Why Marginal Cost (MC) equal Market Price (PC)?

Question

In most models, perfect competition implies that MC = P, shouldn't it be the average cost that is equal to price instead?

If the Average Cost is greater than the Marginal Cost, firms are losing money when they sell at their price P = MC.

Answer 1

In most models, perfect competition implies that MC = P, shouldn't it be the average cost that is equal to price instead?

No, you can verify it yourself mathematically. In perfect competition firms take price $p$ as fixed so the profit function is given by:

$$\Pi = pq -c(q)$$

Where $q$ is quantity produced and $c$ is cost function. Because firm is is a price taker in perfect competition it cannot control price only quantity, so firm choice variable is $q$.

Now if firm maximizes profit we take derivative of profit function wrt $q$ to find first order condition for profit maximization which is:

$$p-c'(q)=0 \implies p=c'(q)$$

$c'(q)$ is unambiguously marginal cost not average cost (which would be $c(q)/q$). So it is indeed a marginal cost not average cost.

If the Average Cost is greater than the Marginal Cost, firms are losing money when they sell at their price P = MC.

It is possible for perfectly competitive firm to have economic loss in a short-run even if it maximizes profit.

There is not much that firm can do here. Perfectly competitive firm cannot charge higher price than exogenously given (from the point of view of the firm) market price without loosing all customers. So $p$ is fixed, $q$ is already set optimally so that profit is maximized (the maximum value of profit can still be negative number). Only other option is to shut down production altogether, but by assumption that can happen only in long-run since in microeconomics short run is defined as a time period when firm dont have enough time to enter/exit market.

Answer 2

in the short run, firms fix the price of goods based on their variable costs and ignore the fixed cost. so while pricing goods profit-maximizing firms ensure P=MC at least, where p=price and MC=marginal cost. but in long run, it should produce at a point where its average cost(AC) is minimum.

similarly, in the perfect market condition, we assume that there are no fixed costs which increases the barrier of entry for a new firm. so no fixed cost means, variable costs or marginal cost(MC) will be the same as average cost(AC). thus in perfect market P=MC.