26 MULTIPLE PURPOSE RIVER DEVELOPMENT 



ment with which the enterprises have to work cannot be altered 

 during the time period under consideration. The main reason for 

 this is to facilitate exposition, although it is noteworthy that 

 changes in the capital stock are basically investment phenomena, 

 which are taken up more systematically in our discussion of the 

 market for investment capital. Second, as a counterpart of the 

 assumption that consumers rationally seek maximum satisfaction, 

 we assume that producers seek maximum profits. Finally, since we 

 are employing the economists' competitive model, we assume that 

 every producer is a price taker in the market, both when he buys 

 his factors and sells his product. 



As a groundwork for understanding the conditions of efficient 

 factor allocation, it is necessary to examine some purely physical 

 relationships. The first of these is what the economists call the 

 producer's "production function." The term "function" in this 

 context has a specialized meaning, being used in its mathematical 

 sense. That is, the producer's output is a function of (varies with) 

 the input of factors. Consider, for example, the operation of a 

 farm which under natural conditions is handicapped by infertile 

 soil and less than adequate moisture. Given the acreage, the soil 

 cultivation, and seed, a given output can be assumed to be attain- 

 able, either by employing additional fertilizer or more water — 

 physical inadequacies being limiting factors in both cases. Let us 

 assume that by addition of an acre-foot of water the physical yield 

 can be increased from 40 to 60 bushels of corn per year. Alterna- 

 tively, the 20 additional bushels could have been achieved by 

 increasing the input of fertilizer by a ton per acre. Of course, 

 increasing both water and fertilizer by the stated amounts would 

 probably increase output by a good deal more than 20 bushels. 

 But the assumption here is that if a given yield is sought, it can be 

 achieved by employing more water alone, more fertilizer alone, or 

 some combination of the two. 



There are, thus, two characteristics of the production function 

 which we wish to develop somewhat more precisely — the substitut- 

 ability of factors, or the different proportions in which factors can 

 combine to achieve a given output; and the characteristics of scale, 

 or variation in the level of output related to changes in total inputs. 

 This, perhaps, can be illustrated better by use of diagrams. 



In Figure 4, the input of two factors, X and Y, is measured 

 along the horizontal and vertical axes. The output produced by 

 employing the two factors in some combination is represented by 



