Welcome back. Last time we looked at Cornout models, where firms made assumptions that other firms in the market would keep their output fixed, and then they would determine what the best output was for them. This time we'll look at a different model for oligopoly called the Dominant Firm Model. In this model which is applicable in other settings, there's a particular firm or set of firms that has some pricing power and it assumes that the remaining firms in the market, the fringe, behaves as if they were perfect competitors. And one example we'll see where this model can be applied fruitfully is with looking at OPEC, where there is set of firms that comprise the Organization of Petroleum Exporting Countries. And then a series of other firms that can reasonably safely be assumed to behave as perfect competitors. If you're running OPEC, what is the best output level and what price should you charge for your product? The Dominant Firm Model tell us why. The model also applies to pharmaceutical pricing. Let's say you have a patent or a product such as Viagra, that's in the case of Pfizer has come off patent and has competition from generic suppliers. How much should you produce as the dominant firm, and what price should you charge? To determine what price to charge an output level, the dominant firm has to figure out its residual demand curve. And we'll see how that's derived in the next figure. We'll assume that the overall market demand is the curve D, D prime. And we'll also assume that the fringe, that a group of firms, not the dominant firm, behaves perfect competitors. And their supply curve is given by the curve SF. The residual demand curve is then determined at each price. The difference between quantity demanded and the quantity supplied by the fringe. And the quantity demanded by the market. That will give us the quantity demanded for the dominant firm. So let's take one extreme where the fringe supplies the entire potential market demand at a price of P1. There'll be nothing left for the dominant firm to supply. So one point on the dominant firm, the dominant firm's residual demand curve is P1. At the other extreme, if the fringe supplies nothing, then the dominant firm has the entire market demand to itself. So any price P2 or below, there's no fringe, the dominant firm has the entire market demand to itself. So point A is another point on the dominant firm's residual demand curve. Below a price of P2, the residual demand curve is the old demand curve. And between P1 and P2, we're subtracting overall market quantity demand from supplied by the fringe. We'd get this black curve between P1 and A. That's the demand curve that the dominant firm faces. What price should you charge? You have to figure out the marginal revenue associated with your residual demand curve, that's MRD. Compare it to your marginal cost. The right quantity for the dominant firm, QD. Charge a price of P. And that's the price that the fringe ends up taking that is set by the dominant firm, and the fringe decides to supply out to where that price hits it supply curve, QF. The total amount supplied, The amount supplied by the dominant firm and the fringe is exactly equal to the market demand at that price. So the dominant firm is the price setter, or the fringe is the price taker, between the two of them they satisfy market demand. Now, we can do some math with that same basic equation, the quantity demanded for the dominant firm equals the quantity demanded by the market, minus the quantity supplied by the fringe. And take my word for it, if you look more closely at the text, you'll figure out how exactly this is derived. But what we can do is come up with an equation for the dominant firm's elasticity demand that's based on three components. The elasticity demand for the overall market, the elasticity of supply for the fringe, and MS or the market share of the dominant firm. And the elasticity of demand demand for the dominant firm is going to go up, the more sensitive the market demand is to price. So as the elasticity of the market demand increases, the elasticity of the dominant firm will increase. As the fringe can respond more quickly to any price increase, that'll make the consumers from the dominant firm also more price sensitive. And as the dominant firm has a lower market share, its demand elasticity will go up. So if it counts for less of the overall market output, it's going to see as it tries to raise price, more consumers run away from its product. And let me give you a simple example in the case of Pfizer, that I alluded to earlier, and producing Viagra, the erectile dysfunction drug. Let's say its market share is 50%, is 0.5. And let's say the elasticity of the market is equal to 1, sorry. And the elasticity of the fringe, the supply elasticity, is equal to 2. And if you do the math there, the elasticity for the dominant firm's demand curve will end up being equal to 4. Now, just to test yourself how this formula works, what if instead of these parameters, what if we assumed Pfizer's market share was equal to 10% as opposed to 50%. Then with the lower market share, the demand elasticity for the dominant firm for Pfizer would be 28. Lower market share, consumers would be much more sensitive to the price charge, they would runaway much more quickly from Viagra's pricing than they would before where Pfizer had half of the market, okay? Instead of that change, let's assume that the only difference with the initial set of parameters was that the elasticity of demand for the market Was equal to 5. So instead of being 1, it was five times this large. Then the elasticity of demand for the dominant firm, You can check me on the map, would equal 12. So instead of an elasticity of demand initially being 4, consumers would be three times as sensitive. Any 1% increase in price would lead to quantity demanded decreasing by 12%, as opposed to 4%. And then the last thing, let's imagine that the elasticity for the fringe supply, the generic drugs that compete with Viagra, was equal to 5 instead of 2. Then the elasticity for Pfizer and its drug Viagra would be equal to 7. Again, larger. And this is just an example to show how the elasticity demand for the dominant firm depends on this three factors. And we observe this in pharmaceutical pricing routinely as a drug goes off patent and that's a saying where its patent expires and requires more generic competition. Its elasticity of demand tends to go up. Why? Because its market share goes down, and the elasticity of the fringe supply, they're more generic producers that can more aggressively over time respond, tending price increase. As both the dominant firm's market share goes down and the elasticity of the fringe supply goes up, the dominant firm's elasticity of demand goes up. Next session we'll see how to apply the dominant for model to OPEC.