Question

1. Let D: P = 20 – Q/4. Calculate when ɛ when P = $10.

2. Let D: P = 1/Q^2. Calculate ɛ along the demand curve.

3. Suppose e = -2, if P is up by 3% by how much will total revenue change?

Answer #1

Ans. Price elasticity pf demand = %Change in Quantity demanded / %Change in price = dQ/dP * P/Q

a) P = 20 - Q/4

at P = $10 , Q = 40 units

=> Elasticity, E = dQ/dP * P/Q = -4*10/40 = -1

b) P = 1/Q^2

=> dP/dQ = -2/Q^3

=> dQ/dP = -Q^3 / 2

=> E = -Q^3 / 2 * (P/Q)

=> E = -Q^3 / 2 * (1/Q^3). [Because P = 1/Q^2]

=> E = -1/2

c) %Change in Quantity demanded = Elasticity * %Change in price = -2*3 = -6%

Total Revenue, TR = Price * Quantity = P*Q

=> New Total Revenue, TR' = (1+0.03)*P * (1-0.06)*Q

=> New Total Revenue, TR' = 0.9682 P*Q = 0.9682*TR

Thus, Chnage in total revenue = (TR' - TR)/TR = -0.0318 or - 3.18%

Thus, total revenue decreased by 3.18%.

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