Good afternoon. Welcome back to Industrial Organization: Strategy and Competition in Business. Today, we will talk about vertical relations. So, production often occur in different stages. It's very rare that one firm will take the product from zero and make it to its final stage. There are some cases like that but they are not very often. So, in most of the cases, production is handled by different firms and the products go through different stages that each stage is done by different firms. So, the output of one firm, in this case, a product that one firm produces might be the input of the other firm. Therefore, we have upstream firms, the ones that they produce the intermediate good, the goods that are in it's initial stage, and then we have the downstream firms which are the firms that they are in contact with the final consumer of the product. They produce the final goods. We will mainly use the example of a manufacturer and retailer. This is a simplified version of reality, so we'll assume that there is a manufacturer who makes actually the final product but then the retailer is the one who has the contact with the final consumer in the end. So, even if the manufacturer makes the final product, makes a finished product, the one who is selling the product to the consumers is the retailer. And therefore, we assume that the manufacturer is the upstream and the retailer is a downstream firm. Now, what is usual to imagine is that the power, the market power, will be with the upstream firms. So, the manufacturer has more power than the retailer. In today's complicated economies, this is not always the case. Today, we have supermarkets that they have several several branches in many cities, some of them in many countries, and they have excessive amount of power over the manufacturers especially if the manufacturers are small companies. So, there are cases where the retailers have more power than the manufacturers. These are examined by complicated supply chain models that they examine in different kinds of analysis. Today, here in Industrial Organization, we are going to examine the case where the market power is with the upstream firms. Let's start with a model in order to be able to understand everything. So, we'll have a very simple model that will compare how market power behaves when we have two firms and when we have an integrated framework. So, let's start when we have two different firms. We have one retailer that we will denote by R and one manufacturer which will be noted by Mf. Not just M because we want to distinguish these from the usual case that we have a monopolist in previous lectures. So, we have R and Mf and then they want to produce a final good, both together they will produce a final good that they will sell to their consumers. The final demand for the consumers, the end demand if you want, will be that quantity is equal to one minus price. We have used this demand curve before. It's as simple as demand curve that we can possibly have. It assumes a maximum size of the market equal to one because this market cannot absorb, as you can see the function, more than one unit of the product. So, manufacturer produces at a constant average cost. We have to assume that our cost is smaller than one because if it's more than the market capacity, the model is not going to work. And the manufacturer sells the intermediate good to the retailer at what we call the transfer price, p_w, that has to be greater than the cost or else the manufacturer would not be interested in the production of this particular good. So, the retailer takes the Intermediate price, the transfer price, as given and selects the retail price, the price that will charge the consumers with. We assume that they are both monopolies in their market. Don't forget here that the manufacturer and the retailer they are in two different markets. They are not in the same market. They are not direct competitors to each other. They play at the same game at different stages but they are not competitors in the same market. The manufacturer does not come into direct contact with the final consumers. Be careful about that because my students usually confuse it. Therefore, we have a two-stage game in which in the first stage, manufacturer selects the transfer price, the price that we'll charge the retailer with, and then we have the retailer to select the final price for the consumers. So, again, backward induction. We are going to start from the end of the game and then progress backwards. In the second stage, the retailer will select the price of the product so that it will maximize their own profit. Retailer here, this is essential for you to understand what is going on, the retailer cares only for their own profit, doesn't care at all for the profit of the manufacturer. What does the choice variable of the retailer? It's the final price. Therefore they have to take the intermediate price, the transfer price, p_w, as it is given, as it is parameter in this model. So, they maximize their profit with respect to the final price. Their profit will be p minus p_w. This is the average profit, the profit per unit, times the amount of units that they will sell. And this is given by the demand function, one minus p. So, once they maximize that, they can solve the first of the condition with respect to p and they will receive one plus p_w over two. Let's call this the relationship one because we are going to use it later on. So, therefore, if we use one we are going to find out what is a profit for the retailer. This is one minus the transfer price and everything squared over four. This is the profit for the retailer. Now, let's go back to the first page and see what is happening to the first stage now that we have information about how the game ends. In the first stage, the manufacturer's profit, so the manufacturer also needs to maximize their own profit, the manufacturer's profit is again their average profit per unit. This is p_w minus c, times the final demand for the product. Now, the retailer will be the demander of the manufacturer's product but the retailer will demand product from the manufacturer according to the final demand. So, here even the manufacturer looks at the final demand because according to these the retailer will demand product from the manufacturer. So, the manufacturer can replace p, the final price, with the relationship one that we have already derived in the second stage and we'll maximize the profit function once you substitute one there. So, this will be maximized of course with respect to the control variable of the manufacturer, which is p_w, and this will yield the optimal price for transfer of the goods from the one player to the other. So, p_w will be one plus c over two. Therefore, we can plug p_w into relationship one from the second stage before. And we will see that the optimal price, in this case the optimal final price, the optimal retail price is p equal to three plus c over four. And therefore, the total profit of the two will be profit of the retailer plus profit of the manufacturer equal to 3(1-c) squared, this parenthesis over 16. These are simple calculations with the algebra that you can go over and you can derive these profits. Now, in the next segment, we're going to talk about the integrated benchmark, how these two firms will behave if they are under a common ownership, if they are one. And then we will compare our separate solution, our solution that the two firms are separate entities with a solution that these firms are joint together, and we will see what is the result in that.