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B derive elizabeths optimum bundle in case the price

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(b) Derive Elizabeth’s optimum bundle in case the price of raspberries is 1 = r p . Two conditions must hold: “slope condition” and budget line: a r a r r p MU p MU r r a a 2 1 1 4 1 2 4 / 3 4 / 1 = = = 50 2 = + r a Combining delivers: 2.5a=50, so a=20, so r=10. The optimum bundle is (a,r)=(20,10) (c) (1) Derive Elizabeth’s individual demand function for raspberries. (2) Is the law of demand satisfied for Elizabeth’s individual demand function? (why or why not?) A: Same two equations, but with r p unknown: a p r p a r r p MU p MU r r r r a a 2 1 4 1 2 4 / 3 4 / 1 = = = 50 2 = + r p a r Combining delivers: 2.5a=50, so a=20, so r=10/ r p . The demand function is r=10/ r p . This is a regular downward-sloping demand function, i.e. the law of demand is satisfied. Question 2-2 Because of concerns that barbequing meat using charcoal may cause cancer, the government decides to impose a 100 percent tax at the retail level on charcoal briquets. This means that in the future shop keepers will have to transfer half of their proceeds from the sale of charcoal briquets to the government. Before the announcement of the government demand for charcoal briquets was given by P=120-2Q and supply by P=30+Q (where P is the price in dollars and Q the number of 10-kg bags of charcoal briquets per day). (a) Compute the equilibrium price and quantity of charcoal briquets before the tax was imposed. (b) Show in a graph what is the impact of the tax on the market for charcoal briquets. (c) Compute the after-tax price and quantity and compute what are the tax revenues (d) Use computations to show whether buyers or sellers, or both buyers and sellers, carry the tax burden.
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3 (e) Identify a complementary good of charcoal briquets. Draw what could be the demand curve for this complementary good and show in your graph how the tax on charcoal briquets affects demand for your complementary good. ANSWER: (a) solve for P and Q, for instance 120-2Q=30+Q so 3Q=90 so Q=30 so P=60. (b) Old supply schedule is P=30+Q. So, with tax we get P X =30+Q, where P X is the price excluding tax. The tax T= 0.5*P, where P is the price incl tax. And also P X =0.5*P. Thus the new schedule is 0.5P=30+Q, i.e. P=60+2Q, a non-parallel shift. (c) From P=60+2Q and P=120-2Q we obtain P=90 and Q=15. Tax receipts: Q*T=Q*0.5*P=15*45=675. (d) Buyers and Sellers share the tax burden. Buyers pay 90 now and before they paid 60, so the share of the tax burden they carry is (90-60)/45=2/3. Seller now obtains 45 and before 60, so the share of their tax burden is (60-45)/45=1/3 (e) BBQ stake or Charcoal BBC grills are two examples. The demand curve shifts inward. <end of quiz>
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1 Economics 203, Fall 2006 Intermediate microeconomics Instructor: Paul Schure QUIZ 2 (50 minutes) Monday 30 October 2006 Quiz 1 is 4 pages long and consists of two parts. Part 1 contains two short-answer questions that are worth 5 marks each. Part 2 has two long-answer questions that are worth 20 marks each. In total you can earn 50 marks, i.e. a minute per mark. You must
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