Question

5. TAXES/SUBSIDIES, AND OTHER GOVERNMENT REGULATIONS 1. Consider the demand and supply for bubbly water in a market represented by the following equations: QD = 15 - 10P QS = 40P - 50 where Q is millions of bottles per year and P measures dollars per bottle. The equilibrium price of bubbly water is $1.30 per bottle and 2 million bottles are sold each year. (a) Calculate the price elasticity of demand and the price elasticity of supply at the equilibrium price and quantity. (b) Calculate the share of a tax that would be borne by consumers and the share borne by producers. (c) If a tax of $0.15 per bottle is created, what would the expected price buyers will pay and what is the expected price suppliers will recieve? (d) Suppose, instead of a tax, the government imposes a subsidy of $0.15. How many bottles will be sold? What is the cost of this subsidy to the government? What is the deadweight loss? 2. Consider the the market for bubbly water described above. (a) What are the consumer surplus and producer surplus when the market is unregulated by the government. (in other words, no taxes, subsidies or other regulations.) (b) Suppse that the government decides to impose a price floor of $1.50. What are the consumer surplus and producer surplus given the price floor? What is the deadweight loss created by this regulation? (c) Suppose instead of the price floor, the government decides to impose a quota of 1.5 million bottles. What is the new market price? What is the new consumer surplus and producer surplus? What is the deadweight loss? Typically such regulations cause some producers to benefit at the expense of the consumers. What is the total transfer from consumers to producers in this case?

Answer 1

price elasticity of demamd : a) 3 6'5 d P price elasticiaya f supp 20 '3 40. es b consumers: borne of tax Share es O'8 es-ed share of Hax borne by producers in : ed 20% O 2 es ea 80% u The tox n o15 pex bottle borne by Consumwc . Them Consumur be payo12 Poducer pay40'03 . amd Expected price buyer wiu pay s 3 o'12 = Expected price supplier wel veceive 'n 2 de mamd A Subsided mcreascs Jnitia aemamd : 2 5-P 5- After sussiay tnu demana : 65 16'5 10P

Subsid equiu brium or, b5-iOP = 40P 50 5 OP 665 ..P 3 3 3 2 Cost af subsid to govt . 3 2 x O15 O48 m Dead weigh lass: O15x ( 32- ) o0a miion 33 '18 2 32 2. a Consumer swepus A '3. O 2 wiion 25 pro ducer swrpun B =(3-2S) x2 o O5 mi Wion price of 5 0 the demamd in geo b A tne PS O O 25 m . DWL = (0 2 o 05) m = e rice consumer wuing to pay A a S ; P 5- "5 35 producer wui ng to receive : 25 6"S 2835 & 35 Mack price would be 6x (v5-1'35) x 15 = 0'125 B+C Ss x (35-287s)*^x( >815-125)r5 CS A Ps = o12185 DWL D= o'25-O 1125 a125 0.015625 muion Re disiviowkion t6 Consu mex (35 -13 x l'5 = 0.015m