Perfect Competition Profit on the Graph

Alright, now let's see how we find the profit maximizing quantity, right? Where we want to produce as well as how we calculate profit on the graph, let's do that now. So the profit maximizing quantity, right? Even in the very first lesson we did, I mentioned where we're gonna produce, right? And we talked about this key formula about marginal benefits and marginal cost right to the firm. Marginal benefits are the marginal revenues, right? The money that they're bringing in and the marginal cost. Well, that's the cost, right? The extra money they're gonna spend to earn that that revenue. So here we go, the profit maximizing quantity is where that marginal revenue equals the marginal cost. Okay. And now, one thing to note is that the profit maximizing it could also mean loss minimizing, right? It doesn't necessarily mean that we're gonna make money, but at least we're gonna lose as little money as possible, right? So marginal revenue equals marginal cost. That is key point on our graph, we're always gonna be looking for this point. Pretty much every time we go to the graph, this is gonna be like a point we're looking for. All right? So let's go ahead and find that on this graph. Right now, we Were given the price on the market, right? Which we saw that the price for a bushel of wheat was $4. So the firm is going to face this flat demand curve, right? This flat curve right here on the graph, that's the firm's demand curve. And we did say that the price right, is going to equal that average revenue and it's going to equal the marginal revenue and perfect competition. Right? So there we go. We've got our marginal revenue curve right there, which is equal to the demand curve for the firm, right? This is the demand curve for the firm and there we go. We've got a marginal cost curve there as well given to us. And we're gonna find our profit maximizing quantity. So we just have to find where these curves cross, which is very simple right here, and this is the profit maximizing quantity. We got to see how much quantity would we produce at this point? Well, it would be right here like 4.5. And let's say, just just for a hypothetical, let's say it was a case that you can't produce 4.5 bushels, right? You can't do like half a bushel of wheat. Well, what would you do, would you produce four? Or would you produce five? What do you think in this case? So look at the graph right here and think of what happens if we produce four units and think of what happens if we produce five if we produce four units? Well, we're right here, right, we would be producing here, we would be bringing in this much revenue and it would cost us this much. Right? So the cost is still less than the revenue. That's a good thing. But if we produce five, notice what happens now, the cost is above the revenue. That's a bad thing, right? We don't want the cost for it to cost more than the money we bring in. So in that hypothetical case where you got to pick one or the other, you're gonna pick the lower one, right? Because if we went up to five, we would lose some money and we wouldn't maximize profit. So ideally we would go right here where the lines cross and that's what you're usually gonna see, pretty much in all the problems that you're not gonna have to deal with this, but I'm just throwing it out there as just an intuitive thing, right? We're gonna produce just a little less. If we have to write we don't, we never want that marginal cost to be greater than our marginal revenue. Alright, so right there is where we would want to produce at 4.5 units, ideally. So let's go ahead and discuss how we how we're gonna calculate the profit or the loss based on this quantity, we know that we want to produce this quantity, how much money is that gonna make us? How do we calculate that? Well, let's go on down here. So we've got our formula for profit first here in the middle of the screen, and what we've got is the price minus the average total cost. Alright, so now we're gonna bring in another curve into the whole mix here, we've been dealing with marginal revenue and marginal cost so far, and now we're gonna deal with average total cost as well. Okay, so that price minus the average total cost. This this uh bracket right here, this parentheses, that's the profit per unit, right? If we take the price, that's the money we're gonna bring in for the unit minus the average total cost, that's what it costs us for that unit times the quantity. Okay, so that that's kind of just a very general profit uh formula. And it's gonna it's gonna work in all market structures. We're gonna keep this formula throughout the next several chapters, price minus average total cost in parentheses to get our profit per unit, and then we multiply that by quantity. Okay, so let's go ahead down to these two graphs down here, knowing what we know about profit now. And let's use these two steps. These two steps are always gonna be relevant when we're trying to calculate profit. Okay, this is gonna work in other market structures as well. So let's go ahead and start here uh with finding the profit maximizing quantity, right, That's always gonna be the first step, how much are we going to produce? And then we're going to calculate the profit. Okay, so the first step, how much are we going to produce? We need to find where marginal revenue and marginal cost curves intersect. Okay, so let's start here on this left graph. So find your marginal revenue curve, your marginal cost curve, and mark the point where we're gonna produce. Alright, I'll give you a second to try it and then I'm gonna market. So right here, right, we've got our marginal revenue, the flat demand curve, right? Which is also our marginal revenue curve in perfect competition, crossing the marginal cost curve right there. Right? So if we go down to our quantity access, right, just like we're used to a quantity axis here a price. Now we're gonna extend this accent access a little bit at this point because it's not just prices that go on this up down axis. Now it's also cost as well. So it's gonna be prices cost, it's just dollar values. Okay, so the idea here is that these are really just dollar values because we're gonna have prices like the price of the product that we see here in the middle, but it also shows costs like we have on these cost curves. So it's just a little better I guess nomenclature to use a whole just wider range. Right? Just to say dollars on that axis. Okay, so back to the point here, we've got our marginal revenue and our marginal cost. We found the point where we're gonna produce and we need to find out what quantity that's gonna be. So we're gonna take it down to the quantity axis and it'll be this quantity right here, right? That would be the quantity that we're going to produce and maximize our profit. Okay, So now how do we calculate the profit? So it tells us we're gonna find the price, which is on the demand curve, right? The price is always gonna be on the demand curve, average revenue, which is price equals our demand curve, every market structures like that. Okay, now, in this one, it's easy because the price, it's the same spot as the marginal revenue, it'll get a little more complicated in other market structures. But right now it's easy, right? We've got our price on the demand curve at that at that point is right there right here in the same dot and we want to find at that same quantity what our average total cost is. So if this is our price, then we've got our average total uh excuse me, average total cost right here, Right, This is our average total cost at that quantity. Well, the price minus the average total cost, right? If price, so let's say I'm gonna do this a little visual example for you here. Um So the price would be this whole line, right? So I'm gonna do it off to the side. The price would have been this whole line right here, right, And the average total cost was this whole area right here, right, this area, I'm doing it off to the side, but I'm talking about that, that quantity, right, that profit maximizing quantity. So if that that whole blue line was the price and the green area I shaded is the average total cost. What's left over here? This little area right here, that's the that's the profit per unit. Right? So that profit is gonna be this this uh this line right here between the marginal revenue curve, excuse me, the price, right? And the average total cost and we multiply it by the quantity. Okay, so the quantity over here, we're gonna get that this whole region right here is our profit, right? So we want to find the price and the average total cost at our profit maximizing quantity and then that is going to be our profit right there, that area. Okay, so this is our profit right here. Okay, and that's because the average total cost was less than the price, right at that quantity. Our average total cost was less than price. So we made profit here, I'm gonna label it here at the top as profit in this case, right? Because our average total cost was less than the price. Now, how about on this right hand graph, look how high up that average total cost curve has become. Alright, so let me go ahead and get out of the way. So we can see the whole graph. And let's do the same thing. Right? Remember we always start by finding marginal revenue equaling marginal cost. Well where's our marginal revenue curve? Where's our marginal cost curve? Go ahead and mark the point, I'm gonna give you a few seconds and then I'm gonna market. Alright, so our profit maximizing quantity will be where this marginal revenue equals marginal cost right here. Okay, so our profit maximizing quantity in this case is right here. Q. Okay. Now our second step, right? We need to find price and average total cost at this quantity. So in perfect competition, it's easy because the price is right there on the same dot that we already picked. And our average total cost at that quantity is right up here. Right? So notice what's happened this time. Now the average total cost is greater than the price at the profit maximizing quantity. So this actually becomes a loss. Minimizing quantity. Right? So this is still where we're gonna want to produce to minimize our loss. Okay, So the same thing is gonna happen. We're gonna take the space right between the two. Right this area or this line right here represents the loss per unit times all the units that we sell, right? We're gonna sell all these units here. And that's gonna be the loss is gonna be this box that I just shaded in. Alright, so that is the amount of our loss. We could calculate that if we had a number for our quantity, a number for our price and average total cost. We could calculate the area of that rectangle. Right? So that would be the loss minimizing quantity, right. If we tried any other point we would increase the loss. Alright So let's go ahead and make some conclusions here about what we've seen. So let's go ahead. Well first let's label this graph. This was the loss graph on the right hand side. Right? That was a loss that we just illustrated. So let's go ahead and make these conclusions down here. If price is greater than average total cost. Uh Just like we saw in that left graph right? The price was greater than average total cost. Well there we're gonna make profit right? Let's go on to the right hand side behind me. Let me get it back out of the way price less than average total cost. So like we saw in the right graph right? The average total cost was above the price. Well we had a loss in that case. And how about in the middle when the price equals the average total cost? Well if you think about that on our profit right here this if this equals this right, price equals average total cost five. If that price is five and average total cost is 55 minus five is zero. Right? So we're gonna end up with zero no profit and no loss. If p equals a. T. C. We're gonna say we break even, okay we don't make a profit and we don't make a loss. Alright so this is how we're going to see um the profit and loss on the graph. Right? So you should be ready to to find these these key points on the graph and calculate profit and lost after this lesson. Alright, so easy steps first. We're gonna find that marginal revenue equals the marginal cost, and then we take it to the price and the average total cost to calculate our our profit or lost. Alright, let's go ahead and practice a little bit before we move on to the next topic. All right, let's do that in the next video.