Similarly, when the series of iso-cost lines and one isoquant is given, then the producer equilibrium will be at the point, where the given isoquant touches the lowest possible iso-cost line (E2 in Fig. 7.10 (b)).

All other points are either not desirable (implying higher total cost indicated by points lying on higher iso-cost line than EF) or not feasible though preferable (points lying on lower iso-cost line than EF), as the given output cannot be produced with factor combinations indicated by these points.

How the entrepreneur ultimately arrives at the point of equilibrium, can best be explained with the help of the concept of marginal rate of technical substitution (MRTS) and the price ratio of the two factors. The producer will not choose to produce the given output at point ‘P’ (on isoquant IQ2 in Fig. 7.10 (a)) or point ‘T’ (on isoquants IQ in Fig. 7.10 (b)), as at these points MRTS (slope of the isoquant) is greater than the price ratios (slopes of the price lines) of the factors.

Hence, producer will use more of factor ‘X’ (labour) for factor ‘Y’ (capital) and go down on the corresponding isoquants to become better off. Similarly, at point ‘Q’ (on isoquant IQ2 in Fig. 7.10 (a)) or point ‘U’ (on isoquant IQ in Fig. 7.10 (b), we face the reverse situation and the producer will substitute factor ‘Y’ (capital) for factor ‘X’ (labour) and will go up on the respective isoquants to ultimately reach the equilibrium points E1 and E2 to achieve greater output or lower cost in the two cases respectively. At these points, marginal rate of technical substitution is equal to the price ratio of the factors and the producer would be maximising the output or minimising the cost using the factor combination in this manner.

Mathematically,

Slop of isoquant = Slop of iso-cost line

That is, at the point of equilibrium, the marginal physical products of the two factors are proportional to the factor prices. In other words, the last rupee spent on one factor (say, labour) is as productive as the last rupee spent on other factor (say, capital) and producer has no incentive to change the combination of two factors.

If, for instance, the price of factor ‘X’ is twice as much as that of factor ‘Y’ then the producer will purchase and use such quantities of the two factors that the marginal physical product of factor ‘X’ is twice the marginal physical product of factor ‘Y’ The result can be extended for more number of factors as MPX/PX = MPy/ PY = MPZ/PZ = …

It is to be noticed that at the point of equilibrium, the isoquant must be convex to the origin; i. e. at the point of equilibrium, MRTSX must be diminishing for equilibrium to be stable. In Fig. 7.11, ‘e’ cannot be the point of equilibrium, as isoquant IQ1 is concave at this point and MRTS increases here. With a concave isoquant, we have corner solution (point e3 in Fig. 7.11). Thus, e2 is the point of stable equilibrium, where isoquant is at a higher level and it is convex.

The behaviour of the producer in choosing the quantities of factors is exactly symmetrical with the behaviour of the consumer. Both the producer and the consumer purchase things in such quantities as to equate marginal rate of substitution with the price ratio.

The consumer, to be in equilibrium, equates his marginal rate of substitution (or the ratio of the marginal utilities of two commodities) with the price ratio of the commodities. The producer equates the marginal rate of technical substitution (or, the ratio of the marginal physical products of the two factors) with the price ratio of the two factors.