In the short run, a profit-maximizing firm should shut down if which of the following is true?

Video transcript

- [Instructor] We've spent several videos already talking about graphs like you see here. This is the graph for a particular firm, maybe it's making donuts so in the donut industry, and we can see how the marginal cost relates to the average variable cost and average total cost. We go into some depth several videos ago, but we see that trend, that marginal cost, can trend down initially because as quantity increases each incremental unit could benefit from things like specialization. And then the marginal cost, the cost of each incremental unit as a function of quantity could go up because of things like coordination costs. And then we've also seen how that relates to average variable costs, that while marginal cost is below average variable cost, every incremental unit is going to bring down the average variable cost, but then when marginal cost crosses average variable cost, well now every incremental unit is going to bring up the average variable cost. And the same thing happens once it crosses the average total cost. And of course the difference between, for any given quantity, between the average total cost and the average variable cost, that is the average fixed cost. Now with that out of the way, we're going to think about how this firm would react under different market conditions. We're going to assume that it's in a very competitive or we could say a perfectly competitive market and so it is a price-taker. And so let's first imagine what would be a positive scenario for this firm. Let's imagine the price up here, so let's call this P sub-one and in a previous video, we already said it would be rational for a profit-maximizing firm to produce at a quantity where the marginal cost and the marginal revenue is meet. And if we're talking about a competitive market, then this price right over here is not going to be a function of the firm's quantity, so that's why it's horizontal, and it would be the same thing as the marginal revenue. So in this situation at P sub-one, the firm would produce Q sub-one, and this is a good situation for the firm because the price that it's getting is higher than its average total cost and so there is going to be a nice amount of profit for this firm. The profit is going to be the price minus the average total cost at that quantity times the actual quantity so because P one is greater than the average total cost, we have a situation where the firm is profitable, firm is profitable, it would want to stay in the market but because you have a profitable firm in this market and you're likely to have many profitable firms in that market, it will probably attract entrants. Other people might say, hey, I wanna make just as much money as this donut company right over here, than this firm, and so you'll probably have more and more entrants into the market, which will probably reduce the prices. Now they could reduce the prices until you get to a price that looks something like this. So I will call that P sub-two. Now, a profit-maximizing firm in this world would keep producing until the marginal cost is equal to the marginal revenue, which in this case is the price, and this would be, my lines aren't completely straight there but you get the idea, so that's Q sub-two. Now in this situation, P sub-two is equal to the average total cost, so the firm is break-even. It's not running at a loss or a profit. So it is break-even and so here the firm is neutral about whether in the long-run, it stays in the market or it exits the market, but you're no longer likely attracting entrants, so no longer attracting, attracting entrants. But it does make sense for the firm to keep operating at this situation even in the long run because it is at least break-even. Now let's imagine another scenario, let's imagine this price level. So for whatever reason, the market price gets to that as we've talked about, a rational firm would be producing at Q sub-three, and at P sub-three right over here, there's some interesting things. Because P sub-three is less than your average total cost, your firm is running at a loss, it's running at a loss here. So running, so firm, firm not profitable. Not profitable. Now you might say, well what is this firm likely to do, would it just shut down? Well in the short-run, it would not make sense for this firm to shut down because the price that it's getting is still higher than its average variable cost, in the short-run, the fixed cost, they've already been spent, so you might as well get as much incremental profit on the margin as you can and so as long as the price is higher than the average variable cost, well outside of their fixed cost, they're still making some money to make up those fixed costs so you have two things going on. So they would stay operating in the short run, stay operating, operating in the short-run, short-run, but what would this firm do in the long-run? Well in the long-run, it makes no sense to have a, to be in a market where you can't make a profit so in the long-run it will exit, so it will exit in the long-run. And in general, the terminology when people are talking about, well, do you start or stop in the short-run, they usually talk about, do you either shut down or operate in the short-run, and then in the long-run, where it's like, hey, are you going to sell your factories or somehow dismantle them or are you going to build new factories, that's all about exiting or entering the industry. And of course, you have another even worse scenario for this firm, which might be down here, where you have price sub-four. Here, in theory, this is where we intersect the marginal cost curve, Q sub-four. Now here it makes no sense for the company to operate at all, so because P sub-four is less than the average total cost, you would want to exit in the long-run, exit in long-run, exit the market but you wouldn't even wait for that long, wait to sell your factories, because P sub-four is less than your average variable cost, you would also just shut down, shut down in the short-run. So big picture from a firm's point of view, you obviously want to be at P one where you make a profit but you might attract entrants. At P sub-two, you as a firm in the long-run are neutral versus exiting the market or entering the market or other people entering the market, you're at breakeven. At P sub-three, in the long-run, you'd wanna exit because you're not profitable if the prices stay at P sub-three, your price is below your average total cost at the rational quantity to produce, so in the long-run, you would exit. But because P sub-three is greater than your average variable cost at the rational quantity, you would stay operating in the short-run and then the last scenario of course is P sub-four where the price gets so low that it just doesn't make sense to even operate another moment.

What happens to profit

When should a firm shut down in the short run?

At what price will the firm decide to shut down in the short run?

What should the firm do to maximize profit in the short run?