Very well. So now what we have to do. We know that the goal, goal of a [inaudible] is to maximize profits so now what we have to do is to answer. To try to find a rule to answer the following question. How much output you should produce in order to maximize profits. That's the question we're going to try to answer. How much output you should produce, how many barbecue sandwiches you should produce in order to maximize your profits. Well see if we can put this into context by giving you kind of an application before I give you the answer. Say you, you produce. Making barbecue sandwich, or you can, you know, change barbecue sandwich with whatever, thing you wanted to produce. And say that at the current level of production, your average total cost, which we talk about already, right? Your average total cost, are $4.08. And that you charge, you have a price for every barbecue sandwich. Your price about $8, which is what kind of Mike said that he would charge 795. Now, if that is the case, and you wanted to increase your profits, what should you do? Should you produce more sandwiches, less sandwiches? Or should you continue to produce the same number of sandwiches you were doing before? Can you answer that question with the information. You have. So, can you answer the question with the information you have? Well, let's see. You know how much, how much profit you, you're making, in fact you can actually calculate the profit per unit you're making. The profit per unit you're making is going to be the, average tot-, the, The revenue per unit, which is a price, eight dollars, minus the cost per unit which is which I'm clear I'm telling you 4.08 and then how many units[UNKNOWN], how many units do you make. Well, in order to answer that, you might actually need, in order to, in order for you to see if what you are doing is the best, you actually may need more information than what you have. Let me explain that by bringing back the table that we had, were using last week. Now this is the same table we had been using last week, and the only thing I'm adding here is the profits which we already know how to calculate, right? The profits are going to be equal to the revenue minus the costs. So when you, when you, when you have one cook, and you produce 40 barbecue sandwiches, your profits are $140. And the way you get that is by taking the, so the profits at that level is going to be the price, the revenue per unit, minus the average total costs, a cost per unit times how many units you produce. So in this case it's going to be 8, when you have 1 cook, it can only be 8 minus 4.50 times 40, which is the units you produce. And that's going to be equal to $140. So when you have one cook. 40 units, you, you make a profit of $140. When you have two cooks, you produce 90 sandwiches, you have $460. When you have 3 cooks, you make a 120 sandwiches, you have $620. Four cooks, $660, 5 cooks, $620. And when you have six cooks in the kitchen, you produce 142 sandwiches and your profits are $556. Which, again, is the situation that I just gave you in the question, right? So in that question, I was telling you that your cost per unit was $4.80 and your price was $8. And I asked you, should you actually produce more or less? Well you don't know much. I mean, just from the question but now that you see the table. It is clear that if you reduce the quantity of hot sandwiches from 142 to 140, you get rid of one of your cooks, instead of having 6 cooks, you have 5 cooks. You will actually make 600, $620 in profits instead of $556. So clearly If you get rid of that cook, your profits go up. So if you actually are making, if, if you knew that, then your answer would have been that you should produce less sandwiches. Because, by producing less sandwiches, you get rid of more costs than revenue and your profits go up. But you didn't know that, so clearly you couldn't answer that question. And the key here, that you need to know, is you need to know the marginal costs. You need to know how much your cost change when you hire the last cook or how much your cost change when you produce the last sandwich. If you don't know that you cannot answer the question. But now that you know that at least for this table that is clear that if you want to maximize profits, the number of units you should produce should be 135 sandwiches which is $660 in profits. Now to understand why that is the best you can do, let's see if, what would the result be if doing something different. So, let's say you're producing for, 135 units of. Sandwiches, 135 sandwiches with four cooks. Let's say that you decide to, well, I'm doing well, let's hire another cook and produce more sandwiches. Let's say that you want to move from, 135 to 140 sandwiches. Well then you produce 140 sandwiches. Your costs are actually changing by how much? Well you have how many more units you produce. You have five more units. Q the changing Q is five units of Q. And then your changing costs, well, your average total cost goes from $3.08 to $3.57. Right? So your average total costs increase by 3.57. Minus 3.11. So you're an average total cost is increasing by that much, right? A change in your average total cost. And, and every unit, you have five more units, so you're actually adding that much cost. So what I'm calculating here is what we talk, is what we have been calling. The marginal cost of producing from 1,[INAUDIBLE] , from 1, 30. From 135 to 140. The change in total cost of the 140th unit will be the changing cost over the, over the changing output. But, all right. So the bottom will be the 5 units, which is the additional units that the, worker brings, the fifth worker brings. And on the top will be the additional cost, which will be the 3.57 minus 3.11. All right? So that turns out to be, $16. So. When you actually hire another worker, the 140th unit brings you, it increases your cost by $16. Now how much money are you making on that, 140th unit? You're only making $8. So when you make a 100, that 140th unit. Your adding $16 of cost to your operation and you're already adding $8 of revenue, so clearly your profits will go up. I mean, I'm sorry, your profits will go down. Why? Well because at, at that extra person, that extra cook only adds output of five units, you're paying that person the same. So that person is increasing your cost by a lot, by $16 and yet you're charging $8. [inaudible]. So clearly you should not hire that other person, because if you hire that other person, the amount of output that other person brings you is not enough to cover the costs that you have to charge, I mean, the revenue you make on the sandwiches. So if you were using five cooks, and you were making a profit of 6.20, if you wanted to increase your profits you should get rid of that fifth person. And increase your profit to 60s. Now how about if you were actually using three cooks and making 120 sandwiches? Well you'd see that if we calculate the marginal costs, the actual, marginal cost of the 135th unit was actually $5.33. So when you produce the 135th sandwich your costs increase by $5.33, per unit. How much did you make on that unit? $8. So clearly, you make more money on that unit, extra, that you actually increase your costs, so that 135th unit actually increases your profits. So you should produce it because that unit will increase your profits. Now beyond that, you should stop because your additional costs are more. So let's summarize what we just said, looking at the table. What we just said is that the profits, which is this symbol here It's going to be, it's going to be the revenue minus the cost. Right? So whenever the last unit you produce add this much revenue, and only this much cost, then your profit go up. Because the last unit, your marginal revenue of the last unit, was actually larger than the marginal cost of the last unit, or additional cost of the last unit. And your profit go up. So when your marginal revenue is, is more than your marginal cost, you should produce more, or continue to produce, right, at least one. Now on the other hand, when your profits, when your revenue of the last unit increased by only this much but the cost of the last unit increases by that much, then in that case your marginal revenue of the last unit was less than your marginal cost and your profits went down. So when your marginal revenue is less than your marginal cost, when they are, the additional revenue of the last unit was less than the additional cost of that unit, you should cut production in order to not pro, or cut that, so you can get rid more of cost, then. So you should produce less, or cut production. And if you produce less, you get rid of more costs. Down revenue. And you know you're doing the best when your marginal revenue equals your marginal cost then that is the highest profits. So, we ask that question at the beginning. What is the rule that you will use to decide how much to produce and maximize profits? This is a rule right here. In order to maximize profits, any business, you produce at a point at which the marginal revenue equals the marginal cost. Now at this point you might be asking well, I mean we, we're making a huge assumption here which is that the price always end up being $8. So we're going to talk about that assumption in our next session. [music] Produced by OCE Atlas Digital Media at the University of Illinois, Urbana-Champagne.