Question

1.A demand function given by: Q = 240 ‒ 3P. What is the price elasticity of demand when the price is P = $10? You will have to use the point elasticity formula. The price elasticity of demand at this price is ___________

2.Consider the same demand equation, Q = 240 ‒ 3P. If a firm sells at the unit elastic price on this demand curve, what is the total revenue it will receive? The total revenue received at this point would be ____________.

Answer 1

1)

Price elasticity of demand = (dQ/dP)*(P/Q) ------------Point elasticity formula

Here Q = 240 - 3P => dQ/dP = -3 and when P = 10 , Q = 240 - 3*10 = 210.

Thus, Price elasticity of demand = (dQ/dP)*(P/Q) = -3*(10/210) = -0.14.

Hence, The price elasticity of demand at this price is -0.14

2)

Price elasticity of demand = (dQ/dP)*(P/Q) ------------Point elasticity formula

Unitary elastic means that Price elasticity of demand = -1

=> (dQ/dP)*(P/Q) = -1

Here, Q = 240 ‒ 3P => dQ/dP = -3

=> -3P/Q = -1

=> Q = 3P

Thus we have Q = 240 - 3P = 3P => P = 40

Hence Q = 3P = 40*3 = 120.

Total Revenue = Price*Quantity = P*Q = 40*120 = 4800

Hence, The total revenue received at this point would be $4800