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Econ440August 2007Peter NormanConsumer Theory: Review ProblemsMost public economics (and any other applied economic theory) is based on the standard consumer theory.While you have seen this both in principles and intermediate courses some of you may bene…t f rom reviewingthis material. I suggest that you pick up your notes and/or textbook from intermediate micro and solve thequestions below to see how much you remember, and then try to …ll in the gaps as soon as you can.You are not required to hand in answers. As a service, I will have a review session where I solve some of theproblems on th e board, but I will not post any answer key.1. Consider the standard textbook world with two goods and an exogenous income wealth. That is, let x1and x2denote quantities of good 1 and 2 respectively and let the prices be denoted by p1and p2: Finally,let m denoted the “income”or “wealth”for some consumer. Recall that the budget set (set of a¤ordableconsumption bundles) consists of all (x1; x2) such that p1x1+ p2x2 m and x1 0 and x2 0:1. For p1= 3; p2= 6 and m = 12; draw the budget set exactly. Be explicit about intercepts with thex1and x2axis.2. Demonstrate how the budget set is a¤ected if p1changes from 3 to 4 and everything else is unchanged.3. Demonstrate how the budget set id a¤ected if m changes from 12 to 16; but prices are kept at(p1; p2) = (3; 6)4. Next, compare the budget set when (p1; p2) = (3; 6) and m = 12 with the budget set when (p1; p2) =(6; 12) and m = 24: Explain.2. True/False: In general, the budget set given (p1; p2; m) is the same as given (p01; p02; m0) = (tp1; tp2; tm) ift is strictly positive: If you argue that the claim is true, provide an explanation/proof. If you argue thatthe claim is false, provide a counter example.3. A professor is allocated a research budget of $2000; which can be used only for copying and p ostage.However, the chair of the department doesn’t think that it is worth the e¤ort to charge for small copyingexpenses and has therefore decided that the …rst 4000 pages are free, but that if copying exce eds 4000pages then 10 cent/copy is charged (also for the …rst 4000 copies). For the postage, assume that eachletter is 33 cents and that a charge will be imposed from the very …rst letter. Draw the budget set. Hints:ignore the impossibility of sending 1/2 of a letter and you may also want to change the scales to eliminatea b unch of zeros.4. Now suppose that the prices on the market are (p1; p2) = (2; 1) and the income is m = 20: However, thegovernment thinks that good x1is very very important and gives away 4 units for free.1. Draw the budget set.2. The (per capita) cost for the policy to give away 4 units for free is 8 dollars. Hence, for the samecost the government could simply increase the disposable income of the c onsu mer to 28: Which isbetter for the consume r? Hint: use a graph with some appropriately drawn indi¤erence curves anda b udget set.3. Suppose instead that the government pays a subsidy s = 1 for each unit of good x1the consumerbuys (total cost will thus be the number of units the consumer buys). Draw the new budget setfor the consumer. Sketch some indi¤erence curves such th at the best consumption bundle for theconsumer is (10; 10) with this subsidy. What is the total cost for the subsidy paid by the government?Suppose the government would give this to the consumer instead of subsidizing consumption. Wouldthe consumer be better or worse o¤? Interpret!5. Carefully depict some of the indi¤erence curves for the following utility functions.1. u (x1; x2) = x1+px22. u (x1; x2) = x131x2323. u (x1; x2) = 55 +x131x23226. Lisa consumes x1and x2and has 15 units of good 1 and 10 units of good 2 before going to the marketplace.At the m arket place one unit of good 1 can be exchanged for 2 units of good 2 (so that 1 unit of good 2can also be traded for12unit of good 1).1. Graph Lisas budget set carefully.2. Suppose that there is a “transaction tax” so that for e ach unit of good 1 sold or bought,14unit ofgood 1 must be given to the Sheri¤ of Nottingham. Carefully graph the bud get set.7. Again consider the standard textbook consumer choice model with two goo ds and an exogenous incomem: Su ppose that the preferences are represented by utility f un ctionu (x1; x2) = x1x2.For those who are not used to this notation, the utility is simply the product of the quantity consumed ofthe two goods. Suppose that p1= 1 and p2= 2 and m = 10:1. Sketch at least 2 indi¤erence curves with at least 5 points on each curve being exactly calculated.2. The optimal consumption bundle is the solution to a maximization problem which may be writtenasmaxx1;x2x1x2subject to x1+ 2x2 10:In words, this notation says that the consumer seeks to get as high utility as he/she possibly can,while s taying in the budget set. Solve this problem (exactly) and illustrate the solution in a


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UNC-Chapel Hill ECON 440 - Consumer Theory- Review Problems

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