Greetings, we're continuing our adventure in figuring out how firm would maximize profits given the firm had its own cost curves and was facing some exogenously given price. And we're doing this exercise because we don't want to, the course that we're studying for is called price theory, but right now we're just going to say suppose there was one price, how would you optimize? So let's go and start thinking about this on our graphing. Remember, profit maximization requires marginal revenue equals marginal cost. We established that as the point where the residuals of revenue in excess of cost would be greatest is when you find the upper point where marginal revenue equals marginal cost. So let's think about that graphically. We start with this axis system that's got output on the horizontal, dollars and cents on the vertical. And what we want to do is we want to find that output point where marginal revenue equals marginal cost. Well, we spent a lot of time thinking what marginal cost curve looks like and we found that in general, the marginal cost curve is a u-shaped curve that looks like this. Again, you might as, how did you know where to draw it there Larry? I don't, I just know it's u-shaped and this is the general form u-shape. If in fact, I had given you a polynomial function that was an equation for what the cost curve look like. You could actually solve the exact point of the marginal cost curve, it will be a little bit difficult because it's got a lot of shape to it. But you could do that. We don't have to do that right now, we're just thinking about the intuition. And then we gotta think about marginal revenue. We discovered that marginal revenue is essentially, the slope of the total revenue function, the derivative of total revenue with respect to output. But total revenue is just price given exogenously times output. And so if you were to take the derivative of that or the slope of that slope would just be that price, okay? So what we're going to do then is I'm going to draw that. I'm going to draw that right here,. Okay, so this will call marginal revenue. And now the question is where do we maximize profits? And so given that horizontal price, I should put this price here. This price is given to you exogenously, given to the firm exogenously and given that price, where's the firm is going to maximize profits? And of course the answer is the firm will choose where marginal revenue equals marginal cost. And as you can see, we have a small problem here because marginal revenue equals marginal cost at alpha and marginal revenue equals marginal cost of beta. And so both alpha and beta satisfy our rule of marginal revenue equals marginal cost. So we're kind of have a problem, what's happened here? I mean, if I was able to show earlier that that's the way the thing goes. Well, I want you to think about the intuitively about these two points just for a moment, okay? So humor me, I'm going to make a copy of this. Every page five and I'll just go back here to page four. Just for a moment imagine you're at this output point Q sub alpha. If you write Q sub alpha and you decided to go ahead and increase your output by just one unit, what would happen to your revenues and your cost? Well, if you increased output one unit past Q alpha, what would the extra revenue be from that unit? This is marginal revenue, that's the extra revenue, the change in revenue for a change in output. What's the cost? Down here that means that for that unit, you're getting back into your cash register more than you actually paid out to produce it unambiguously profits are going up. In fact, if you did it with another unit, you'd still get that much for that extra unit and cost would be this. If you did for another unit and so you can see that each extra unit you produce you're actually adding this vertical bar to your profits until you get out here to beta. And once you get the beta, suppose you, let's label this point Q sub beta. Now suppose you increased one more unit past Q sub beta, what happened? Well, that extra unit past Q sub beta would give you this amount of revenue, but the cost of that unit would have been higher than the amount of revenue that you got back, not a good idea. You're going to pay more to produce that product and what consumers will actually pay you for it. So you're going to stop at beta, okay? You're not going to stop short of beta, you're not going to go pass beta. So Q sub beta is the profit-maximizing output. You might ask yourself the question, wait a minute Larry, what about Q alpha? You kept telling me what alpha and beta of keys. So that's the next step is we need to figure out did I really make a mistake here or am I trying to confuse you or what? We'll turn to that in the next video.