# Aggregating individual demand curves

I'm aggregating individual demand curves but the demand curves are inelastic or elastic. Say, 20 people have an elastic demand for a product at price of $2. Another 40 people have an elastic demand for a product at price of$4. There is a third category who have an inelastic demand of 50 units.

How do I aggregate these demand curves (graphically and in equation form)?

Graph of Aggregate Demand Curve is as follows :

• Can you explain why? That would be helpful. – user708015 Oct 17 '19 at 7:50
• When $p >4$, only people in the third category demands 50 units. When $p =4$, there is perfectly elastic demand for the product by those in the second category i.e. they can demand any non-negative quantity $[0, \infty)$. When we add 50 to it, we get demand as $[50, \infty)$. For $p <4$, quantity demanded is infinite (by the second category). – Amit Oct 17 '19 at 8:01
• What about price less than 2? Also, can you help me understand how to think about it when faced with similar problems? – user708015 Oct 17 '19 at 8:03
• Category 1 consumers don't matter in the aggregate demand as there is already infinite demand for the commodity by category 2 consumers for any $p < 4$. – Amit Oct 17 '19 at 8:09

## Mathematically

To calculate the total demand curve (aggregate demand has a different meaning), you just need to ask yourself that for each price, how many units will be demanded.

You have three groups:

• A. 20 people, perfectly elastic at $$p = 2$$. This group will buy 20 units as long as $$p \leq 2$$.
• B. 40 people, perfectly elastic at $$p = 4$$. This group will buy 40 units as long as $$p \leq 4$$.
• C. 50 people, perfectly inelastic. This group will buy 50 units no matter what.

Mathematically,

$$A(p) = \begin{cases} 20 & \text{if p \leq 2} \\ 0 & \text{otherwise}\end{cases},\quad B(p) = \begin{cases} 40 & \text{if p \leq 4} \\ 0 & \text{otherwise}\end{cases},\quad C(p) = 50$$

Total demand is just a function of $$p$$: $$Q(p) = A(p) + B(p) + C(p)$$. If we start at $$p = 1$$, what's $$A(1) + B(1) + C(1)$$? Do this for all prices, and you'll get the total demand curve.

## Graphically

You could also do this graphically... draw up the demand curve (would look like a rectangle) for each group. The total demand curve will just be the horizontal stack of these rectangles.

• Won't the market demand end up in sections? I will have a vertical line at 2500 units and two horizontal lines at prices 20 and 40. – user708015 Oct 17 '19 at 7:20
• I've just edited my answer. Let me know if that clears things up for you. – Art Oct 17 '19 at 7:21
• I think you misunderstood my question - the first two groups have a perfectly elastic demand at prices 2 and 4 respectively. There are no units mentioned. It is infinite. – user708015 Oct 17 '19 at 7:24
• Hm... by saying the first group has 20 people who has perfectly elastic demand, I think this is how the number of people would come into play. Otherwise I'm not sure what the point of specifying number of people in each group is... So having 20 or 2 or 200 people in the first group wouldn't make a difference if each person could demand infinitely many units. – Art Oct 17 '19 at 7:42
• I thought the same. It has just been put in a tricky way. Is my first comment correct in that case? – user708015 Oct 17 '19 at 7:43