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?
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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