Welcome back. So, far this week we've covered consumer preferences and then the constraints on those consumer preferences. The former we addressed through indifference curves and indifference maps. The latter represented by budget constraint, and determined by consumer's income level and the prices of the goods she faces that she would like to purchase. Now let's bring those two together, to determine the consumer's optimal choice. And what you'll see on page fifteen is a lot of different equations. A way, and we'll intuitively walk through what these equations represent. Let's first turn to the next page though. To see where these equations come from. The consumer has a certain amount of income, and is constrained by certain prices, against that, certain consumer preferences. So, bring those two together, where this consumer will end up is maximizing the satisfaction she can get, with the income level at her disposal, and with the prices that she faces. And where that'll end up is where, her budget constraint just touches the highest possible indifference curve, in this case U2, at point W. Where she ends up consuming six movie passes a week, and two compact discs. She'd be even more satisfied on indifference curve U3. But the budget constraint doesn't allow her to reach that level of satisfaction. And with her budget constraints she could definitely reach a lower indifference curve like you want. For example, at point R on U1, the budget constraint at her disposal allows her to reach point R. But at point R, she's willing to give up three movie passes for one additional compact disc. Her marginal rate of substitution. The rate at which she's willing to give up movie passes for compact discs, is greater than the rate at which she has to, based on market prices. The slope of the budget constraint is two. The slope of her indifference curve when we take it in absolute value terms of point R is three. So, the benefit she gets from additional, compact discs and giving up movie passes of three, exceeds the cost in the marketplace of two. She would want to keep trading movie passes for compact discs. Likewise at point Y, This is the point where the marginal rate of substitution of indifference curve U1 is one for one. At point Y she'd be willing to give up, one compact disc in return for getting one movie pass. So, her rate of being willing to move to the left and upward on indifference curve U1, a one for one rate, is lower than the returns she can get in the market. In the market with prices of compact discs being twice as high as for movie passes. She could get two movie passes for each compact disc, so she can do better than the point Y. She'll end up with point W, at that optimal point, where the following equations hold. This is where we'll jump back to the preceding page. At her optimal point, point W, the rate at which she's willing to give up movie passes for compact discs. The change in M over the change in C in, in absolute value terms we'll take the, because it's a downward sloping curve we'll take the negative of them. Is equal to the price ratio the price of compact discs to the price of movie passes. It's equal to the slope of the budget constraint. And what that translates to in the second line is, the marginal rate of substitution equals the marginal benefit to the consumer of getting more movie passes or getting more compact discs in exchange for movie passes. The price ratio equals the marginal cost. Now, that gets us to the third line, By the slopes when the budget constraint is just tangent to the indifference curve. That means the marginal benefit of an additional movie pass, of an additional compact disk, relative to movie passes is equal to the marginal cost. The slope of the indifference curve, in addition to reflecting the marginal benefit, we can also take it to be a ratio of marginal utilities. Specifically, the ratio of the marginal utility of compact discs, over the marginal utility of movie passes. Why is this the case? If the consumer is willing to give up three movie passes to get an additional compact disc, that means that the margin, the utility she gets out of an additional compact disc is three times as great as the utility she gets out of a movie pass. And at the tangency point, the ratio of marginal utilities, is two for one. The marginal utility she gets out of a compact disc is twice as great as the marginal utility of a movie pass. That has to equal the ratio of prices. The slope of the budget constraint, which is the price ratio, price of compact disc to price of movie passes. If we rearrange line three, then we get a ratio of marginal utilities to prices across the costs of goods that the consumer's interested in consuming. At the consumer's optimal choice point, her marginal utility, of compact discs per price paid per compact disc, has to equal the ratio of marginal utility of movie passes, equal to the price paid for movie passes. In this particular case the marginal utility of movie passes let's say it wasn't the case, I guess, a better way to put it. Let's say the ratio of marginal utilities to prices was equal for compact discs was equal to three, whereas the marginal utility for movie passes relative to the price was equal to two. What would be wrong with a case like that? By analogy, and, and what these marginal utility price ratios mean is, per dollar spent, on a good, how much utility do I get in return? So, if the ratio of marginal utility to price for compact discs is three, what it indicates is, per dollar spent on compact disks, I'm getting three units of utility on that good. And if I get more satisfaction, three to one, than per dollar spent on movie passes, two to one, I'm not allocating my dollars in the best possible fashion. An analogy would be let's say you had money and spread across two different banks, you have $10 million and you put it in both bank A and bank B. In bank A you had $5 million and it earned an annual predictable rate return of 3%. Bank B, it earned 2% a year, predictable. No difference in risk across holding money in the two banks. If you're ever in such a situation we'd say look you're making the wrong allocation. You should shift more money out of bank B into bank A where you're earning a higher return. And you should keep making the shift, so long as the ratio of marginal utility to price is higher in that bank A. The same intuition applies for consumers when they're banking their income in to different goods and services. Wherever the ratio of marginal utility prices is higher, for one good than for another, purchases should be shifted into that good and away from the other. So, let's go back to the graph at point R, where the consumer is willing to trade off three movies passes to one compact disc. But the market only makes her give up two movie passes per each compact disc. In such a situation, she's not allocating her given income, in the most productive way. And she needs to keep shifting, that income toward compact discs away from movie passes. And that shift will keep on occurring until she reaches the optimum point W. Now, to test your understanding and to refine the optimal choice concept, a little bit farther, consumers don't need to purchase a particular good. Based on their incomes and their preferences, they may decide not to purchase this particular good. Case in point, Dom Perignon champagne. Arguably one of the world's finest, but also incredibly pricey at $100 plus per bottle is un, is not an unusual price to pay. In this particular case depicted in page 17 figure 3.12, the consumer may end up at a corner at point A. Because the rate at which the market makes her pay for Dom Perignon relative to clothing, is greater than the rate at which she's willing to give up clothing for Dom Perignon. So, it's entirely conceivable that a consumer in the simple case may end up devoting all her income, at a particular corner to just the good of clothing. Economists also have a way, because the world is, is not as simple as just a two good case, of how do we depict optimal decision making by consumers, when there're multiple goods. And the way we do it is through what's known as the composite-good convention. We put a particular good that we want to investigate, like compact discs on the horizontal axis. And we look at outlays on all other goods on the vertical axis, measured in dollar terms. A key assumption and behind this approach is that the prices of other goods, remain constant as the price of compact discs change. If the prices of other goods weren't held constant, it would be a rubbery index, but what it allows us to do is describe the much more complex reality in which we live. The same result holds on this composite-good convention. That we expect consumers at their optimal point to seek the highest possible indifference curve. The one where their budget constraint, just nicks, that indifference curve U2, on figure 3.3, 3.13. At a point like B, where the consumer is willing to give up $22 for another compact disc. She can do better than that. If the market makes her give up $18 per compact discs, the slope of the budget constraint. So, she needs to keep reallocating a point like W moving closer, more compact disc consumption, and devoting more of her dollars spent on other goods toward compact disc consumption. Case in point nowadays, from the real world there's a fast growing segment of the fast food market called fresh casual. Chipotle has been one of the hottest companies on the stock market in recent years. It's now up to $3 billion in revenue, has over 1,400 locations across 43 different states, and three countries around the globe. What companies like Chipotle, and then also Five Guys, and In-n-out, and Chopped have found is that there's a real willingness to give up dollars by consumers, if the food can be made to order and fresher ingredients are used. for those of us who have tried Chipotle how you place an order, and the ingredients are there combined they're prepared recently, they're prepared assembly line style, it's a more limited menu, but a real focus on the freshness of the ingredients. A Chipotle also uses a sous-vide preparation there're some of their ingredients mainly the barbacow and the carnitas that are prepared in the central location with this very elaborate cooking technique. Where the meat is prepared in plastic bags cooked under, cooked in a water vat under the right temperature. so that it can be standardized and then shipped out to all their locations. So, they, they figured out certain ingredients how to prepare in a very high quality fashion, then distribute. And the rest to assemble to combine, to consumer's preferences on the spot. And it's, it's been an incredible growth story one of the hottest companies over the last six years in terms of growth and stock market performance. But again, this segment has found that consumers are willing to give up, on the vertical axis dollars, if the ingredients can be prepared freshly and then made to order to the consumer's preferences on the spot.