E identify a complementary good of charcoal briquets

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(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: <end of quiz>
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1 Economics 203, Fall 2006 Intermediate microeconomics Instructor: Paul Schure ANSWERS QUIZ 1 (No graphs): Preliminary note: it is important to outline your argument in all these questions. The logic logic behind the steps must be made clear, but to the point. Question 1-1. Show in the two diagrams below that an inferior good may be a Giffen good or not. [Don’t forget to label your axes, and to quickly clarify matters...] ANSWER: Fig 4-8 (page 100) shows the income and substitution effect of an inferior good which is not a Giffen good. The income effect for an inferior good works in the opposite way as the substitution effect. A Giffen good is an inferior good for which the income effect is stronger than the substitution effect. Question 1-2. Prove that two indifference curves of the same person cannot cross each other. I suggest you use the diagram below. Label your axes and clarify briefly what is going on in your diagram. Also state which assumption(s) on preferences your proof relies upon. ANSWER: Picture like Fig 3-11 [1 mark]. Explanation: By “transitivity” [1 mark] points D, E, and F have same utility. However F has more of good 1 and more of good 2 than E. Hence “nonsatiation” [1 mark] implies that F has higher utility than E. Contradiction [explanation sound: 2 marks]. Axes not labeled –1 mark. Question 1-3. Demand for whale watching tours of Victorians is given by V q p / 5 = while tourist demand for whale watching tours is given by . 10 T q p = Derive and graph the (aggregated) demand function for whale watching tours. ANSWER: Steps: 1. Rearrange demand functions in proper form for aggregation: p q V / 5 = and . 10 p q T = Aggregate demand function is p q agg / 5 = if 10 > p and p p q agg + = 10 / 5 if . 10 0 p Picture: make clear there is a bend at p=10 and, as usual, labels the axes. Question 2-1 Elizabeth only cares for raspberries r and apples a. In fact, her utility function is given by a r a r U 4 / 1 ) , ( = . Assume Elizabeth has a budget of 50 = M , and let the price of apples be 2 = a p .
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2 (a) Write down the consumer's problem that Elizabeth solves in case the price of raspberries is 1 = r p . Explain in words what it says. A: a r a r 4 / 1 , max Subject to 50 2 + r a In words: Elizabeth maximizes her utility by choosing r and a subject to her budget restriction [and taking the price for a and r as well as her budget given]. Note: Students must work with the actual utility function, not with the generic form. (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?)
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