question_answer

Why is the equality between marginal cost and marginal revenue necessary for a firm to be in equilibrium? Is it sufficient to ensure equilibrium? Explain.

Answer:

According to MR - MC approach, the firm (or producer) will attain equilibrium where the following two necessary and sufficient conditions are fulfilled.

Case A: If Price (MR) > MC

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\[O{{Q}_{2}}\].

Case B: If Price (MR) < MC

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 due to the fact that the firm can increase its profit by reducing its output level to\[O{{Q}_{2}}\]. Thus, we can conclude that at profit maximisation output, the equilibrium price (or MR) must be equal to the MC curve and it cannot be greater or lesser than the MC curve. The equality of MR and MC is only the necessary condition, the sufficient condition is that the MC should be rising at the point of intersection with MR.

In the figure, the MC curve cuts the price line (or MR) at two different points i.e., at ?Z? and ?E?. The first order condition of profit maximisation, i.e., Price (or MR) ?MC is fulfilled at both of these points. Now let us evaluate which of the following two cases fulfill the second order condition of profit maximisation.

Case A: At point ?Z?

At point ?Z?, price is equal to MC but MC is falling and is negatively sloped. At this point, any output level slightly more than the \[O{{Q}_{0}},\] the firm is facing price that exceeds the MC. This implies that, the profit can be maximised by increasing output level beyond\[O{{Q}_{0}}\]. Therefore,\[O{{Q}_{0}}\] is not a profit maximisation output.

Case B: At point ?E?

To the left of the point ?E?, if the firm produces slightly lesser level of output than\[O{{Q}_{2}}\], then the firm is facing price that exceeds the MC. This implies that higher profits can be achieved by increasing the level of output to\[O{{Q}_{2}}\]. On the other hand, to the right of the point ?E?, if the firm produces slightly higher level of output than\[O{{Q}_{2}}\], then the firm is facing price that falls short of the MC. This implies that higher profits can be achieved by reducing the output level to\[O{{Q}_{2}}\]. Thus, the point E is the producer?s equilibrium and\[O{{Q}_{2}}\] is the profit maximizing output level, where Price = MC and also MC curve is rising.