Researches Into the Mathematical Principles of the Theory of Wealth

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Macmillan, 1897 - Economics, Mathematical - 213 pages
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Page 127 - So far we have studied how, for each commodity by itself, the law of demand in connection with the conditions of production of that commodity, determines the price of it and regulates the incomes of its producers. We considered as given and invariable the prices of other commodities and the incomes of other producers; but in reality the economic system is a whole of which all the parts are connected and react on each other. An increase in the income of the producers of commodity A will affect the...
Page 53 - F', according to Lagrange's notation, denotes the differential coefficient of function F. FIGURE i If we lay out the curve anb (Figure 1) of which the abscissas oq and the ordinates qn represent the variables p and D, the root of equation ( 1 ) will be the abscissa of the point n from which the triangle ont, formed by the tangent nt and the radius vector on, is isosceles, so that we have oq = qt.
Page 57 - ... must finally be fixed by the competition of customers. 27. In this simplest case, chosen for a type, the producer has no cost of production to bear, or the cost can be considered insignificant. Let us go on to that of a man who possesses the secret of a medical preparation or an artificial mineral water, for which the materials and labour must be paid for. It will no longer be the function pF(p), or the annual gross receipts, which the producer should strive to carry to its maximum value, but...
Page 165 - By means of glasses, hot-beds, and hot-walls, very good grapes can be raised in Scotland, and very good wine too can be made of them, at about thirty times the expense for which at least equally good can be brought from foreign countries.
Page 5 - I am far from having thought of writing in support of any system, and from joining the banners of any party ; I believe that there is an immense step in passing from theory to governmental applications ; I believe that theory loses none of its value in thus remaining preserved from contact with impassioned polemics ; and I believe, if this essay is of any practical value, it will be chiefly in making clear how far we are from being able to solve, with full knowledge of the case, a multitude of questions...
Page 24 - In general, whenever it is desired to change the standard of value, it will suffice to multiply the numerical expressions of individual values by a constant factor, greater or less than unity; just as with a system of points conditioned to remain in a straight line, it would suffice to know the distances from these points to any one of their number, to determine by the addition of a constant number, positive or negative, their distances referred to another point of the system, taken as the new origin....
Page 53 - ... so great that the demand for the article and the production of it would cease. Since the function pF(p) at first increases, and then decreases as p increases, there is therefore a value of p which makes this function a maximum, and which is given by the equation.
Page 59 - We shall call attention also to the fact that necessarily / > }n , for dD being the increase of production, </[<£ (Z>)] is the increase in the cost, pdD is the increase of the gross receipts, and whatever may be the abundance of the source of production, the producer will always stop when the increase in expense exceeds the increase in receipts.
Page 60 - ... increases with D; and, as we shall soon see, it is in consequence of this fact alone that farms, mines, and quarries yield a net revenue to their owners, long before all has been extracted from the soil which it is physically able to produce, and notwithstanding the great subdivision of these properties, which causes between producers a competition which can be considered as unlimited. On the contrary, investments made under the condition that as D increases...

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