Application of Equal Product Curves to Returns to Scale
The equal product curves can be used to show how returns to factors of production will vary as the scale of product}on is varied. In the figure 19.8, IPo ‘ IPI’ and IP2 are the three equal product curves. They constitute the firm’s equal product map like an indifference map. Along the X Axis, we indicate factor A and along the Yvaxis the factor B. We take here the returns with two variable factors. LM, L’ M’ and L” M” are the price lines or outlay lines tangential to the respective equal product curves. In this situation, according to the proportionality rule As in the case of indifference curves indicating the consumer’s equilibrium, in this case also the producer will be in equilibrium position at the points P. P’ and P” respectively on the equal product curves IP() , IPI . and 11’2 ‘ because at these points the price lines arc tangential to their respective curves. This means that only at these points will the firm be producing in the cheapest manner. At any other point (say other than P on the equal product curve IP0>, the producer will have to use either more than 0 1of factor A or more than OL of factor B. At the points 1′, P’ and P”, the marginal productivity of factor A in terms uf factor B is edqual to the relative money prices of factors A and B.

By joining P, P’ and P” we get what is known as. the Scale Line corresponding to the income consumption curve in the case of indifference curves map. It is on some point along the scale line that the firm will Iix its scale of output given the relative prices of the two factors. The scale line shows how a producer varies his scale of operations. It indicates the most economical combination of the factors of production or the cheapest way of producing each output. The shape of the equal product curves and the relative prices of the factors used will determine the shape of the scale line. Thus, the scale line shows the varying combinations of the factors of production as the scale of output is varied. A change in the relative prices of the factors will change the course of the scale line. The equal product map like the one given above shows (a) whether the returns to scale will increase decrease or remain constant as the scale of production is varied. and (b) whether the proportion between the factors of production employed will vary or remain constant as we move along the scale line.

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