History of Economic Analysis part 105. At the time of his death in 1950, Joseph Schumpeter-one of the major figures in economics during the first half of the 20th century-was working on his monumental History of Economic Analysis. A complete history of humankind's theoretical efforts to understand economic phenomena from ancient Greece to the present, this book is an important contribution to the history of ideas as well as to economics. | History of economic analysis 1002 tion as the second of the two descriptive functions that I have called the two pillars of the classic theory of that The old laws of returns properly generalized and polished lay at hand to supply the properties which the production function was to enjoy either generally or normally and which we shall now restate again. If we wish to define marginal productivity of a service as the partial derivative of the production function with respect to the quantity of that service we must as has been pointed out already assume first of all that these partial derivatives exist. We may postulate in addition that they are positive that is that a small increase in the quantity of any services will increase the quantity of the 26 Following Turgot we may postulate further that this rate of I w 01 increase itself increases at first v f then passes through a single maximum and after having reached this point keeps on declining 2 o law of decreasing returns in the primary sense J V An this case two corollaries follow 1 there exists a point beyond which the average productivity of every service x v decreases also law of decreasing returns in the secondary sense 2 cross derivatives are positive which means that if I increase the quantity of a productive service vt by a small amount this will not only decrease after the point indicated its own marginal productivity but also increase the marginal f productivities of all the other productive services A methodological remark may be usefully inserted here. Among the properties to be assigned to the production function there are some that follow from others and therefore may be proved deductively or stated as theorems. Thus decrease of average productivity after a certain point may be deduced from or proved by the decrease of marginal productivity and there is then no need for any separate observational or experimental proof. Thus Wicksell see his article in the Thunen Archiv 1909 was .
