How do you maximize profit, if you're a perfectly competitive firm? You want to compare total revenue with total cost, across the different output levels, you can choose. What we're going to be interested in, is pi, or profit, the difference between total revenue and cost. Average profit is another piece of information to keep track of, but it's going to be less important, than the actual dollars to the bottom line, the pi. Let's turn to table 9.1, and this is a situation where, we can tell, we're operating in a perfectly competitive market. Because price remains constant in that second column, no matter how much output we produce, $12 per unit. Total revenue keeps going up for output, but at the rate of $12 per additional output, we're just multiplying q times the price received, which is constant. Total cost and total variable cost have the same general shapes, we've encountered before. They're associated with average total cost curves and average variable cost curves, that we've covered before. The next column's profit. The difference between total revenue and total cost. Would've chose, as if, we chose an output level of zero. Profit would be negative 15. We'd still be stuck with certain costs, and earning no revenue. In the short run, we'd still be stuck with the total fixed costs. As we keep varying output, what we see happen here is, the profit starts to increase. It becomes less of a first negative number, and then it becomes more positive, but then it, after a certain point, declines. Profit per output, or average profit, is the next column. It just divides profit by quantity. What it'll turn out, the important rule of thumb, to determining the appropriate output level, is comparing incremental cost to incremental revenue. So, when I vary output, how, how much do my costs go up by, marginal cost, relative to how much, does my revenue goal up by, per unit, or marginal revenue? Marginal cost is the rate at which total cost changes, per unit of output. It's the next to last column. Marginal revenue, is how much total revenue goes up by per unit. In a perfectly competitive setting, it's going to always be the same as price. Always the same old, so is average revenue, $12 per unit. Now, let's look how this rule of thumb operates. When we go from output of one to two to three, the marginal cost, up til we reach seven units of output, falls below marginal revenue. Each of those steps, we're adding less to cost, than we're adding to revenue. So along that range, where marginal cost is less than marginal revenue, profit keeps increasing. And the intuition here is, if that's the case, if you're continuing to build the profit pile, keep going, keep expanding output. When marginal cost equals marginal revenue, which it occurs approximately at an output level of eight, that's where profit's maximized, at $11.10 in this particular table. Beyond that, marginal cost is greater than marginal revenue, if we keep expanding output, where we're adding more to the cost, than we're adding to the revenue. And notice what happens to profit, beyond an output of eight, it starts to decline. Eventually, it falls back in output level of 11 to zero. Let's represent those same numbers, graphically, figure 9.2. Notice, first the total revenue, the blue curve. It has a constant slope. It starts at the origin, because if you produce zero, even if the price is $12, total revenue's zero. For a perfectly competitive firm, the slope of the total revenue or the marginal revenue, equals the going price, $12 per unit. Total cost has that same familiar shape that we've seen, first, it starts off at a level of total fix cost, it rises, but at a slower rate, where the, there are advantages to teamwork or specialization. Then, it starts increasing in slope, where the law of diminishing returns kicks in. Now, what the green line depicts, is the difference in height between total revenue and total cost, the pi. We want to maximize the height of this pi the height of this green curve. At zero, the height is minus total fixed costs, but then, it keeps rising in height. It becomes less negative, and finally reaches a peak, point C, at an output level of eight. Notice, that this occurs, where the difference in height, between total revenue and total cost, is greatest, and where that difference in height between the total curves is greatest, is also the same as, the same point, where the slopes of the total revenue and total costs, are the same. Think about output level q0, where total revenue equals total costs. So the profit in the green curve, is zero. Beyond that point, the slope of the total revenue curve, is greater than the slope of the total cost curve. So, the area between total revenue and total cost, the height difference keeps widening. And then, we reach an output a level q1, where it's height between total revenue and total cost, the difference in height is maximized. That's the point, where the slope of the total revenue and totals cost are equal, where marginal revenue equals marginal cost. And beyond that point, marginal cost, or the slope of the total cost curve, is greater than marginal revenue. The difference in heights between the total curves, starts to constrict. The green curve, profit, starts to fall. How do we figure profit from the, looking at incremental cost curves, and the firm's demand curve, the price curve? Figure 9.3 depicts that. What a firm wants to do, is keep producing output, so long as marginal revenue exceeds marginal cost, and up to the point, where the marginal curves are equal, up to output level eight. So, as long as we keep taking the, those steps, we're adding to the total profit hill. How do we depict total profit on these, on this per unit cross curve? We use the average curve, to do that. Specifically, at an output level of eight, profit equals average revenue, minus average total cost, multiplied by output. So profit at this point, is the rectangle, the blue rectangle, BCDA: the height difference between the averages, multiplied by output. We use the marginal curves, the m-curves, to get to the right output level, we use the a-curves to figure out graphically, the output level. Key take away here is, the importance of thinking of the margin. And when we apply this rule, it's not always going to be at the most minuscule output levels. Let's say, I'm in farming. I'm probably not going to think about, should I apply an extra square centimeter to farming a particular crop. I may be thinking more, should I apply an extra square hectare or an extra square acre, to rice or corn or another type of crop. It's similar, if you were ever held up, at gun point in central park or another tough location, at night. if the would-be robber said, your money or your life, you probably would just think of the relevant margin being giving all my money, and preserving my life. As opposed to, trying to bargain with the robber to say, look, I'll give you $50 if you rough me up only a little bit. or I'll, I'll give you $25 if you rough me up even more, and send me to the hospital. So, the relevant margin can differ by a particular setting we're in. But the key insight is, you always want to be comparing at the, at the level that you can measure it. How much do I add to marginal revenue, and how much do I add to marginal cost? And I'm going to be increasing profit, the overall outcome as a producer, if I keep going to the point, until those two marginal curves are equal. Now, what this implies is, we can determine the firm's short-run supply curve, in a competitive setting. And we can also look, where it's better to shut down. The fundamental rule for the firm in its decision to supply, is to keep shooting out, to where price intersects marginal costs, to where marginal revenue equals marginal costs. So long, as you're at least, covering your variable cost. Take the case of figure 9.4. At a price of $8 per unit, shooting that price out as your demand curve, that marginal revenue curve. You'd want to produce out to q1 outputs of output, so long as, at that point, you were above average variable cost. You're still going to be losing money in this situation, and let's see why. Av, total profit at this point, where marginal cost equals marginal revenue, be negative. Why? Because we compared the height of the average total cost curve, with the average revenue curve. You're earning on average, a negative amount per unit, a distance of c f, multiplied by q 1 units of output. So the profit you make, by following the marginal rule, would be negative. But you'll still want to produce out, to this output level because if you opt to shut down, you'll lose even more. How can we see that? The amount you'll lose, if you shut down, is total fixed cost, cost you're stuck with, no matter what. How can we depict total fixed costs, at an output level of q1? An interesting thing, an interesting way to depict total fixed costs, it's the height of the average fixed cost curve, at any output level, multiplied by quantity. An average fixed cost at q1, is just the difference between average total cost, and average variable cost. It's the only other cost out there, that's gets added into the total. So, we multiply that height of cd, times q1, we end up with an even larger loss. b c d a, the orange and the blue triangle, the amount of total fixed cost we'd lose, if we shut down. So, this is a case for following the marginal rule. We still lose money, but we bleed by less, by following the marginal rule. If we're below average variable cost, so let's say, price came in below where, marginal cost intersect average variable cost, that's a situation, where it'd be better to shut down. That's a situation where, basically, you're bleeding, but by remaining around, you're picking at the scab and making it worse. So, the fundamental rule, marginal cost is the firm's supply curve, in a perfectly competitive setting, so long as we're above, where that marginal cost curve, intersects the average variable cost.