Industrial Production Models: A Theoretical Study by Sven Dano

By Sven Dano

This publication is as a result of the a long time' curiosity within the monetary conception of professional­ duction, first aroused by way of the examining of Professor ERICH SCHNEIDER'S vintage Theorie der Produktion. A supply from the Danish-Norwegian starting place made it attainable for me to spend six months on the Institute of Economics, collage of Oslo, the place I turned accustomed to Professor RAGNAR FRISCH'S penetrating pioneer works during this box and the place the plan of writing the current e-book was once conceived. extra experiences as a Rockefeller fellow at numerous American univer­ sities, specially an 8 months' remain on the Harvard fiscal learn professional­ ject, and a trip to the Unione Industriale di Torino have given priceless impulses. For those beneficiant gives you, and for the assistance and recommendation given through many of the associations i've got visited, i'm profoundly thankful. My honest thank you also are as a result of the collage of Copenhagen for the ex­ ceptionally beneficial operating stipulations which i've got loved there, and to the Institute of Economics-especially its director, Professor P. N0RREGAARD RASMUSsEN-for sufferer and inspiring curiosity in my paintings. I additionally desire to thank the Institute's workplace employees, omit G. SUENSON and Mrs. G. STEN0R, for his or her consistent helpfulness, and Mrs. E. HAUGEBO for her effective paintings in getting ready the manuscript, which used to be accomplished within the spring of 1965.

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Appendix 1. a Consider the minimization of (6) subject to (7) and (3) as a formal problem of linear programming, to be solved by the simplex method (see Appendix 1). Then we know from the fundamental theorem of linear programming that a single activity will suffice to give an optimal solution since there is only one linear side condition, (7). Now suppose that, for example, the first activity has the lowest unit cost: Cl

The parallelogram of forces. Point P of Fig. 580 is illustrated in this way in the factor dia- . -. 1 Cf. Ch. bove. g. with the factor combination Q, using the second and Fill. tion E (cf. the dotted isoquant which represents an x> 1). Thus we are left with points on the segments A B, B 0, and 0 D so that the set of efficient combinations for x=1 is represented by the broken line segment ABOD, which is convex to the origin and along which the marginal rate of substitution I dV2/dvl I ,,-i is piecewise constant, discontinuous at the kinks.

For p = 15, for example, profit is a maximum at 0 where x = As = 12, marginal cost being {16(>15) for x >12 dc dx = 12« 15) for x <12. This result could have been arrived at directly by maximizing the profit function (21) subject to the capacity restriction (15) for Ak > 0 and r:;;::: o. sI= 12, all other variables equal to zero!. lOa-c More generally, for parametric p the optimal level of output is that which makes the profit function Z= PX-2V2= (p-4)AI + (p-6)A2+ (p- 8)Aa+ (p-12)M a maximum subject to (15).

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