You are given the following information: (a) Your firm\'s demand equation is def
ID: 2496170 • Letter: Y
Question
You are given the following information: (a) Your firm's demand equation is defined as follows: Qd=100-4Pa+2Ps+1I, where Qd is the quantity demanded for your product, Pa is the price that you chare for your product, Ps is the price that a competitor charges for a substitute product, and I is the income for your consumers. You have a current estimate for all of the variables (at the present levels): (a) Qd: 160, (b) Pa: $20.00, (c) Ps:$20.00, and (d) I: $1,000. Answer the following questins:
(a) Calculate the elasticity of demand with respect to changes in your price. Comment on what this result implies.
(b) Calculate the elasticity of demand with respect to changes in your competitor's price. Comment on what this result implies.
(c) Calculate the elasticity of demand with respect to changes in the income of your consumer. Comment on what this result implies.
Explanation / Answer
ANS:
a.) Pa = 20 , Qd = 160 , %change in Pa = -4*20= -80 , %change in Qd = 100 - 4*20 + 2*20= 100 - 120= -20
Price elasticity of demand = Pa / Qd * % change in Qd / %change in Pa.
Price elasticity of demand = 20 / 160 * -20 / -80 = 1 / 32 = 0.0312.
Therefore, then demand is Price Inelastic.
b.) Ps = 20 , Qd = 160 , %change in Ps = 2*20= -40 , %change in Qd = 100 - 4*20 + 2*20= 100 - 120= -20
Price elasticity of demand = Ps / Qd * % change in Qd / %change in Ps.
Price elasticity of demand = 20 / 160 * -20 / 40 = -1 / 16 = - 0.063.
Therefore, then demand is Price Inelastic.
c.) I = 20 , Qd = 160 , %change in I = 1*1000= 1000 , %change in Qd = 100 - 4*20 + 2*20+1*1000= 100 - 1120= -1020
Price elasticity of demand = I / Qd * % change in Qd / %change in I.
Price elasticity of demand = 1000 / 160 * -1020 / 1000 = -1020 / 16 = -6.38.
Therefore, then demand is negative elasticity means inferior good.
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