How is a market demand curve derived from individual demand curves?

Answer 1

Demand CurvesThe way I learned it was this. Start with two commodities that you like. Say steaks and chicken breasts. Then draw a graph, with "steaks consumed" on the Y axis and "chicken breasts consumed" on the X axis. On this graph, you are going to draw a series of "utility curves". A utility curve is the set of all combinations of steaks and chicken breastss that give you the same level of satisfaction, or "utility". For example, 3 steaks and 2 chicken breasts might give you as much satisfaction as 1 steak and 6 chicken breasts.

At this point, let's stop and consider the shape of one of these utility curves. Assuming that you like consuming both steaks and chicken breasts, the more of each you have, the more satisfaction you will get. But when we're drawing a single utility curve, keep in mind that satisfaction must remain constant. So, when you get more of one commodity, you must give up some of the other commodity. So, in general, the utility curve slopes down and to the right (as number of steaks decreases, number of chicken breasts increases.

But let's get more precise about the shape of the utility curve by considering the relationship between the goods. If the two goods were "perfect substitutes" then a consumer will willingly exchange them at a fixed rate no matter how many of each he has. Though "perfect substitutes" don't exist in real life, we can approximate this relationship by considering two very specific goods that are almost identical. For example, "8-oz choice ribeye steaks" and "10-oz choice ribeye steaks". Most folks would willingly trade 5 8-oz ribeye steaks for 4 10-oz ribeye steaks (perfect substitution does not require a one-for-one trade ratio, but merely a constant trade ratio). Furthermore, no matter how many of each you have, you would still make this trade. In this case, the utility curve is a straight, downward sloping line. And at every point on that line, you receive the same amount of satisfaction, or utility.

On the other hand, if the goods were "perfect compliments", then a consumer must consume the two together in fixed ratios. Again, perfect compliments don't exist in real life, but for an example, we will use "hot dog wieners" and "hot dog buns" (if you combine one of each, you have one hot dog, and we'll assume, for the sake of approximating a pair of perfect compliments, that neither the weiners nor the buns have any possible use other than Hot Dogs). So now say you have exactly 5 wieners and 5 buns, and that gives you 5 units of satisfaction (or utils). Would you trade one of the wieners for an additional bun? No, because then you have enough wieners for only 4 hot dogs, and you have 2 buns that will not be eaten, and thus will give you no utility. So you would experience a net loss of utility if you made this trade. In fact, if you start with an equal number of weiners and buns, you will not give up any number of wieners for any number of additional buns; nor would you give up any number of buns for any number of additional weiners. Now, what if you had 1,000 wieners and still just 5 buns? How much satisfaction would you get from that? Not one bit more than if you had just the original 5 wieners and 5 buns, because you can still only make 5 hot dogs. Same thing for 5 wieners and 1,000 buns. So, in this case, the utility curve starts out as a straight vertical line (at 5 buns and any number of wieners greater than or equal to 5), then turns into a straight horizontal line (at 5 wieners and any number of buns greater than or equal to five). No point on this curve gives you any more or less statisfaction than the combination of 5 wieners and 5 buns.

Graphs don't work too well in this forum, but think of the perfect-substitutes utility curve as a backslash ( \ ), and the perfect-compliments utility curve as a the letter L. These are the two extremes, and neither really occurs in real life. So, for a "normal" pair of goods, that are neither perfect substitutes nor perfect compliments, the utility curve will be somewhere in between the two. It will, of course, still be downward sloping, but the slope will change over the course of the curve, starting out steep, then gradually lessening to nearly flat. Going back to the original steaks vs chicken breasts example, this makes sense. There is a saying that "variety is the spice of life", but this saying is more than just a homily when we're talking about utility. I don't care how much you like steak - every now and then, you want chicken. And vice versa. Therefore, most consumers will get more satisfaction from 5 steaks and 5 chicken breasts than from 10 steaks or 10 chicken breasts. Or, keeping satisfaction constant, as you give up steaks for chicken breasts, you will have to get more chicken breasts to compensate for the lack of variety in your diet. For example, starting at 5 of each, if you gave up 1 steak (S), you would need 2 chicken breasts (C). So, 4S + 7C gives you the same satisfaction as 5S + 5C. From there, if you gave up another steak, you might need 3 chicken breasts to get the same satisfaction, so 3S + 10C is another point on your utility curve. Let's extend it on out to 2S + 14C, 1S + 19C, and 0S, 25C. Then we can extend the curve back the other way by giving up chicken breasts for more and more steaks. I can't draw a graph here, but imagine a curve somewhere in between the ' \ ' of perfect substitute and the ' L ' of perfect compliments.

Okay, now that we have one utility curve, we can theorize that there are an ifinite number of utitlity curves in this same space, each giving the consumer a different level of satisfaction. Of course, at this point, we have to allow infinite divisibility of the two goods, because every point in this space has to be on one of these utility curves.

And now, for the first time, we introduce the notion of "prices". And the exercise becomes one of maximizing satisfaction with an income constraint. Say you have just $100 dollars to spend, and you want to go out and buy steaks and chicken breasts. You will purchase the single combination of steaks and chicken breasts, at the current prices, that puts you on the highest possible utility curve (gives you the most satisfaction). Basically, you will draw a "price line". Say steaks are $5 and chicken breasts are $4. With $100, you can buy 20 steaks, or 25 chicken breasts, or 4 steaks and 20 chicken breasts, or 8 steaks and 15 chicken breasts, or 12 steaks and 10 chicken breats, or 16 steaks and 5 chicken breasts. Note that this line, unlike the utility curve, is a straight line. Note also that you can buy fractions of both steaks and chicken breasts, for example, 14.1946 steaks and 7.2568 chicken breasts. Now you want to achieve the highest possible satisfaction. Looking at the utility curves, you will see that there are some curves, with higher utility levels, that do not touch your price line at all, meaning that you simply cannot achieve that much utility with the $100 you have to spend. There are other utility curves, with lower utility levels, that cross your price line twice. But there is one and only one utility curve that just touches your price line at a single tangent point. This is the highest utility that you can achieve with your $100.

I could quantify this level of utility (the measure is "utils"), but it really doesn't matter. All that matters is that, for a given income and prices, we have established how many steaks and how many chicken breasts you will purchase. But let's ignore the chickens and focus on the steaks. How many steaks did you end up buying when they cost $5? Well, that depends on the shape of your utility curves, but let's say you bought 10 steaks. Now we're going to transfer that quanitity of steaks to a new graph, a demand curve for steaks, with price on the vertical axis and quantity on the horizontal axis. Plot this point, P = $5, Q = 10. Now change the price of steaks to $4 and repeat the utility-maximization exercise in the paragraph above. You will be able to achieve higher satisfaction because of the lower steak price, but again, that is not important. What is important is that you will buy more steaks, say 12 of them. And you have another point on your demand curve. Keep changing the price of steaks and repeating the utility maximization exercise until you have a whole set of points on your demand curve (there will actually be an infinite number of points on this curve, but 4-5 will give you enough to see the general shape of the curve. This is how the individual demand curve is derived.

(Note that, because there are a lot more commodities out there than just steaks and chicken breasts, economists often generalize the utility curve theory by considering the second commodity to be "all other goods", or some such manipulation. The "problem" of perfect substitutes and perfect compliments goes away when you do this because when the "other commodity" is "everything else", "everythng else" is neither a perfect substitute nor a perfect compliment.)

Now, how about market demand curves? Well, you just add up all the individual demand curves. Here, it is worth noting that, even if some individual consumer considers two goods to be either perfect substitutes or perfect compliments, other consumers would not necessarily feel the same way. So, the market demand curve, even more so than the individual demand curve, is based on the normal, concave-shaped utility curves.

That is the best I can do without being able to use graphs. .

Answer 2

Add up quantities demanded by all individual consumers for each price.

Answer 3

By simply adding them together.