We know that profits are equal to revenue minus total cost of revenue is 50 times 100 of 5000. We can go ahead and calculate profits if we want. This is the profit maximizing output and price. 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. 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. 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. In this case, it's 150- 2Q = Q, or solving for Q we get that the monopolist output is equal to 50. Finding the profit maximizing output is setting marginal revenue equal to marginal costs.
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.
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, this marginal cost curve is missing the part that first goes down, and then increases. If we had to draw this marginal cost curve it would be an upward sloping line. 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. And these are the total variable cost because they are dependent on quantity, and they increase as quantity increases. So of course, this is the fixed cost of production because this is the amount that is not dependent on quantity. So we have the demand curve, and we have the marginal revenue curve, we need to introduce the cost structure for the firm. Because every time you lower the price, you have to give a discount on bigger and bigger previous quantities. So again, the marginal revenue lies below the demand curve and its steeper than the demand curve. So it's a linear straight line demand curve with an intercept of 150. Let's continue with the demand curve that I introduced earlier, P = 150- Q. I'd like us to go through the profit maximizing quantity and price for a monopolist with a specific numeric example.
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