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# Monopolist optimizing price: Dead weight loss

## Video transcript

Based on what we've done in the last 2 videos we've been able to figure out what the marginal revenue curve looks like for the monopolist year, for the monopolist in the orange market and this is what we got. Right over here, it was a line with a slope twice as steep as the slope of the demand curve, we'll see that's actually generalizable. There's an optional video that I'll do very shortly where I prove it with a little bit of calculus. It's very important to realize that this marginal revenue curve looks very different than the marginal revenue curve if we were dealing with perfect competition. If we were dealing with perfect competition there would be some equilibrium price in the market and all of the competitors would essentially just have to take that price. Let's say that that equilibrium price was $3 per pound then our marginal revenue curve would look like this if we were not a monopolist, if we were one of the many perfect competitors. I guess you could view it that way. Because we would just have to take that price. If we wanted to sell 1000 pounds, each of those pounds we would get$3 per pound and then if we want to sell 1001, we'll just get $3 per pound for the next one. It doesn't change. We're just taking that price. With the monopolist things do change because we are the only producer in the market. The price at which we can get changes depending on what we produce because we are the entire supply for the market and we have this downward sloping marginal revenue curve. Now, with that out of the way, let's think about what will be the optimal quantity for us to produce if we wanted to maximize profit? If we think in pure economic terms, that's what firms try to do. They exist to maximise profit. To do that, we're going to have to think about, and remember, it's not to maximize revenue. To maximize revenue we would have said, "Oh, they should just produce 3000 pounds." It's not about maximizing revenue, it's about maximizing profit. We have to take the cost into consideration. To do that, we'll have to draw a marginal cost curve. Let's say I did the research. Let's say we're the owners of this firm and we have a marginal cost curve that looks something like this. Let's say our marginal cost curve looks like this. It's important to realize, we are the market. We are the only producers here. This isn't just our marginal cost curve. This is a marginal cost curve for the market. Another way to think about it, this is the supply curve for the market. It tells you at any given price how much the market is willing to supply. You could view it as a marginal cost or you could view it as a supply curve and we've talked about it before. You could view a supply curve as a marginal cost curve. If you want the market to produce 1 extra pound, what's the minimum price you would have to give? that is the marginal cost. Now, with this out of the way, let's think about what you would produce. Well, you would definitely want to produce something you definitely start to produce a few pounds right over here because the marginal revenue you're getting is way above your marginal cost. Each incremental pound you're producing right over here, you're getting much more revenue, you're getting$5 or $6 of revenue and it's only costing you a little over a dollar. It's like, "Okay, I'm going to keep producing. "I'm going to keep producing." Over here, you're still, each incremental unit you're getting, you're still getting more revenue than the cost of that incremental unit. That keeps being true all the way until you get to 2000 pounds right over here. At this point right over here you don't want to produce an incremental unit because if you produce one more unit, if you produce that 2001st pound right over here then for that 2001st pound, your cost is going to be slightly higher than the revenue you get in. You will actually take a slight loss on that. Your total profit will start to go down and you don't want to produce less than this because you'll be leaving a little money on the table. You'll be leaving that little incremental pound where the total revenue was just slightly higher, or the marginal revenue on that incremental pound was just slightly higher than your marginal cost on that incremental pound. You will produce right over there. Now, this is interesting because this is a different equilibrium, or I guess we say this is a different price or this is a different price and quantity than we would get if we were dealing with perfect competition. If we were dealing with perfect competition, our equilibrium price and quantity would be where our supply and demand curves intersect. It would be right over here. It would be a price of$3 per pound and a quantity of 3000 pounds. Now, in order to maximize profit, we are intersecting between the marginal revenue curve or our quantity that we want to produce as the monopolist is the intersection between our marginal revenue curve and our marginal cost curve which is right over here. So we can see that there is a dead weight loss. There is a dead weight loss by being a monopoly although it's good for us. It's good for the monopolist, it's not good for a society at least in this example and there's very few where I can imagine it being good but I guess there are a few if you're trying to protect the national industry or something like that. Over here, this is the quantity that we are deciding to produce. The consumer surplus is the area above the price and below the demand curve. This right over here is the consumer surplus. The producer surplus is looking pretty good and this is essentially what we're trying to optimize. Our producer surplus is this whole area. Our producer surplus is this whole area right over here. Producer surplus right over there. But we have a dead weight cost. There's a total surplus that we would have gotten, that society would have gotten if we were dealing with perfect competition, right over here that's now being lost. But as we lose that, we were able to increase the producer surplus and decrease the consumer surplus. Beyond just having this dead weight loss over here, it's also obviously given much more value to the producer, to the monopolist and given much less value to the consumer.