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UNC-Chapel Hill ECON 410 - Practice Problems -- Deriving Demand Curves and Other Applications

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Econ. 410Spring 2008TauchenPractice Problems -- Deriving Demand Curves and Other Applications1. Jennifer consumes two goods – X and Y. Her income is $100/ time period and the price of good X is $1. Use her indifference map as shown below to construct her demand curve for good Y for prices $1, $2,and $3. 01020304050607080901000 20 40 60 80 100 120XY2. Shown to the right is Ben’s demand curve forgood Y. Construct an indifference mapconsistent with the amount of good Y hedemands at prices of $1, $2, and $3 for good Y. Dem and Function for Good YI=$400, px=$1012340 5 10 15 20 25 30 35 40 45 50 55 60units Y per time periodpy3. We can apply the consumer theory model to understand the decisions faced by government agencies and public officials. Governments have budget constraints determined by their funding sources and governments (or government officials) make choices given their preferences. We will use this model to explain some of the opposition to across-the-board budget cuts.Assume that the government allocates its funds between education and law enforcement expenditures. (Indefining the goods in terms of expenditures, we are assuming that the prices of goods used in education and law enforcement are not changing during the time period for which we are considering the government budgeting.) The government’s preferences for law enforcement and education expenditures satisfy the usual properties of the consumer theory model. a. The government has a fixed budget amount B that it can allocate between the two goods. Use a graph to describe the choice problem and the characteristics of the optimum allocation. b. Suppose that the budget falls by 25 % and that the legislature reduces the previous expenditures on all services by 25%. Use the consumer theory model to explain whether this is the best reaction to the budget reduction. 4. Ben consumes two goods, X and Y. His preferences satisfy the usual assumptions. The market price of each good is $1.Ben works for a firm that produces and sells good X. Ben’s salary is $1000/week. In addition, the firm allows its employees to purchase good X at a discount of 50%. Given his budget and his preferences, Ben purchases 1000 units of X per week.a. Construct a graph and show an indifference map consistent with the information given above. There are many indifference maps consistent with this information. You are asked to show one such indifference map.b. Ben’s employer proposes eliminating its employee discount program and increasing salaries. Since employees purchased, on average, 1000 units of X per week under the discount program, the firm proposes compensating employees for the elimination of the discount by increasing each worker’s salary by $500. Does the elimination of the discount program, along with the salary increase, make Ben better off or worse off? Use the graph to explain your answer.c. Would all workers’ well-being be affected in the same direction as Ben’s? Use a graph to support your answer.d. Use the graph that you constructed for parts a. and b. to determine the minimum salary increase (approximately)required to compensate Ben for the loss of the discount program. e. One of the firm’s accountants advises that the firm re-consider the proposed salary increase. She pointsout that employees are required to shop at off-peak times and need very little customer assistance. Hence,the employee discount program costs the firm less than $500/employee (on average). The accountant estimates that the cost to the firm of the 50% employee discount is only $.25 per unit sold to an employee rather than $.50. Thus, she suggests that the firm increase salaries by only $250 per person if it eliminatesthe discount program.Would eliminating the discount and increasing his salary by $250 necessarily make Ben worse off than with the original discount program? Use a graph to support your answer.01020304050607080901000 10 20 30 40 50 60 70 80 90 100XYBLNBL0g. Provide an economic justification for the employee discounts offered by many firms. 5. The initial and new budget lines are labeled BL0 and BLN respectively. a. What change in income and/or prices would cause this rotation in the budget line?b. Determine the income and substitution effects for this change in the budget line. Is good X a normal or an inferior good (for this part of the indifference map)? Is good Y a normal or an inferior good (for thispart of the indifference map)?6. A household consumes two goods: educational quality and good Y. The household’s preferences satisfy the usual assumptions. The household has income I; educational quality and good Y can be purchased at market prices. Public education is not available. The household decides how much educational quality and how much of good Y to purchase. We’ll assume that the household has only one child so that we do not have to consider the possibility of different quality for different children.a. Construct a graph on which you show school quality on the horizontal axis and good Y on the vertical axis. Use the standard consumer theory model to describe the household’s choice problem. You are not given numerical values for income or the prices of the good but can apply the consumer theory model to describe the choice problem that the family faces.b. The government now offers free,public education of quality levelQg. The government selects thequality of the public education.(We are ignoring taxes used tosupport the schools.) A household’schoices are to (i) purchase privateeducational quality as in part a or(ii) send the child to the publicschool of quality Qg for free. Keep in mind that if the householdselects public education, then it canspend all of its income on good Y.If you have any difficulty with thebudget set, then try making upsimple numbers. Once youunderstand the budget set for asimple numerical example, you canoften figure out the general budgetset.] b1. For each family, identify theoptimum education quality choiceif the free public education werenot available. b2. For each family, determine theoptimum choice with free publicschools of quality Qg available.b3. For each family, compare thequality of education chosen (i)when no free education is availableand-(ii) when free public educationof quality Qg is available.c. Suppose now that thegovernment offers householdsanother option. They may selectthe public education for free or theymay have a


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UNC-Chapel Hill ECON 410 - Practice Problems -- Deriving Demand Curves and Other Applications

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