# Introduction to Linear Demand Equations

A simple equation can be used to express the relationship between the price of a good and the demand among that good’s consumers. This lesson will examine the different variables included in the typical equation for demand, expressed as Qd = a – bP.

We will use a simple equation for demand to plot a demand schedule and a demand curve for pizzas.

Once you’ve watched this video, see if you can complete the following Khan Academy excercises:

In-class activity: Use the linear demand function for cappuccinos, Qd = 500 – 25P to answer the questions that follow:

1. Create a demand schedule for cappuccinos with the prices of \$0, \$1, \$3, \$5, \$7 and \$9
2. Create a demand curve for cappuccinos, plotting the points from your demand schedule.
3. Assume the price of latte machiatos, a close substitute for cappuccinos, decreases, and causes the a variable in the demand function to fall to 300. Create a new demand schedule, with the adjusted values for Qd.
4. On your previous diagram, illustrate the new demand curve.
5. Assume that due to falling incomes, cappuccino consumers become more sensitive to changes in the price of cappuccinos, and the variable in the original demand function increases to 40. Using the same prices, create a new demand schedule.
6. On the same graph as your original demand curve, illustrate the new demand for cappuccinos following the decline in consumers’ incomes.

Linear Demand Equations – Part 1

### 4 Responses

1. Sudha Jatwani says:

Hi Jason,

Thanks for the videos. They are really insightful. I have a few doubts though. Requesting you to clarify.

I am unable to understand why is there a demand at price zero and why is there a change in demand from 800 to 600 when there is a fall in the price of hamburger? At price zero how can the demand for pizza fall?
Finally can you also let me know the reason why demand curve is touching the X axis? According to me, the demand for any product should be free floating in case the price is zero.

Requesting you to clarify as soon as you can.

Thanks & Best Regards,

Sudha

• Jason Welker says:

Sudha Jatwani » Hi Sudha, let me respond to your questions below:

1) Why is there a demand at price zero and why is there a change in demand from 800 to 600 when there is a fall in the price of hamburger?
The reason demand for pizzas decreases from 800 to 600 is that hamburgers are a substitute good, therefore consumers will demand fewer pizzas at every price when hamburgers become cheaper. The decrease from 800 to 600 signifies an inward shift of the demand curve, meaning demand for pizzas decreases when hamburgers become cheaper. The demand for pizza will fall at the price of zero and at all other possible prices greater than zero, since even when pizza is free fewer people will want to consume it if hamburgers are cheaper.

2) can you also let me know the reason why demand curve is touching the X axis?
Of course, in most real markets the demand quantity of a good demanded will increase at and increasing rate as the price approaches zero, so demand would therefore flatten out as rational consumers would likely demand ever increasing quantities as price approaches zero. In our case, however, we study LINEAR demand equations. This is a very simple model of demand, and since every demand curve is a straight line, it must intersect the x-axis (which we call the quantity axis) at some point. The point of intersection is understood as the “autonomous level of demand” , or the quantity that would be demanded when price is zero. Presumably, there is a maximum amount of a product that consumers would demand even if it were free. In the case of pizzas, we can assume that the market above represents a small town with a few thousand people in it, and the demand above represents the demand in a certain period of time (let’s say one week). So, if pizza was free, this town will consume no more than 800 pizzas in a week. That is not an unreasonable assumption. If it were the WORLD demand for pizzas and there were billions of consumers, of course the demand would be greater. Or if we extended the time period to one month or one year, then the Q-intercept would be greater.