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### Course: Microeconomics > Unit 8

Lesson 2: Changes in factor demand and supply# Adding demand curves

In this video we explore how to derive the demand for a factor of production based on how productive that factor is and how much additional revenue that factor brings in. Created by Sal Khan.

## Want to join the conversation?

- At0:25, can anyone else explain a little more?

I haven't understand when the adding is useful.

I would appreciate you beforehand, thanks.(6 votes)- It's just like market demand curves for products. To get the the market demand curve for bread, for example, we add up every person's (in the maket) demand curve for bread. The supply curve could then be added to show equiibrium price of bread. Similarly, to get the market demand curve for car washers, we add up all the firms' (in the market) demand for car washers. From this, we could derive equilibrium wage by also drawing in the supply curve (i.e. how many people are willing to be employed at every given wage level).(4 votes)

- Thanks! graphing was intuitive. Could you please give some formulas as well?(3 votes)
- Sure, but they might be a bit underwhelming. It all has to do with how you set up the functions. If you let price be the independent variable—as it should be, despite its position on the vertical axis—then we have two functions Q_1(P) and Q_2(P) for the two firms. Then the total market demand is Q_total(P) = Q_1(P) + Q_2(P). If you plot this with Q_total on the horizontal axis and P on the vertical axis, you'll get the same graphs as above.(5 votes)

- Why is the combined curve have two linear parts? Why is it not at curve?

I don't get it.

Thank you ;)(2 votes) - I still don't understand how you add up the horizontal demand curves, and how do you know what it looks like?(2 votes)
- I thought if you were talking about the market it is big Q, but if you are labelling specific firms in the market, do you not use little q's? I have noticed the same thing in the comments.(2 votes)
- When you have "complex" curves like this, how do you determine market equilibrium? All the examples I can find simplify things and use normal linear curves for supply and demand.(2 votes)
- We would have to have more information/parameters regarding the supply/supply curve, then graph that curve and find the intersection point between the supply curve and the demand curve in order to find the market equilibrium between supply and demand.(1 vote)

- What about subtracting a demand curve? I need to answer the folling question: The aggregate demand of two consumers is p(q)=7-q. One of them lives the market, his/her individual demand curve was p(q')=4-2q'. What is the remaining aggregate demand curve i.e. the demand of the person who remains in the market? (Actually I need to compute the loss of consumer surplus in a competitive market and constant marginal cost equal 3, but I think can do that if I find de demand curve)

I drew this (inverse) curve in red: https://www.desmos.com/calculator/lihgzsqeec

But I believe it's not right.(1 vote)- I think you are looking more for something like this: https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/unit-2-supply-and-demnd/micro-demand/v/market-demand-as-the-sum-of-individual-demand

You subtract rather than add.(1 vote)

- Wait! O_O

Why is firm 2's graph so different?

Why doesn't price equal quantity?(1 vote) - If individual demand curves are added up like this to get the whole market's demand, how does it work in perfect competition? In PC, each firm has a demand curve that is essentially horizontal at the equilibrium price, but somehow adding that all up gives you a downward sloping demand curve for the market?(1 vote)
- for this example car wash business it shows they make ten dollars an hour and as they hire more the extra person becomes less helpful but u also have taxes, the price of the cleaner, the land or building u wash cars at. so basically its hard to make money if you have 2 or more employees(0 votes)

## Video transcript

>>In the last few videos, we constructed a marginal
product revenue curve for our little competitive car wash, and we essentially figured out how this is really just the demand curve for labor from this firm. I talked about on the very first video that if you know the demand curve for, in a certain market, and this is the market for
labor of a certain kind, maybe the type of labor that would work at a car wash, then if you knew it from one firm and all of the other firms in the market for that type of labor, you could add their demand curves to get the entire market demand for that type of labor, for that good or service. What I want to do in this
video is to make sure you understand what it
means to add demand curves. It's, on one level, straightforward, but on another level,
a little non-intuitive because of the ways that
the axes are defined in economics, that the price axis is the vertical axis. Let's draw the demand curve for two firms. I'll do simplified versions. I won't use this one right over here. I'll just do two simplified demand curves. This doesn't apply just to labor markets. This applies to any demand curve. If I want to add two demand curves, this is one entity's demand, so this is one firm's demand. That's price, and this is quantity. This is quantity. Let's say at a price of 10, they demand nothing, if that's the hourly wages, and if the price were 0, they would essentially get up to they would demand 10 people. And so you have a situation. You have a demand curve
that would look something, a demand curve that would
look something like that, a dot, a demand curve that would look like that. I'll do one other point
on the demand curve. At a price of 5 a
quantity, or $5 per hour, this firm would demand, if we're thinking of it in terms of labor, at a price of $5 per hour of labor, this firm would demand 5 people per hour. Obviously, what I'm going to do is
general to any demand curve, but we'll just keep it
in the labor mindset. This is Firm 1. This is a firm's demand. Firm 1. If we're talking about
this as demand for oranges, then this wouldn't be a firm. This would be a consumer
or maybe a wholesaler or something like that. This is Firm 1's demand for labor. Let's say Firm 2's demand
looks something like this. I'll try to align them. Firm 2's demand looks something like this. The axes are going to have
the exact same labels. This is Quantity. This is Price right over here. This is 5. This is 10. Then this is 15. Let's say that this is 5, and let's say this is 6 right over here. Their demand curve looks like this. It looks like that. Let me make it a little bit neater. That looks less neat. It looks something like that. I could put some extra points here. At a price of 10, this firm will demand 2 units. If we're thinking of labor, $10 per hour, they'll get 2 people per hour. At a price of 5, they will demand 4. They will demand 4 units. These are all ... We've looked at a couple of points on this demand curve. Now we are ready to add them together. This is Firm 2, Firm 2's demand for labor. Let's add these two curves. When I said it's unintuitive, we're actually going to look at ... For a given price, how much total quantity
of labor is now demanded? We're going to essentially
add it horizontally, and you're going to see
what I'm talking about in a second. When I add them together, I add them together, I'm going to have the same axes. Let's say this is 5. This is 10. Actually, let me get a little bit further on this axis, on this second axis. The second axis, I'll make it as straight as possible. Let's say that this is 5, 10, 15, 5, 10, 15, and this is 5, 10, 15. I'm doing my best to
align it horizontally, that this 15 is this 15, that this 10 is with this 10, is with that 10, and that 5 is with that 5 and with that 5. At a price of 15 in the market, what is the total quantity demanded? It's still going to be 0 because even this firm
is still demanding 0. But then if we go to a price of 10, this firm, the Firm 1 is demanding 0, but Firm 2 over here is demanding 2. So we're going to go 10. It's going to be right over there. This is right about 2. That distance is right about 2. Then if we go to 5, at a price of 5, Firm 1 is going to demand 5. Firm 2 is going to
demand 4 units of labor. At a price of 5, you're going to have 5 plus 4. At a price of 5, you're going to have 5
plus 4 or 9 units of labor, 9 units of labor. Then at a price of 0, if labor is free, this firm would demand 10 units, and this firm would demand 6 units. You add them together, you get 16 units. You'd get 16 units. The combined demand for labor curve will look something like ... I'll do it in ... or actually, I'll do it in blue. The combined demand for labor curve will look like this. Between $15 and $10, only Firm 1 is interested
in getting any labor. So this part right over here
will look just like that. But then after that point, you're going to essentially add Firm 1 to the mix, and then Firm 1, maybe I'll do that part
in a different color, it will look something like ... it will look something like that. We have essentially added, we've horizontally added
this line to this line. You could imagine taking this line, and at any given point, so at 5 right over here, you're taking its value and quantity and adding to this quantity here. The reason why I said this is
a little bit nonintuitive is this would have been easier
at least for me to add with the background of
the traditional algebraic conventions we're used to. We're used to adding vertically. If we were to flip price and quantity, then we could stack these
on top of each other and add them vertically. That's why it's a little nonintuitive. But hopefully, this makes sense. We're just looking at each
of their demand curves at any given price, and we're saying, "OK, what is the demand from Firm 2? "What is the demand from Firm 1?" and we're adding them together, and then we get this. We get this combined market demand curve, Firm 1 plus Firm 2.