Welfare as an economic quantity . number of rectangularhyperbolae, in such a way that all the axes of ordinates co-incide, and that the area subtended by the resultant curve(, between it and the axis of abscissae) and lying betweenany two ordinates is the sum of the areas between thecorresponding ordinates of the constituent curves, is itseKa rectangular hyperbola. ^ Given: Pjand Pj any two points on a rectangulai* hjT)erbola X7j = c;Qi and Q2 any two points on another rectangular hyperbola xy = h (re-r ferred to same axes of coor- dinates) ; Ml, a point whoseabscissa is the same as thatof
Welfare as an economic quantity . number of rectangularhyperbolae, in such a way that all the axes of ordinates co-incide, and that the area subtended by the resultant curve(, between it and the axis of abscissae) and lying betweenany two ordinates is the sum of the areas between thecorresponding ordinates of the constituent curves, is itseKa rectangular hyperbola. ^ Given: Pjand Pj any two points on a rectangulai* hjT)erbola X7j = c;Qi and Q2 any two points on another rectangular hyperbola xy = h (re-r ferred to same axes of coor- dinates) ; Ml, a point whoseabscissa is the same as thatof Pi or Qi and whose ordi-nate is equal to the algebraicsum of the ordinates of Pjand Qi, that is 2/1 = 2/1+ 2//; andMj, apoint similar to i!/j. To prove that the coordi-nates of Ml and ilf2 satisfythe equation of a rectangularhyperbola. Proof: The equations ofcondition for the points PyP2, Qi, and Q2 are XiVi = c x.^2 = c Xivi = k x^Vz = ft ? XiVi = c . .-. 2/1 = - 3:22/2 = c .-. 2/2 = - Xl <^2 — -^ and X2 = X2 = X2 X\ *2. Since Xj ~ Xj^ ~ Xj XiVi = h :. 2/1 THE SCOPE OF DIMINISHING UTILITY 61 It is, of course, the area subtended by the curve that re-presents the quantity of utility or of demand. The methodand results of summating these areas constitute the sub-ject under consideration. In the case just mentioned theyare added by way of the ordinates. Such addition of util-ity or demand curves raises a question as to what thenhappens to the significance of a unit of the horizontaland vertical scales, respectively. Price is measured along the vertical axis. This scaleremains the same for the summated as for the componentcurve. But if we should add a number of curves, the levelof the resultant curve might be raised to an inconvenientheight, hence it may be well to reduce the scale or plot theresultant curve on a smaller scale than the componentcurves, perhaps by dividing the summated scale by the num-ber of component curves. This will give the resultant curvea mean position
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectwealth, bookyear1915
