[MUSIC] I'd like us to go through the profit maximizing quantity and price for a monopolist with a specific numeric example. Let's continue with the demand curve that I introduced earlier, P = 150- Q. So it's a linear straight line demand curve with an intercept of 150. And this implies that the MR = 150- 2Q. So again, the marginal revenue lies below the demand curve and its steeper than the demand curve. Because every time you lower the price, you have to give a discount on bigger and bigger previous quantities. So we have the demand curve, and we have the marginal revenue curve, we need to introduce the cost structure for the firm. So here is the total cost function. TC = 1,000 + .5Q squared. So of course, this is the fixed cost of production because this is the amount that is not dependent on quantity. And these are the total variable cost because they are dependent on quantity, and they increase as quantity increases. We can derive the marginal cost curve. It's the derivative of the total cost with respect to quantity, or if you don't like calculus, just believe me the MC = Q. If we had to draw this marginal cost curve it would be an upward sloping line. That looks something like this. So, this marginal cost curve is missing the part that first goes down, and then increases. But in some sense we can disregard that part, because we know the firm is never going to produce at the point that is below the average variable cost. So again, here's a numerical example, downward sloping demand curve, downward sloping marginal revenue curve, upward sloping marginal cost curve, so let's go ahead and solve for the monopolist quantity and price. Finding the profit maximizing output is setting marginal revenue equal to marginal costs. In this case, it's 150- 2Q = Q, or solving for Q we get that the monopolist output is equal to 50. So suppose this firm is making jeans their monopoly output is where marginal costs equals marginal revenue, and the firm should go ahead and produce 50 units. And what is the price? We have to take this quantity and plug it back into the demand curve, so that the pm=150-50. It's equal to $100 per unit. Graphically what we're doing is we're taking this quantity, plugging it back into the demand curve, and we get that the price is equal to $100. This is the profit maximizing output and price. We can go ahead and calculate profits if we want. We know that profits are equal to revenue minus total cost of revenue is 50 times 100 of 5000. And what our costs? We're given the total cost curve here, we have the fixed cost of a 1000, and we have the variable cost which are .5 times a quantity of 50 squared. And we could go ahead and calculate this if we wish.