So, in this lecture, we're going to discuss market structure, and how the different types of consumers in the market and companies in the market actually affect our choice of optimum price of the maximum profit that we found in the previous lectures. So, before we begin, let's try to think for a minute. Would it make a difference if we knew that in this market there was a single consumer or multiple consumers that were buying the product? Also, does it matter if there's a competing product to the product we're selling? So, why I am asking these questions? Let's see a very simple example. If there are competing products for the products I'm selling, if I increase the price, maybe some of the consumers buy less of my product, maybe they just switch to buy a cheaper product, and they become more brand loyal to that other product, and will never return to buy my product again. So, let's take a look at what market structure is, and how different examples actually change the maximum profit we can gain in different market structures. So, the structure of the market is the part of the model, and so far, in the model, what we tried to answer is how do the actions affect the goal or the objective we're trying to maximize. Now, we're also adding the question, what else is everyone else in the market doing when we're taking these actions? So, for example, if we change the price, do other companies in the market also change the price? And the question is, can we use the same descriptive data that we have before also affect and guide our decision to find an optimal price under different market structures and different models? And the answer is of course, we can. And let's see two of these examples. In the first example, I would like to show you the answer to the question, what happens when we know that in our market, there are many consumers who purchase the product? So, let's assume now, for example, that in this market, there are many, many, many consumers, and the demand curve we've seen in the graph was generated by each consumer purchasing up to one item. So, either a consumer purchases zero items or one items, but no consumers want to purchase more. If we decrease the price to nothing, every consumer will take at most one product and use them. Is the price of 6.5 still optimal, that the price we found in our previous lecture that maximizes the profit. The answer is actually yes. If you think about it, there's no change in the demand function of the graph or the revenue table we generated, by the fact that we know there are multiple consumers, each one wanted to buy, at most, one item. What I would like to look at now is what would happen if we knew that the demand curve, that we saw before, came from a single consumer. And the question is, what is the difference if we know that we have one single consumer in the market versus multiple consumers in the market? One thing that we can think about or notice is that if there is a single consumer and the demand curve shows that at different prices there are multiple items being sold, it probably means that the consumer may want to purchase more than one item. So, what we can do is we can try and change the way we're selling items to the consumer. The question is, will the consumer be willing to pay different prices for different amounts of the same item? Can we sell item at a different price than a second item, etc. So, let's take a look at the following table to understand how this works. What we would like to do is calculate something called willingness to pay. And willingness to pay is how much, at most, a consumer is willing to pay for the next item we're selling them. So, imagine the following sales process, the consumer comes and I'm going to tell them, the first item costs $10.70 and the second item is going to cost $9 and the third item is going to cost $7. Will the consumer still willing to buy all of these products? On the table on the right-hand side, you can see this calculation in quantities of half items, and generally, you can do that for whole number of items, half items, quarter items, etc., depending on the type of the product. What we can see on the right-hand side is that for a different quantity of items sold, I'm calculating the price of the next item to be sold. For example, if I already sold one item for the next half item, the consumer will be willing to pay between $10.14 to $9.59, which is basically the prices on the demand curve. And then, the prices, let's say, of the next half item between three items, so 3.5 items is going to be $7.92 to a price of $7.37. We can take these numbers and try to calculate an average price the consumer will be willing to pay for this additional half item. The way to do that is to calculate the surface below the demand curve or the graph, because basically, it gives us kind of the average price that the consumer will be willing to pay for each fractional part of the item. So, lets take a look at two examples. If I never sold any item to the consumer, I know that for the first fractional item, the consumer is willing to pay a price of $11.26, and when the consumer reaches half an item, they will be willing to pay at most $10.70 for this additional fraction. And if we do this average price, which is basically the trapezoid surface below the curve, we will get a willingness to pay of $5.49. We can do this same analysis for items between three and three and a half Items. And we will see that for a quantity between three and three and a half items, the willingness to pay will be $3.82. Now, we know how much a consumer is willing to pay for each additional item, the question is what is the profit we're making? In order to understand the profit, we need to look at the cost as well, which is the fourth column on the table, and compare it to the willingness to pay which is the third column on the table. If we do the calculation, basically we will take the willingness to pay minus the cost. And we'll get the profit we will make for each additional half item we're selling to the consumer. So, for the first half item, we will get $4.49. For the second half item, we'll get $4.29, and then, that means for that one first item, that is first half plus the second half, we will get a profit of $4.49 plus $4.29. Now, if we're looking how much we will make for the fourth item we're selling, which means between three to four items, then we will be getting the willingness to pay between 3 to 3.5. The profit is 2.82, and the profit between 3.5 and 4, and the profit is 2.54. And that sum will be the profit for the fourth item that we're selling. What we can do is we can calculate the total profit we will be making for each bundle, or each quantity of products we will be selling. So, we can do it for up to one item, up to two items, up to three items, etc. And all the way going down to up to nine items. And what you will notice is that at the ninth half item at the end, actually it's the 18th half item, but it's the ninth item we're selling, the profit is becoming negative. That is the willingness to pay of the consumer is less than the cost it is costing us to actually produce the product. It means that it's not worthwhile for me, and I'm not making a profit from sending an additional item to the consumer, and I would probably like to stop. So, how can we use all of this to increase our profit? What we can do is we can sell something called a bundle. And a bundle is basically a take it or leave it offer to the consumer. In a bundle, we're telling this consumer, you can buy this quantity of items at this fixed price, or you can get nothing, and it's your choice. So, what would happen if we offered the consumer eight and a half items at the price of $55.53. The first question we want to ask is, is the consumer going to still buy our bundle, and the answer is yes. The answer is yes, because this is the sum of the consumer's willingness to pay, and we know that for each one of those partial items, the consumer will still be willing to pay this price. The second question we would like to ask is, what is the total cost of producing this bundle? And the answer is, eight and a half items times $2, which is the cost for a whole item we're going to produce. This is $17. And the profit will be the revenue, $55.53 minus 17 dollars, which totals $38.53. The interesting thing to notice is that if we compare this case, which is selling one bundle to one consumer, we actually are sending a higher quantity of product to the consumers and we're also making a much higher profit. Comparably to the previous case of multiple consumers, we see that the optimal profit is almost twice as high, and previously, we also sold a much lower quantity to the consumers and couldn't do any better. The conclusion here is that if we know a little bit, whether it's a single consumer or a multiple consumer, and whether those consumers actually want one item or two items, we can choose whether to sell them in bundles, which will increase our profit. Or we need to price every item at the same price for every consumer, and then, we cannot make use of the willingness to pay to try and bundle those products together.
