Question

The demand curve is P=2-4Q. If we know that price elasticity e=1, what are P and Q?

Answer 1

Answer: Qty =0.25 and Price=1.

Solution: Given the inverse demand function:

P= 2-4Q ....(1)

Now convert it into a equation where quantity is a function of Price as below:

Q= (2-P)/4

Now the formula for price elasticity of demand is

PED= -[(dQ/ dP)*P/Q. ...(2)

Now dQ/dP = d [(2-P)/4]/dP

dQ/ dP= 1/4* (-1)= -1/4

Put this value in equation (2)

PED= -(-1/4)*P/Q

1= (1/4)* (2-4Q/Q)..... from equation (1)

4= (2/Q)-4

8= 2/Q

Q= 0.25

Put the value of Q in equation (1).

P= 2-4Q

P= 2- 4(0.25)

P = 2-1=1