Question

The demand is given by P = 100 – 2Q, where P is the price and Q is the quantity demanded. Find the price at which the own-price elasticity is – 2.

Answer 1

price elasticity= (dQ/Q)*(P/dP)= dQ/dP)*(P/Q)--- (a)

Now P= 100-2Q

So, Q= (100-P)/2=50-P/2

So, dQ/dP= -1/2

put the values of elasticity= -2, Q, dQ/dP in equation (a), we get:

-2= -(1/2)*(P/50-P/2)

Solving this equation to get the value of P:

we get P= (50*2)/3= 33.33