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Elasticity and taxation
Consider the market for automobiles in Beijing City and Qingdao City (These two cities are located in China). Suppose the demand for automobiles in Beijing is given by: Q = 10000 The demand for automobiles in Qingdao is: Q = 8000 2P The market supply for the two markets is identical, given by:
Q = 2P 2000 Assume these two markets are totally separated from one another. (Chinese currency unit is RMB.)
(a) Find the equilibrium price and quantity in the automobile market in both Beijing and Qingdao.
(b) Calculate the price elasticity of demand in both Beijing and Qingdao at equilibrium.
(c) Calculate the price elasticity of supply in both Beijing and Qingdao at equilibrium.
Now suppose the local government in Beijing imposes an excise tax of RMB 1,000/car on the producers of automobiles and the local government in Qingdao imposes an excise tax of RMB 500/car on consumers of automobiles.
(d) Calculate the government revenue, consumers tax incidence, producers tax incidence, and deadweight loss in both Beijing and Qingdao due to the excise tax in each city.
(e) Compare the fraction of the economic incidence borne by consumers to the total tax incidence in both cities. Explain your results in terms of elasticity.
a) In Beijing: solve the two equations of Q = 10000 and Q = 2 P 2000, so the equilibrium price is P = 6000 and the equilibrium quantity is Q = 10,000 cars. In Qingdao: solve the two equations of Q = 8000 2 P and Q = 2 P 2000, so the equilibrium price is P = 2500 and the equilibrium quantity is Q = 3000 cars. b) In Beijing: since the demand is perfectly inelastic, the price elasticity of demand is 0. In Qingdao: rearrange the demand equation to obtain P -intercept form P = 4000 0.5 Q ; thus, at P = 2500 and Q = 3000, the price elasticity of demand is: | (1/Slope of demand curve) x ( P / Q ) | = | (1/0.5) x (2500/3000) | = 5/3 = 1.67 c) Rearrange the supply equation to obtain P-intercept for P = 0.5Q 1000 In Beijing: at P = 6000 and Q = 10000, the price elasticity of supply is: (1/Slope of supply curve) x (P/Q) = (1/0.5) x (6000/10000) | = 1.2 In Qingdao: at P = 2500 and Q = 3000, the price elasticity of supply is: (1/Slope of supply curve) x (P/Q) = (1/0.5) x (2500/3000) = 5/3 = 1.67 d) In Beijing: the supply is shifted up by RMB 1000/car; thus, P = 0.5 Q 2000 after tax. Solve for the equilibrium price and quantity with tax by equating P = 0.5 Q 2000 (supply with tax) and Q = 10000 (demand), so PT = 7000 and QT = 10000. The price producers receives is Pnet = 7000 1000 = 6000. Since 10000 cars sold are subjected to RMB 1000/car, the government revenue is 10000 x 1000 = RMB 10 million. Since the demand is perfect inelastic, producers tax incidence is RMB 0,…

tax incidence is RMB 10 million and there is no deadweight loss. In Qingdao: the demand is shifted down by RMB 500/car; thus P = 3500 0.5 Q after tax. Solve for the equilibrium price and quantity with tax by equating P = 0.5 Q 1000 (supply) and P = 3500 0.5 Q (demand with tax), so QT = 2500 and price producers receive Pnet = 2250. The price consumers pay is PT = 2250 500 = 2750. Since 2500 cars sold are subjected to RMB 500/car, the government revenue is 2500 x 500 = RMB 1.25 million. Equilibrium price without tax was RMB 2500, but producers now receive RMB 2250/car and consumers now pay RMB 2750/car. Thus, producers tax incidence is (2500 2250) x 2500 = RMB 625000 and consumers tax incidence is (2750 2500) x 2500 = RMB 625000. The deadweight loss is 1/2 x (3000 2500) x 500 = RMB 125000. e) In Beijing, consumers tax incidence is 100% of the total tax incidence, since the demand in Beijing is perfectly inelastic. However, consumers tax incidence in Qingdao is 50% of the total tax incidence, since the demand and supply in Qingdao have equal elasticity.

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