By Frank H. Stephen
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Additional info for The Economic Analysis of Producers’ Cooperatives
1 < 0 knd labour falls below L .. 1 Otherwile the firm 1pays p\ Therefore 1 MODIFICATIONS OF THE BASIC HODEL (Y. • The first-order condition for maximising yi with respect to L. is that the partial derivative of Y. w1th respect to L. ls equal to w. This implies that fof all firms that r~main in operation, the value of the marginal revenue product of labour is identical. Thus, no re-allocation of labour between firms can increase welfare. Since w is the shadow wage rate, Y. - wL. is the 'shadow profit' at that valuation of labour.
Estrin has shown that the response of the W-V-M firm to changes in parameters can be decomposed into factor substitution and scale effects. Consider the objective function of the W-V-M firm, y = (pX - rK)/L. This may be rewritten as K = pX/r - yL/r. 10) is the W-V-M firm's equivalent to the isocost line of conventional micro-economic theory. 10) may be influenced by its decisions, since both X and y are decision variables, not parameters of the system. 10). ng y. If the price of output rises top', the intercept shifts upwards to p'X 1/r.
Y JY 1. +La .. 18) must be negative. Consequently, concern for others reduces the labour input. The optimal degree of concern will be such as to reduce h. e. h/u. = pfh. J JY Let a .. h/U. h/U. e. h/U. /H) 1. ~ Thus a .. h/U. e. he gets the same satisfaction from a given income/hours trade-off for another as he would if he were in that position.
The Economic Analysis of Producers’ Cooperatives by Frank H. Stephen