Consider the following supply and demand function, QD = 65 − 2P and QS = 1.5P − 5, and assume a $17.50 excise tax is collected from consumers.(a) Calculate price and quantity in this market before (P1 and Q1) and after the tax (P2 and Q2).(b) What is the amount of tax revenue that is collected from con- sumers, producers and in total?(c) What is the relative tax burden of consumers and producers?(d) Show how the elasticity of supply and demand determine the shar- ing of the tax burden.(e) What is the relative tax burden of producers and consumers if the tax is collected from producers, instead?

Demand function: Demand function shows the maximum price the consumers are willing to pay to purchase a particular quantity Supply function: Supply function shows the minimum price at which the sellers are willing to sell a particular quantity Market equilibrium: At the market equilibrium we have demand equals to supply. Or at market equilibrium point the maximum price which the consumers are willing to pay is exactly equals the minimum price at which the sellers are willing to sell.Given: Demand function : Q = 65- 2P , inverse demand function : P = 32.5 - 0.5Q --(1) Supply function : Q = 1.5P - 5 => P = (Q/1.5) + (5/1.5) --(2) Part A Before Tax Before tax equilibrium in the market requires: demand (1) = supply (2) => 32.5 - 0.5Q = (Q/1.5) + (5/1.5) => 29.17 = 1.17Q => Q = 25 units Hence, P = 32.5 - 0.5Q = 32.5 - 0.5*25 = 20 {before tax market clearing price) After Tax As the tax ($17.5 per unit) is imposed on the consumers, Hence after tax demand function would be: P = 32.5 - 0.5Q - 17.5 = 15 - 0.5Q -- (3) Hence after tax market equilibrium requires : after tax demand (3) = after tax supply (2) => 15 - 0.5Q = (Q/1.5) + (5/1.5) => 11.67 = 1.17Q => Q = 10 units P = 32.5 - 0.5Q = 32.5 - 0.5*10 = 32.5 - 5 = 27.5 Part B Total tax collection = tax rate * equilibrium quantity after tax = 17.5 * 10 = 175 Part C Burden on consumers = price paid after tax - price paid before tax = 27.5 - 20 = 7.5 Burden on suppliers = Price received before tax - price received after tax = 20 - ((Q/1.5) + (5/1.5)) = 20 - 10 = 10

Answered: Consider the following supply and…

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Consider the following supply and demand function, QD = 65 − 2P and QS = 1.5P − 5, and assume a $17.50 excise tax is collected from consumers.
1. (a) Calculate price and quantity in this market before (P1 and Q1) and after the tax (P2 and Q2).
2. (b) What is the amount of tax revenue that is collected from con- sumers, producers and in total?
3. (c) What is the relative tax burden of consumers and producers?
4. (d) Show how the elasticity of supply and demand determine the shar- ing of the tax burden.
5. (e) What is the relative tax burden of producers and consumers if the tax is collected from producers, instead?

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