The Concept of Economic Efficiency 27 



the contour lines Zq, Z^, Zg, and Z3. Any point along a given con- 

 tour represents a constant level of output and, in this sense, these 

 constant product curves are not unlike the indifference curves of 

 Figures 1 and 3. For example, an input of Oxq of factor X and Oyo 

 of factor Y would -produce an output equivalent to Zq in the 

 vicinity of point J. Now an addition of one unit of X, the input 

 of Y remaining as before, would increase output to the level of Z^ 

 in the vicinity of K. Alternatively, decreasing X to the original 

 amount (Oxq) and increasing the input of Y by a unit would 

 increase output to Z^ in the vicinity of L. In short, a substitution 

 between a unit of X and Y would produce the same level of output 

 using the two factors combined in different proportions. However, 

 unless the two factors were perfect substitutes (a condition incom- 

 patible with their being "different" factors), the marginal rate of 

 substitution at any point necessary to maintain total product con- 

 stant would vary with changes in the proportions in which the two 

 factors were used. This phenomenon of diminishing marginal rate 

 of substitution between factors accounts for the convexity of the 

 constant product curves. 



The second characteristic of the production function also can be 

 shown in Figure 4. Although the output can be increased from Zq 

 in the vicinity of J to Z^ by the increment of a unit input of either 

 X or Y, it can be increased beyond Zi by a unit increase in both 

 factors — that is, from Zq at J to Z^ at K by a unit increase in factor 

 X, and from Z^ at K to Zg' at M by an increase of a unit of Y. If 

 we assume, however, that factor Y happens to be fixed and that all 

 additions to output must be achieved by changes in the input of X 

 alone, output can be increased from Zq in the vicinity of J to Z^ at 

 K and Z2 at N, etc., only by more than proportional increases in 

 the input of factor X. 



This can be observed better perhaps in a diagram commonly 

 used to illustrate the "law of diminishing returns." In Figure 5, 

 factor X and output Z are measured, respectively, along the hori- 

 zontal and vertical axes. Diagonal movements from the origin 

 upward and to the right correspond to the movement from posi- 

 tions such as J, K, and N, on the constant product curves Zo, Zj, 

 and Z2 of Figure 4, when the input of Y is held constant at Oyo 

 while the inputs of factor X are increased. The change in total 

 output per unit increase in factor X is defined as the marginal 

 physical product of X, or its marginal productivity. Conversely, 

 the amount of X which is required to increase output by one unit 



