Marginal Productivity Theory with Many Inputs

The distribution of output is determined by  product principles, Total wages are the lower erectness- (equal to the wage rate times the quantity of labor Land gel the residual upper triangle , Note additionally that the positions of land and could be reversed to get a complete theory of distribution. To switch the roles of labor and land hold labor constant and add successive able land to fixed labor. Calculate each successive acre’s marginal product.

Then draw a demand curve showing how many acres labor owners will demand of land at each rent rate. In the new version of Figure 12-8 that you draw, find a new E point of equilibrium, Identify land’s rectangle of rent as determined by rent times quantity of land. Identify labor’s residual wage triangle. Finally. note the complete symmetry of the factors. This new graph shows that we should think “r the distributive shares of each and every factor of production as being simultaneously determined by their interdependent marginal products. That is not all. Instead of labor and land, suppose the only two·factors were labor and some versatile capital goods. Suppose a smooth production function relates Qto labor and capital with the same general properties as in Figure 12-8. In this case, you
can redraw Figure 12-8 and get an identical picture of income distribution between labor and capital. Indeed, we can perform the same operation for three, four. or any number of factors. 239

In competitive markets. the demand for inputs is determined bv the marginal products of factors. In the simplified case where factors arc paid in terms of the single output. we get
“‘age product of labor Rent = marginal product of land and so forth for any factor. This distributes 100 percent or no more and no less. among all the of production.

We see. then, that the aggregate theory of the distribution of income is compatible with the competitive pricing of any number of goods produced by’ any numberof factors. This simple but powerful shows how the distribution of income is related to productivity in a competitive market economy.

Now that we are armed with the general principles underlying the pricing of factors of production and the determination of the distribution of income, we can turn to a detailed discussion of the special features in “the three major factor markets-e-land, labor, and capital.

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