Question

Question 9 The demand function for books is Q = 8-0.2p. For what price is elasticity equal to 1? O 10 04 020 O Cannot be determined from information 08

Answer 1

Answer: 3^rd option

Elasticity = E

Price = P

Total revenue = TR

Marginal revenue = MR

Given,

Q = 8 – 0.2P ………… (1)

By rearranging,

0.2P = 8 – Q

Or, P = 8/0.2 – Q/0.2

Or, P = 40 – 5Q

Hence,

TR = P × Q = 40Q – 5Q^2

Now,

MR = Derivatives of TR

       = (d/dQ) [40Q – 5Q^2]

       = 40 – 10Q

Therefore, the elasticity formula as below,

MR = P (1 + 1/E))

40 – 10Q = P (1 + 1(-1)) [price elasticity always must be in negative]

40 – 10Q = P (1 – 1)

40 – 10Q = P × 0

40 – 10Q = 0

40 = 10Q

Q = 4

Now, by putting this value in equation (1),

Q = 8 – 0.2P ………… (1)

4 = 8 – 0.2P

Or, 4 – 8 = 0.2P

Or, - 4 = - 0.2P

Or, 0.2P = 4

Or, P = 4/0.2

          = 20