Now, we will see how the firms would behave if there were one entity, if they were under common ownership, and they cared to maximize their joint benefit, not only the benefit of themselves, but the joint benefit of the two of them. So, this will be used only as a benchmark to see how it compares to our previous solution. So, if the manufacturer and the retailer, they make a joint decision, they will maximize the joint profit function. That is the average overall profit from producing the goods. This will be p minus c, this is the average profit per unit, p minus c times the final demand as we have done in the past. So, this has to be maximized with respect to p, to the final price. And, once we do that we are going to derive their optimal price, which now, I will use an index j to distinguish it from the previous price that we derived when firms are acting separately as separate entities. So, PJ is the final price that the joint firm will charge the final consumers with, and this would be 1+c/2. And, the joint profit in this case, would be 1-c2/4. Now, it's interesting to compare what is happening with the integrated benchmark case if it is compared with the separate decision case. When firms are independent, when firms are acting in a separate manner. Then, the final price ends up to be higher. You can see these results that we derived in this section and, in the previous one and, PJ is smaller than P. So, the joint price is lower than the price that they would charge the final price that were separated, the independent structure or charge. Also, the profit is lower under independent decisions. So, if firms make each their own decision about P W and P profit will end up to be lower. If the firms are integrated, they will end up having a higher profit. This is a very interesting situation. We see that we have two firms that they tried to do their best for themselves separately. And, they ended up to an inferior result than if they're acting as they were one. This is a very interesting fact and, it's known in the literature as double marginalization. It's the problem of double marginalization that non-integration leads the industry to profits lower than the first best. And the first best in this case is if the firms acted as an integrated, one integrated structure. So, the double marginalization is a problem that first was pointed out by Joseph Spengler in 1950. And, it hurts both firms, but also the consumers. So, both firms are doing worse off, but also the consumers are ending up paying high prices and consuming less product in the end. So, everyone is worse off from the double marginalization problem. This is something very useful and we will need to take it into account in the very end of today's lecture, that we will talk about policy for vertical relationships between firms. So, keep it in mind because we will need it later. Why does this happen? Mathematically, for those of you that have mathematical mind that you understand the models in a mathematical way, you will see that the two-stage optimization that we are doing in the separate decision case is equivalent to a constraint one stage optimization that in which case we have the same objective function subject to the first of the condition from the second stage. So, what do we actually have is one constrained optimization problem. So, economically though because we mainly care about the economic intuition of our models and this is why our models are useful and we cannot explain the same things without having those models. Economically, when the retailer chooses the final price the problem is that the retailer at this point does not care about the effect of their decision on the profit of their other partner. So, they only care about their own profit. They do not care about the result that they cause to the profit of the other firm. This is an egoistic decision that the retailer is taking into the end. So, this is usually referred to as a vertical externality in prices. There is an externality, the behavior of the retailer causes a vertical problem because there is a vertical relationship causes a vertical problem to the manufacturer. And, this is when a decision about price is made. Let's see how we can avoid this problem because there are methods firms have developed business methods that they solve these problems. These problems are very usual in reality and they have been addressed with business techniques, that they are very effective in solving them. So, one of them is vertical restraints. So, assume that the manufacturer has the bargaining power. That is because the manufacturer is creating the product. And, the manufacturer has a choice to who he is going to give this product for retail. So, this can give some bargaining power to the manufacturer side. But, as we said there are cases where the retailer is very big will also have significant negotiation power over the manufacturer. So, in this case if we assume that all the bargaining power is on the manufacturer side, what we can do is that the manufacturer can behave in a smart way that we have also seen before in a previous lesson. That, probably you do not really know, your mind doesn't really go there. So, what is it going to do? It's going to apply a two-part tariff. It will charge a very low, the lowest possible transfer price equal to cost. So, the manufacturer will just break even from the production. And then, charge a franchise fee like an entry fee as we used to call it in when we talked about price discrimination. And, these franchise fee will be equal to the entire profit of their retailer. So, this is exactly like the same thing that their monopolies was doing. So, will charge a very low price and then the entry fee would be equal to the entire consumer surplus that we have in this case. So, in this case the franchise fee A again would be equal to the profit of their retailer in case that they charged the joint price. And, this is very important, be careful here. So, the manufacturer will tax with the franchise fee the retailer as if the retailer had charged the price that is optimal for the first best. That is P J, English P J. Price of joint of the joint case. So, this would be equal to 1-c2/4. And, once this is happening the retailer will be forced to indeed charge P J, the price of integration as we calculated before, this will be P = 1+c/2. And, therefore with this action by the manufacturer, the retailer will be forced to behave, as if they were joint firms. And, we achieved the first best efficiency of the integrated benchmarks. So, the vertical restraints seem here that they do solve the problem. However, this method is not without side effects. We have some important side effects. First of all, the retailer indeed in real-world bears all the cost and demand risk. If you have cost and demand uncertainty, the retailer will be the one who will be responsible for them. If demand does not turn out well, the McDonald's franchise will be the one which will have losses, not the McDonald's company. Alright, the small franchise will be the one that will have the problem. And, another side effect is that as we saw back in the price discrimination lecture, that now comes very handy is that when you have different types of retailer, different kinds of retailer, a single two-part tariff, meaning a single franchise fee is not sufficient to extract the profit of the retailers. Again, you have to do this trick, that you have to charge the franchise fee for the lower type of retailer. And, then allow the high types of retailers to get away with some profit anyway. So, this is how vertical restraints work in principle. We're going to see much more specific cases from now on. And, we will continue by extending this analysis when we have also services involved that the retailer is also able to provide some presale services, which creates also an extension to the double marginalization problem. Stay with us.