations can be determined (if they exist), without knowledge of the disturbance variances. The estimates are discussed from the viewpoint of probability convergence. In the case of two investigational and one instrumental variable, all three variables distributed on the normal surface, the distribution of the estimate of the coefficient is found exactly for all sample sizes, on certain hypotheses. The distribution function is remarkably simple. The applicability of the theorem to economic time series is discussed by (a) comparing the probability inferences derived from this Model A with those for the simplest stationary time-series model, termed Model B, and (b) by comparing the large-sample variances on several models. It is found that the theory can be used with confidence when the series are not too short and the error variances not too large. The theory is applied to a particular time series, showing that the accuracy of the estimate of the coefficient depends on the correlation between the instrumental variable and the two investigational variables. The theory to which reference is made in Sections II, III, and IV, relating to the two-investigational-variable case, is extended to many variables and tests are given, applicable when samples are not small, for determining the significance of coefficient estimates.

So long as the marginal propensity to consume out of is greater than that out of profits, any rise in wage rates at the expense of profits will the aggregate marginal propensity to consume-since the marginal propensity to consume out of will receive an increased weight relative to that out of profits-thus raising the level of income that can be supported by a given level of investment and federal expenditure. And the marginal propensity to consume out of will be higher than the marginal propensity to consume out of profits so long as the average wage income is lower than the average profit income, which may be expected. This for two reasons: (1) the marginal tax rate on high incomes is higher than that on low incomes; (2) the evidence shows that the marginal propensity to consume out of disposable income is lower at higher disposable incomes. It is occasionally asserted that wise business policy would favor increasing wage rates at the expense of profits, since the consumption effect would the general level of activity and reverberate to the benefit of profits. The argument runs as in the previous paragraph until an increased level of income is proved a consequence; then the conclusion is drawn that higher aggregate profits will accompany the higher income level. Whether or not the last step of this argument is taken with tongue in cheek, it is interesting to see whether total profits can be raised through decreasing the relative profit share of income and, if they can, what the conditions are under which they may be so increased and whether these conditions may likely prevail. Mathematically it can be shown that there are conditions, extreme but not unreasonable conditions, under which the raise profits through higher wages argument is valid; the conclusions mathematically arrived at can be demonstrated verbally. The analysis here is entirely static: the values of all economic variables are assumed to be mutually determined by simultaneous solution of demand functions and economic identities. For simplicity, all functions are taken as linear. The conclusions can be stated as follows: 1. So long as government expenditure and investment are constant a rise in wage rates at the expense of profits will increase aggregate income but decrease profits, if the marginal propensity to consume out of is less than unity. 2. When we complicate our system by admitting relationships between, e.g., investment and income, or government expenditures and