Deriving the Supply Curve: What is Sunk Cost: Shutdown price
What's a supply curve? It's the curve that shows how much of a good the firm's willing to supply at each price of the good. Here's the table showing the marginal cost to producing another Golden Snitch at each level of production from earlier when the prices snitches was $30 the firm shows to produce eights Snitches this is the point at which price equals marginal cost. See The Graph Where the x-axis is quantity and the y-axis is price if the price were different the firm would make a different choice. The price of a snitch was $10 for the marginal cost to be equal to the price and profit to be maximized.
The firm would need to produce six snitches and if the price is $20 the firm would want produce seven snitches to get marginal costs equal to price maximizing profit. We can do the same thing for prices of $4 and $50 and we can connect the dots to include intermediate prices like $13 and 4750 each of these points on the curve captures the answer the firm gets the following question asked over and over again for different prices how many snitches should it produce to maximize profits at that price? Since the answer to this question the short-run is the firm's should produce until the marginal cost is equal the price. The marginal cost curve for given quantity the corresponding price given by this curve is the marginal cost at that level of production but you usually hear this curve referred to by its more common name the supply curve. So the supply curve traces out the quantities of firm would choose at any price to maximize profit but what if the maximum profit is negative. What if the whole production is a money loser remember then the short-run. The firm doesn't just have marginal cost. It also has fixed the cost of capital like factories and equipment these costs are paid. No matter how much the firm produces and because it can't do a thing about these fixed costs in the short run. The firm ignores them when it makes that production decision it just compares the marginal cost to the price. So even if the firm sells a bunch units into a marginal cost equals price it may still have negative profits. Imagine if the fixed cost for the snitch factory was back to $200 stead of $100 and all else is the same. If the price of a snitch is $30 the firm still maximizes profits by producing eight snitches but it is losing $40 this production level this doesn't sound like a very good deal for the stench maker.
So this raises the question if the best firm can do is get negative profits should the firm just pack it in and shut down production not necessarily. Let's think about this if the snitch maker called it quits and stopped all production. It's still on the hook for the $200 in fixed costs that's equivalent having profits of negative 200. This is even worse than the profit maximizing choice to produce eight snitches for a profit of negative 40. It might not sound like a very good deal but I think we can all agree that losing $40 the whole lot better than losing $200. This doesn't mean the firm will lose money forever. Once it gets to the long run it can adjust its capital costs and have a chance of making positive profits. The key insight here is that some cost that have already been incurred and cannot be recovered should not impact a firm's decision about future actions. Some costs are sunk . So when should a firm decide to shut down production the short run. If revenues greater than variable costs the firm should stay open if not the firm should shut down revenue is just price multiplied by the number of units produced. And variable costs is just average variable costs multiplied by the same number units produced. So the price of the good in the market ever falls below the average variable cost for the firm. The firm will cease production in the short run this price threshold is known as a shutdown price. If the market price drops below the shutdown price the firm will cease production and supply for the firm drops to zero. So all this helps us understand where supply curve for individual firms come from but what about the market supply curve. Just like we saw with demand curves the market supply simply the horizontal sum of the supply of all firms in the market at each price. Imagine we have two firms in the market with the same individual supply curve shown here then you get a market supply curve that is double the quantity at any given price. Compared to the individual supply curve at a price of $30 one firm supplies eight units to the market but at this price two firms would combine to supply 16 notice that when more identical firms produce the good the supply curve becomes flatter that is to supply the good becomes more elastic.
As
there are more firms in the market the price elasticity of supply is greater supply
is more responsive to changes in price when there are more firms. Why is this
because a given increase in price stimulates a larger increase in supply when
there are lots of firms then one is just one firm.
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