Producer's (Firm's) Equilibrium: Marginal Revenue and Marginal Cost Approach

• A producer is in equilibrium when it produces that level of output at which profit is maximum or loss is minimum, and it has no incentive to increase or decrease output.​
• Under the Marginal Revenue–Marginal Cost (MR–MC) approach, equilibrium output is decided by comparing extra revenue (MR) and extra cost (MC) from each additional unit of output.​

In the short run a firm must decide whether to produce at all.

• Even if the firm produces zero output, it must still pay fixed costs (FC).
• If it produces some output, it must at least cover variable costs; otherwise, producing increases loss.

Shutdown rule (short run):

• The firm should produce only if
  \[P\mathrm{or}AR\geq AVC\quad(\mathrm{or}TR\geq TVC)\]
• If P = AVC, the firm covers only variable costs. Loss = fixed cost in both cases (produce or shut down).
• If P > AVC, the firm covers all variable costs and part of fixed costs, so loss is less than in shutdown. It should continue production.
• If P < AVC, revenue is not enough to cover variable costs. Loss is smaller if the firm shuts down and bears only fixed costs.

Once the firm decides it is better to produce than shut down, it must decide how much to produce.

• If MR > MC, each extra unit adds more to revenue than to cost, so an extra unit increases profit. The firm should increase output.
• If MR < MC, each extra unit adds more to cost than to revenue, so the extra unit reduces profit. The firm should reduce output.
• When MR = MC, there is no incentive to increase or decrease output.

Rule 2 (necessary condition for equilibrium):
A firm’s profit is maximised at the output level where
MR = MC
This is called the first-order condition for producer’s equilibrium.

Equality of MR and MC alone does not guarantee maximum profit.

• Sometimes MR = MC may occur at more than one level of output.
• One of these may give minimum profit (or just break-even), not maximum profit.​

To ensure maximum profit:

• At output just below equilibrium, MC < MR (increasing output raises profit).
• At output just above equilibrium, MC > MR (increasing output beyond this level reduces profit).

In diagram terms:

• MC curve must cut MR curve from below, and be rising at the point of intersection.
• So:
  Left of equilibrium: MC < MR
  At equilibrium: MC = MR
  Right of equilibrium: MC > MR

This is called the second-order condition for producer’s equilibrium.​

Think of a coaching centre. Monthly rent and licence fees are fixed. Teacher payments per batch and electricity are variable. If fees collected per month at least cover teacher and electricity costs (AVC), it may keep classes running even if the owner’s own income is low, because closing down still requires paying rent.

• Producer’s equilibrium is the situation where a producer maximises profit or minimises loss and has no tendency to change output.
• Rule 1 (Shutdown rule): In the short run, produce only if P or AR ≥ AVC; if P < AVC, shut down.
• Rule 2 (First-order condition): Profit is maximised when MR = MC.
• Rule 3 (Second-order condition): At equilibrium, MC is rising and cuts MR from below, so MC < MR just before equilibrium and MC > MR just after equilibrium.
• Both MR = MC and MC cutting MR from below are necessary and sufficient for producer’s equilibrium under the MR–MC approach.​