Strategy To Find The Optimal Short Run Quantity

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Strategy to Find the Optimal Short Run Quantity

We can summarize the strategy for finding the point where the firm maximizes its short-run profit in a few steps:

  • Find the point where MC = MR and where the MC curve is increasing.
  • Is that point above (or equal to) AVC, i.e. is p = MR ≥ AVC? In that case, choose to produce the corresponding quantity.
  • In the opposite case, i.e. if p = MR < AVC, choose to produce nothing at all; q = 0. The condition p = MR < AVC is called the shut down condition.

Also, note for bullet points 2 and 3, the reasoning behind the condition MR ≥ AVC: Since we are looking at the short run, the fixed cost, FC, cannot be changed. The firm can always choose to produce nothing. If it does so, it receives no revenues and incurs no variable costs, but it will still incur the total fixed cost, FC. Total profit will then be a loss of -FC. This means that the firm will choose to produce as long as it can at least recover some of that loss.
Moreover, the firm will do so as long as the price, and therefore MR, is larger than or as large as AVC. In the short run, the firm can consequently accept to produce at a (small) loss, since the loss will be smaller than if one chooses to shut down production completely. If instead MR < AVC, the revenues from additional units sold cannot even cover the average variable cost of producing them. Then it is better to shut down.

The Firm’s Short-Run Supply Curve

What happens if the market price changes? Then MR changes, and the point of intersection between MR and MC also changes. The firm will then choose to produce the quantity that corresponds to the new point of intersection, so the quantity supplied follows the MC curve as the price changes. However, this is only true as long as the price is higher than AVC. To see why, look at the shut down condition above again. Suppose the market price falls to the point where the MC curve intersects the AVC curve, i.e. at the quantity q = 72 in the figure. At that point, MR = p = MC = AVC and the profit becomes q*(p - AVC) - FC = 72*0 - FC = -FC. Note that p – AVC is what the firm gets paid in excess of average variable cost for each unit it sells; q*(p - AVC) is then what it gets paid in excess of average variable cost for all units it sells; finally, subtracting FC yields what it gets paid in excess of all costs (= profit). The loss is consequently as large as if we choose to produce nothing at all. If the price falls even more, the losses increase and it is better to produce nothing. The conclusion of this is that, the firm’s short-run supply curve is the part of the MC curve that lies above AVC,

The Market’s Short-Run Supply Curve

The market is the sum of all individual firms. We get the market’s supply curve by summing all individual firms’ supply curves horizontally.

Short-Run Equilibrium

In Figure 9.2, we have summarized the equilibrium in the market and the equilibrium for an individual representative firm. To the right in the figure, we have the individual firm’s MC-, ATC-, and AVC curves. The short-run supply curve of the firm is the part of the MC curve that is above AVC. For prices below pmin, there is consequently no supply at all. If we sum all firms’ supply curves, we get the market’s supply curve, S, to the left in the figure. (Σ(MC) means "the sum of all MC curves.")

In the market, supply meets demand, D, and an equilibrium price, p*, and an that the individual firm receives for each unit of the good it sells. Since there are a large number of firms, no individual firm can charge a higher price than p*. If some firm did, the consumers would choose one of its competitors instead. The MR curve of an individual firm is consequently horizontal and equal to the price, p*. The firm chooses to produce the quantity q*, as this quantity makes MC = MR and, consequently, maximizes profit.
In the short run, a firm in a perfectly competitive market can make a profit. In Figure 9.2, the profit corresponds to the grey rectangle on the right-hand side. To see that this is the profit, note that in a perfectly competitive market AR Revenue) is as large as MR is, since the firm is paid the same amount for each unit sold. Furthermore, q*AR = TR and q*ATC = TC. Profit is then π = TR - TC. To summarize, we have that

The right-hand side of this expression corresponds to the grey rectangle in Figure 9.2. With the example we used before, we get that π = 78*(2.20 - 131/78) = 41.

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