Question

Elasticity

The demand for good X is given by:

QDX = 200 – 10 PX.

a. Calculate the price elasticity of demand when PX = $10.

b. At what price, if any, the demand is unitary elastic?

c. Calculate the price elasticity of demand when PX = $5.

d. According to your answer in “c” what will happen to total revenue as we raise the price?

e. Calculate the change in TR as PX  from $5 to $8.

Answer 1

The demand for good X is given by QDX = 200 – 10 PX.

a. Price elasticity of demand = ed = dQ/dP * P/Q

ed when PX = $10, is given by -10 * 10/(200 - 10*10) = -1.

Hence price elasticity is -1.

b. At P = $10 the demand is unitary elastic because ed is 1 as shown in a).

c. Price elasticity of demand = ed = dQ/dP * P/Q

ed when PX = $5, is given by -10 * 10/(200 - 10*5) = -0.67

Hence price elasticity is -0.67

d. We expect the total revenue to increase as we raise the price. This is because demand is inelastic in c).

e. TR (P = 5) = 5*(200 - 10*5) = 750

TR (P = 8) = 8*(200 - 10*8) = 960

Hence revenue is increased by $210.