More generally, the total product for a factor of production, such as labor, can be expressed as a function relating output to the quantity of the resource employed. Continuing the example, the total product of X is given by the production function
This equation relates the output quantity Q (the total product of X) to the quantity of input X employed, fixing the quantity of Y at two units. One would, of course, obtain other total product functions for X if the factor Y were fixed at levels other than two units.
Figure 7.3(a) and 7.3(b) illustrate the more general concept of the total product of an input as the schedule of output obtained as that input increases, holding constant the amounts of other inputs employed. This figure depicts a continuous production function in which inputs can be varied in a marginal unbroken fashion rather than discretely. Suppose the firm wishes to fix the amount of input Y at the level Yr The total product curve of input X, holding input Y constant at Y = Yv rises along the production surface as the use of input X is increased.
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