Question

Explain the rationale behind the consition of equilibrium of a producer.

Answer 1

The rationale behind the conditions of equilibrium of a producer is profit maximisation. This can be achieved by following the MR-MC approach. According to this approach, a firm will attain its equilibrium and will maximise its profit when the following conditions are met.

1. Price $\left(MR\right)=MC$

2. $MC$ is rising or the slope of the $MC$ curve is greater than the slope of the $MR$ curve at subsequent output levels beyond the point where $MC=MR$

Let us evaluate the first two main conditions carefully.

Condition-1: Price (MR) = Marginal Cost

The first condition of the producers equilibrium is that at equilibrium, price must be equal to the $MC$.

Case A: If Price $\left(MR\right)>MC$ (Ref. image)

Let us analyse what happens if price is greater than the $MC$. 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 maximising 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 $\left(MR\right)<MC$ (Ref. image)

Let us analyse what happens if price is less than the $MC$. At output $Q3$, 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 maximising 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.

Condition-2: MC curve should be rising at the point of intersection with MR

Let us analyse two different situations, where $MC$ cuts $MR$. 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 fulfils 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 a 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 producers equilibrium and $O{Q}_2$ is the profit maximising output level, where Price $=MC$ and also $MC$ curve is rising.