question_answer

Explain the conditions of a producer's equilibrium in terms of marginal cost and marginal revenue. Use diagram.

Answer:

According to MR-MC approach, the producer attains equilibrium where the following two conditions are satisfied

(i) Necessary condition of First Order Condition (FOC)

MR = MC

Or,        \[\frac{d(TR)}{dx}=\frac{d(TC)}{dx}\]

(ii) Sufficient condition or Second Order Condition (SOC)

MC curve is rising and cuts MR curve from belo:

That is, Slope of MC > 0

\[\frac{d(MC)}{dx}>0\]

The conditions are explained below diagrammatically.

(i) Condition 1: MR = MC

If price is greater than the MC the firm can increase profit by increasing the production. In figure (i) At output\[O{{Q}_{1}}\], price is \[K{{Q}_{1}}\] and the marginal cost is \[L{{Q}_{1}}\], such that \[K{{Q}_{1}}\] >\[L{{Q}_{1}}\]. Therefore, \[O{{Q}_{1}}\] is not the profit maximizing output. This is due to the fact that the firm can increase its profit by increasing the production of output to\[O{{Q}_{2}}\]

On the other hand, if price is less than MC the firm can increase profit by lowering the production. At output\[O{{Q}_{3}}\], price is\[H{{Q}_{3}}\] and the marginal cost is\[G{{Q}_{3}}\], such that\[H{{Q}_{3}}\] <\[G{{Q}_{3}}\]. Therefore, \[O{{Q}_{3}}\] is not the profit maximizing output. This is because the firm can increase its profit by reducing its output level to\[O{{Q}_{2}}\].

(ii) Condition 2: MC curve should be rising at the point of intersection with MR

In the diagram, the MC curve cuts the price line (or MR) at two different points i.e., at ?Z5 and ?E5. The first order condition of profit maximization, i.e. Price (or MR = MQ is fulfilled at both these points.

At Point Z: MC is falling and is negatively sloped. Any slight increase in the output would imply that the price exceeds MC. This implies that the firm can increase profit by increasing the production.

At Point E: MR is equal to MC and also MC is rising. Any deviation from this point results in a lowering of profit for the firm. Thus, both the first order condition (MR = MQ and the second order condition (MC curve should be rising at the point of intersection with MR) are satisfied at point E. Hence, point E is the equilibrium point.