Microeconomics with Calculus
Exam Answer Key
Course Introduction
Microeconomics with Calculus explores the fundamental principles of microeconomic theory using mathematical tools to provide a deeper and more precise understanding of economic analysis. The course covers topics such as consumer and producer behavior, market equilibrium, elasticity, and welfare analysis, employing calculus techniques like differentiation and optimization to solve complex problems. Students will learn how to model economic scenarios quantitatively, analyze how individuals and firms make decisions under constraints, and interpret the mathematical results in an economic context. This blend of theory and mathematics prepares students for more advanced economic coursework and equips them with analytical skills applicable to real-world economic issues.
Recommended Textbook
Microeconomics An Intuitive Approach with Calculus 1st Edition by Thomas Nechyba
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Page 2
Chapter 1: Introduction
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Sample Questions
Q1) Economists talk about tradeoffs a lot because they have come to understand that whenever there is a winner from a policy or transaction,there must also be a loser.
A)True
B)False
Answer: False
Q2) If medical patients are rational (in the way economists think of the term),they will do what medical experts believe is best for them.
A)True
B)False
Answer: False
Q3) Positive economics can tell us which policies are efficient and which are not.
A)True
B)False
Answer: True
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Page 3
Chapter 2: A Consumers Economic Circumstances
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Q1) When the good on the vertical axis is a composite good,the slope of the budget line is equal to minus the price of the good on the horizontal axis.
A)True
B)False
Answer: True
Q2) Kinks in budget constraints always produce non-convexities in choice sets.
A)True
B)False
Answer: False
Q3) While the endowment bundle must lie on the original budget line,it need not lie on the budget line when prices change.
A)True
B)False Answer: False
Q4) The only way for a consumer choice set to be non-convex is for the budget line to be kinked.
A)True
B)False Answer: False
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Chapter 3: Economic Circumstances in Labor and Financial Markets
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Q1) Since interest rates for borrowing are usually higher than interest rates for savings,the intertemporal budget constraint has an inward kink for individuals that earn income now and in the future.
A)True
B)False
Answer: False
Q2) Write down the budget constraint equation as well as the choice set for a worker who has 100 possible hours of leisure per week and can earn a wage of $25 per hour. Answer: Equation: \(c = 2500 - 25 \ell\) Choice Set: \(C = \left\{ ( c , \ell ) \in R _ { + } ^ { 2 } \mid c = 2500 - 25 \ell \right\}\)
Q3) A decrease in a wage taxes causes the opportunity cost of leisure to increase.
A)True
B)False
Answer: True
Q4) A bond that promises to pay $X in 10 years must be worth less than $X now.
A)True
B)False
Answer: True
Page 5
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Chapter 4: Tastes and Indifference Curves
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Sample Questions
Q1) Complete tastes are tastes that make people desire at least some of every good.
A)True
B)False
Q2) If you observe me choosing bundle A over bundle B on Monday,bundle B over bundle C on Tuesday and bundle C over bundle A on Wednesday,it must be that my tastes violate transitivity.
A)True
B)False
Q3) Prove formally that the rationality axioms alone rule out the possibility of indifference curves crossing.
Q4) The number of units of the good on the horizontal axis that we are willing to give up to get one more unit of the good on the vertical axis is equal to the absolute value of the slope of the indifference curve.
A)True
B)False
Q5) Explain the following statement: Individuals with different tastes might have the same tastes at the margin at their current consumption bundles.
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6
Chapter 5: Different Types of Tastes
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Q1) Consider the utility function \(u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 1 } ^ { \alpha } x _ { 2 } ^ { \beta }\) .Which of the following are true statements about the indifference maps represented by this function.
a.
MRS=-1 along the 45 degree line if and only if \(\alpha = \beta\) .
b.
MRS=-1 along a ray steeper than the 45 degree line if and only if \(\alpha > \beta\) .
c.
MRS=-1 along a ray shallower than the 45 degree line if and only if \(\alpha < \beta\) .
d.
All of the above.
e.
None of the above.
Q2) Homothetic tastes are always tastes over essential goods. A)True B)False
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Chapter
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Q1) The only way a consumer can optimize at a corner of her budget is if at least one of the goods is not essential.
A)True
B)False
Q2) Currently,the price of consuming housing is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption and at the same time lowers taxes on all other goods.
a.With housing consumption on the horizontal axis and all other consumption on the vertical,illustrate you current optimal consumption bundle.
b.After looking over the government's proposal,you decide that you don't care one way or another whether the government implements this proposal.On your graph,indicate your new budget constraint and new optimal bundle under the proposal.
c.I also look over the proposal and find that my current consumption bundle also lies on the budget constraint I would face under the proposal.Am I also indifferent between the two proposals?
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Chapter 7: Income and Substitution Effects in Consumer
Goods Markets
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Sample Questions
Q1) Suppose the only two goods you care about in the world are French wine (x)and Cuban cigars (y)and your utility function is given by u(x,y)=xy.You have no income,and the only thing in the world you possess is a large box you have just inherited from your rich uncle who passed away last week (of liver and lung cancer.)You open the box,and much to your liking,you find it contains 9 bottles of fine French wine and 3 boxes of exquisite Cuban cigars.Currently,the wine sells for $1 per bottle,and the cigars sell for $9 per box.Just as you receive the inheritance,you read the headline: "President Lifts Embargo - Price of Cuban Cigars Falls to $4 per Box!"
a.Determine the income (or wealth)and substitution effects of a decrease of the price of cigars from 9 to 4.(Assume fractions of bottles and cigars can be bought.)
b.Are cigars a normal or inferior good for you?
c.How much would you have been willing to pay the President in order not to lift the embargo?
Q2) The price of peaches goes up and I observe you buying more strawberries.This implies strawberries must be a normal good.
A)True
B)False
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Page 9
Chapter 8: Wealth and Substitution Effects in Labor and Capital Markets
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Sample Questions
Q1) In a model of consumption and leisure,a drop in the wage will cause workers to work more if tastes are quasilinear in consumption.
A)True
B)False
Q2) When the elasticity of substitution in the constant elasticity of substitution utility function lies above 1,an increase in the interest rate will cause a saver to save less. A)True
B)False
Q3) The more substitutable current consumption is with future consumption,the more likely it is that an increase in the interest rate will cause an increase in savings.
A)True
B)False
Q4) As long as both current and future consumption are normal goods,a decrease in the interest rate will result in a drop in savings. A)True
B)False
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Chapter 9: Demand for Goods and Supply of Labor and Capital
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Sample Questions
Q1) An increase in the price of good 2 will cause the demand curve for good 1 to shift out.
A)True
B)False
Q2) Suppose your tastes over consumption and leisure have constant elasticity of substitution.I observe that,when your wage went up,you continued to work the same number of hours.From this,I can conclude that you have Cobb-Douglas tastes.
A)True
B)False
Q3) Goods like exclusive designer clothes carry with them prestige value linked to their price.As a result,some people demand more of such goods as the price increases.For those people,such goods are Giffen goods.
A)True
B)False
Q4) Assuming the same sized substitution effect,normal goods have steeper cross-price demand curves than inferior goods.
A)True
B)False
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Chapter 10: Consumer Surplus and Deadweight Loss
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Sample Questions
Q1) For perfect complements,the (uncompensated)demand curve slopes down and the compensated demand (or MWTP)curve is perfectly vertical.
A)True
B)False
Q2) Indirect utility functions are homogeneous of degree 1 in income.
A)True
B)False
Q3) An increase in income causes compensated demand curves to shift inward and regular demand curves to shift outward.
A)True
B)False
Q4) Whenever indifference curves have kinks,marginal willingness to pay curves have horizontal "flat spots".
A)True
B)False
Q5) As we move to higher indifference curves,compensated demand (or MWTP)curves shift to the right.
A)True
B)False
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Chapter 11: One Input and One Output: a Short-Run
Producer Model
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Sample Questions
Q1) Calvin buys newspapers and delivers them (by bike)to his customers' houses while Hobbes sells lemonade at his lemonade stand.One day they compare notes and find that Calvin,after paying for the newspapers and the maintenance on his bike,clears $5 per hour while Hobbes,after paying for the lemonade ingredients and upkeep of his lemonade stand,clears $4.50 per hour.The newspaper and lemonade businesses are the only possible trades for Calvin and Hobbes.
a.If Calvin and Hobbes are identical,how much economic profit (per hour)is each making?
b.Suppose Hobbes is slower on his bike than Calvin -- and he could only deliver half as many newspapers per hour.What's his economic profit in the lemonade business?
Q2) Labor demand curves are homogeneous of degree zero.
A)True
B)False
Q3) If the single-input producer choice set is fully convex,the first order conditions of the profit maximization problem are necessary but not sufficient for identifying the profit maximizing production plan.
A)True B)False
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Chapter 12: Production With Multiple Inputs
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Sample Questions
Q1) Just as indifference maps represent consumer tastes,so isoquant maps represent a producer tastes.
A)True
B)False
Q2) Production technologies A and B can have the same-shaped isoquant map,with technology A having decreasing returns to scale and technology B having increasing returns to scale.
A)True
B)False
Q3) If a production technology has diminishing marginal product of all inputs throughout,then the producer choice set is convex.
A)True
B)False
Q4) Cost functions must be homogeneous of degree 1 in (input and output)prices.
A)True
B)False
Q5) All economically efficient production plans are technologically efficient.
A)True
B)False
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Chapter 13: Production Decisions in the Short and Long Run
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Q1) (Long run)average cost curves are U-shaped when the production technology has increasing returns to scale and the firm faces recurring fixed costs.
A)True
B)False
Q2) The parameter A re-scales the production function \(f ( k , \ell ) = A \left( \alpha \ell ^ { - \rho } + ( 1 - \alpha ) k ^ { - \rho } \right) ^ { - \beta / \rho }\) -- allowing us to transform a decreasing returns to scale production function to an increasing returns to scale production function.
A)True
B)False
Q3) The fixed expense on a fixed level of capital in the short run becomes a fixed cost for the firm in the long run.
A)True
B)False
Q4) Long run average cost curves are downward sloping for increasing returns to scale production technologies.
A)True
B)False
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Page 15
Chapter 14: Competitive Market Equilibrium
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Sample Questions
Q1) Suppose Congress passes a one-time tax refund of all taxes paid by firms in an industry last year.This will lead to a drop in output price in the industry.
A)True
B)False
Q2) If a firm makes negative short run profits,it will exit the industry in the long run.
A)True
B)False
Q3) Suppose there are no recurring fixed costs and the daily production process for all identical firms in a perfectly competitive industry has decreasing returns to scale throughout.Then each firm will only produce a single good each day when the industry is in long run equilibrium.
A)True
B)False
Q4) The long run market supply curve is formed by adding up individual firm supply curves in the industry.
A)True
B)False
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Chapter 15: The Invisible Hand and the First Welfare
Theorem
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Q1) Absent any violations of the first welfare theorem,the competitive equilibrium is efficient.
A)True
B)False
Q2) Suppose the conditions of the first welfare theorem hold.If the government redistributes income prior to production and trade occurring,the market outcome (resulting from production and trade)will be the same as it would have been had the government not redistributed income (so long as redistribution does not produce deadweight losses).
A)True
B)False
Q3) In a 2-good model,suppose that all individuals have tastes that are quasilinear in either good 1 or in good 2 (with some of each represented in the group.)The quasilinearity of everyone's tastes is then sufficient to insure that we can treat the group as if it were a single representative consumer.
A)True
B)False
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Page 17
Chapter 16: General Equilibrium
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Sample Questions
Q1) Any efficient allocation has to be such that everyone would agree to switch to that allocation from the endowment allocation -- or at least no one would object to such a switch.
A)True
B)False
Q2) If the production technology in a Robinson Crusoe economy has increasing returns to scale,there is not competitive equilibrium.
A)True
B)False
Q3) Suppose we live in an exchange economy with two goods.Together,we own 300 of good 1 and 300 of good 2.My tastes are captured by the utility function \(u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 50 \ln x _ { 1 }\) and yours are captured by the utility function \(u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 100 \ln x _ { 1 }\) .
a.Calculate the portion of the contract curve that lies in the interior of the Edgeworth Box. b.Can you make intuitive sense of your answer?
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18
Chapter 17: Choice and Markets in the Presence of Risk
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Sample Questions
Q1) The certainty equivalent is less than the expected value of a gamble when tastes are risk averse.
A)True
B)False
Q2) Suppose an individual has state-independent tastes and invests in risky stocks rather than safe bonds.We can infer that he must be risk loving.
A)True
B)False
Q3) Suppose that individuals with state-independent and risk-averse tastes insure each other through state-contingent trades.If there is no aggregate risk,the competitive equilibrium price will then result in actuarily fair insurance terms.
A)True
B)False
Q4) If the probability of the bad outcome is 0.5,the benefit level of actuarily fair insurance will be half the premium.
A)True
B)False
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Page 19
Chapter
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Q1) When leisure is an inferior good,the wage elasticity of labor supply is always positive.
A)True
B)False
Q2) The price elasticity of output supply is greater in the long run than in the short run.
A)True
B)False
Q3) The reduction in the market output resulting from the imposition of a price floor depends on both the price elasticity of demand and the price elasticity of supply.
A)True
B)False
Q4) If a consumer's demand curve as constant own-price elasticity of -2,the consumer's spending will fall as price increases.
A)True
B)False
Q5) The wage elasticity of labor demand is always negative. A)True
B)False
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Page 20
Chapter 19: Distortionary Taxes and Subsidies
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Sample Questions
Q1) Regardless of whether goods are inferior or normal,the deadweight loss from a per-unit tax is always greater the more price elastic the market demand curve for a good.
A)True
B)False
Q2) If demand is linear,tax revenue rises at a constant rate as per unit taxes increase.
A)True
B)False
Q3) When tastes are quasilinear,the sole reason for the deadweight loss from a per-unit tax is that output falls under the tax.
A)True
B)False
Q4) The burden of a per-unit tax will fall disproportionately on consumers when the supply curve is relatively more elastic than the demand curve.
A)True
B)False
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21
Chapter 20: Prices and Distortions Across Markets
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Q1) When tariffs on exports are eliminated,there is at least in principle a way for everyone to benefit.
A)True
B)False
Q2) In a world of certainty about future demand and supply,speculators cause price fluctuations across time to decrease.
A)True
B)False
Q3) Suppose the price of good x in country A is lower than the price of good x in country B when no trade is permitted.In the absence of transportation costs,if the supply curve for good x in the two countries is sufficiently elastic,free trade in good x implies that country B will stop producing x.
A)True
B)False
Q4) If worker productivity is the same in each country,outsourcing and labor migration will both result in an equalization of wages across the two countries.
A)True
B)False
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Chapter 21: Externalities in Competitive Markets
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Q1) The Coase Theorem implies that the reason people sue each other in court is that transactions costs are too high.
A)True
B)False
Q2) The Coase Theorem implies that the reason people sue each other in court is that property rights have not been sufficiently well specified.
A)True
B)False
Q3) In order for a cap-and-trade system to work,it must be that pollution permits are bought by producing firms -- and not given to them as part of an attempt to prevent them to lobby against the cap-and-trade system
A)True
B)False
Q4) Explain how a pollution tax is different from a Pigouvian tax.Discuss how incentives for firms differ under the two types of taxes,and what would be required of the government if it were to structure a Pigouvian tax system to mimic the effects of a pollution tax.
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Chapter 22: Asymmetric Information in Competitive Markets
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Q1) Whether or not a pooling equilibrium exists in a competitive market with adverse selection depends on what fraction of consumers is of the high cost type and what fraction is of the low cost type.
A)True
B)False
Q2) Adverse selection in insurance markets results in missing markets because people engage in riskier behavior once they are insured.
A)True
B)False
Q3) Firms that employ statistical discrimination in the labor market will earn higher profits in expectation than firms that do not discriminate (and have no effective screens).
A)True
B)False
Q4) Suppose a competitive market with adverse selection has settled into a pooling equilibrium where everyone is offered the same price.If firms then screen consumers,the outcome may and may not be more efficient.
A)True
B)False
24
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Chapter 23: Monopoly
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Q1) If a monopolist were allowed (and able)to first degree price discrimination,there would be no efficiency/equity tradeoff so long as the government can tax the profits of the firm and redistribute the tax revenues in a lump sum way.
A)True
B)False
Q2) For any constant-elasticity market demand curve,a monopolist is profit maximizing regardless of what quantity he produces so long as marginal costs are zero.
A)True
B)False
Q3) How would a regulator of a monopoly think differently about regulating price discrimination depending on whether the regulator's objective is to maximize efficiency or to maximize consumer surplus?
Q4) In the absence of recurring fixed costs,a monopolist will always produce a positive output quantity.
A)True B)False
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Page 25
Chapter 24: Strategic Thinking and Game Theory
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Q1) If everyone has a dominant strategy in a simultaneous move game,then the action that is played by that strategy is played in all stages of any finitely repeated version of that game in any subgame perfect equilibrium.
A)True
B)False
Q2) In a Bayesian incomplete information game,a "belief" is represented as the probability you place on your opponent playing one strategy versus another.
A)True
B)False
Q3) If a separating equilibrium is played in a signaling game,the receiver will "update" his beliefs during the game.
A)True
B)False
Q4) In a Prisoners' Dilemma,both players are willing to pay to be forced to cooperate.
A)True
B)False
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26
Chapter 25: Oligopoly
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Q1) Just because a firm can deter entry by a competitor does not mean it will deter entry.
A)True
B)False
Q2) Explain why firms in a cartel might lobby for government regulation.
Q3) Suppose a market is currently served by an incumbent firm.If a potential entrant can enter prior to the incumbent firm announcing its output (or price),the incumbent cannot deter entry through its actions.
A)True
B)False
Q4) Recurring fixed costs may lead to only one firm producing in a Cournot oligopoly model.
A)True
B)False
Q5) Explain how two Bertrand price competitors can price above marginal cost in an infinitely repeated game setting.
Q6) Two firms in an oligopoly can always do better if one firm buys the other. A)True
B)False
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Chapter 26: Product Differentiation and Innovation in Markets
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Q1) Describe the tradeoffs involved when thinking about setting the time over which a patent grants an innovator exclusive monopoly rights.
Q2) In a monopolistically competitive market with Dixit-Stiglitz preferences,equilibrium price falls as the goods in the differentiated product market become more substitutable.
A)True
B)False
Q3) In a monopolistically competitive market with Dixit-Stiglitz preferences,the number of firms in the differentiated product market falls as goods in that market become less substitutable.
A)True
B)False
Q4) Since firms outside an industry cannot have an incentive to enter the industry in equilibrium,firms inside a monopolistically competitive equilibrium must be making zero profit.
A)True
B)False
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Chapter 27: Public Goods
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Q1) Suppose you run a charity that raises money for a worthy public good.Your donors may be concerned about how much of each dollar that is raised is put back into more fund-raising.
a.Suppose the marginal product of a dollar put into fundraising is initially increasing but eventually diminishing.How much will the last dollar spend on fundraising raise?
b.If everyone considers their own contribution to this charity as the marginal contribution,what will be their impression of how much they are really helping the public good?
c.Would you expect your answer to (b)to make it harder for you to raise money for your charity?
d.How might your answer to (c)explain why some charities make a point of informing people that they have placed a cap on their fund raising budget -- or that they have placed a cap on how many people will be approached during the fund raising campaign?
Q2) When the government contributes to a public good,private contributions will fall.
A)True B)False
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Chapter 28: Governments and Politics
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Q1) Vote trading in legislatures can lead to efficient outcomes that might otherwise not have been reached.
A)True
B)False
Q2) Consider voter preferences over a public good y that is being funded by a proportional income tax.
a.Illustrate how this might lead to single peaked voter preferences.
b.Suppose there exists a privately available good x that is substitute for y.How does this introduce non-single peakedness?
c.Now suppose x is relatively complementary to y.What would you expect to happen to voter preferences as this complementarity gets stronger?
Q3) Discuss how a politicians "policy differentiation" from his opponent in an election softens the competition over how much in political rents the politician will be able to collect.
Q4) In settings where the policy space is single dimensional,non-single peaked preferences by some implies there is no Condorcet winner.
A)True
B)False
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Chapter 29: What Is Good Challenges From Psychology and Philosophy
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Q1) Since it lies in 2-dimensions,one of the drawbacks of using Lorenz curves to think about inequality is that we are restricted to thinking about only two types of individuals. A)True
B)False
Q2) Because wealth is more concentrated than income,the Gini coefficient for the wealth distribution is greater than the Gini coefficient for the income distribution.
A)True
B)False
Q3) One way to think of ideas coming out of behavioral economics is to map the ideas into either impacting "tastes" or "constraints".Can you give an example of each?
Q4) Positive economics does not require us to believe that actual happiness is the same as utility as modeled in economic theory.
A)True
B)False
Q5) What's the Easterlin Paradox -- and in what sense does it suggest reference-dependent preferences?
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