Question

Patrick’s inverse demand for basketball shorts is given by p = 20 ? q/3 .

Isaac has inverse demand of p= 60 ? q/2. At what price will they buy a total of 20 shorts?

Answer is 50

Could you please show me how to solve this?

Thank you

Answer 1

From inverse demand functions, we derive the direct demand function for both.

Patrick: P = 20 - q/3, 3P = 60 - q, q = 60 - 3P

Issac: P = 60 - q/2, 2P = 120 - q, q = 120 - 2P

We can now calculate the aggregate demand

Q = 180 - 5P for 0<= P <=20 [If price is below 20, then both Patrick and Issac will demand and hence, Aggregate demand = 60 - 3P + 120 - 2P]

Q = 120 - 2P for 20<P<=50 [It implies that if Price is greater than 20, then only Issac will buy the product]

Q = 0 For P>50 [If the price is above 50, no one will demand]

Now We are given Q = 20

We take the firm case was aggregate demand is 180 - 5P.

Hence, 20 = 180 - 5P . Solving we get P = 32. Hence this is not required AD

Now we take the second aggregate demand, 120 - 2P

20 = 120 - 2P. Solving we get P = 50.