IB Economics 2.11.4 Rational Producer Behaviour Notes

Rational Firms Produce Where MC = MR

1. A rational producer wants the greatest possible profit, which is what is left once total cost is taken from total revenue.
2. Perfect competition is the clearest place to see how a firm reaches that goal, so start there.
3. A firm follows one rule: keep producing while the next unit adds more to revenue than it adds to cost.
4. It stops when the two are equal, at the output where marginal cost equals marginal revenue, $MC = MR$.
5. In perfect competition the firm is a price taker, selling every unit at the same market price.
6. So its marginal revenue is simply that price, $MR = P$, and the rule becomes produce where $MC = P$.
   1. A firm with market power is different: because it must lower price to sell more, its marginal revenue lies below price.

Marginal Cost: Falling Then Rising

1. Marginal cost ($MC$) is the cost of producing one more unit.
   1. It falls at first, as early units gain from specialisation and better use of resources.
   2. Then it rises, as diminishing returns set in and each extra unit costs more.
2. That gives the $MC$ curve its distinctive U-shape, low in the middle and steep on the right.
   1. Reading the curve, marginal cost is about 20 at 100 units, dips to about 10 near 175, then climbs to about 60 by 350.
   2. The schedule later in this article carries those same marginal costs, alongside revenue and profit.

Why Marginal Cost Cuts Average Cost at Its Lowest Point

1. Average total cost ($ATC$) is the cost per unit produced so far, and it is also U-shaped.
2. Marginal cost always cuts $ATC$ at the very bottom of that U.
3. The reason is how an average responds to the next value added.
   1. While $MC$ is below $ATC$, the extra unit costs less than the running average and pulls it down.
   2. Once $MC$ rises above $ATC$, the extra unit costs more than the average and pulls it up.
   3. The two are equal exactly at the lowest point of $ATC$.

When to Produce and When to Shut Down

1. A rational producer also decides whether to produce at all in the short run, by comparing price with two points on the cost curves.
2. Break-even point: where price equals minimum $ATC$, so the firm just covers all its costs and earns normal profit.
   1. Above it the firm makes abnormal profit, and below it a loss.
3. Shutdown point: where price equals minimum average variable cost ($AVC$).
   1. If price is above minimum $AVC$, the firm keeps producing, since it covers its variable costs and part of its fixed costs.
   2. If price falls below minimum $AVC$, it shuts down, since producing would lose more than the fixed costs it must pay anyway.
4. $MC$ cuts both $ATC$ and $AVC$ at their lowest points, which is why those minima mark the two thresholds.

Reading Profit from One Schedule

1. With output set at $MC = P$, profit reads two equivalent ways.
   1. As totals, profit is total revenue minus total cost, $TR - TC$.
   2. Per unit, profit is average revenue minus average cost, $AR - ATC$.
2. A single schedule at a fixed price lays all of this out, so the total revenue curve is never needed.
   1. Total revenue is just the price times quantity, and profit is total revenue minus total cost.
   2. The marginal cost column is taken straight from the curve above, so the table and the graph line up.
   3. The firm keeps expanding while marginal cost stays below the 40 dollar price, so it stops at 300 units, where marginal cost has risen to 40.
   4. Profit peaks there at 3,200 dollars, the highest in the table, even though the lowest marginal cost was back at 175 units.