Question

True or False:

If Castor’s demand curve is described by q = 40 - p and Pollux’s demand curve is given by q = 60 -2p, then each of their demand curves will pass through the point q = 20, p = 20. Therefore if they are the only two consumers in a market, the market demand curve will also pass through q = 20, p = 20.

Answer 1

In this case,

q1=40-p clearly q1=0 for p>40

q2=60-2p clearly q2 =0 for p>30

Combined demand curve is given by

q=q1+q2=(40-p)+(60-2p)=100-3p for

q=q1+q2=(40-p)+0=40-p for

q=0 for

We can see that point given by q=20 and p=20 satisfies, satisfy both equations. So, q1 and q2 will pass through p=20, q=20

Now let us calculate market demand at p=20

q=100-3p=100-3*20=40

So, we can see that q is different from 20. It means that market demand curve will not pass through p=20, q=20

So, Given statement is

False