Mathematical Economics
Final Exam
Course Introduction
Mathematical Economics is a course that explores the application of mathematical methods and techniques to represent economic theories and analyze problems in economics. Students will learn how to use calculus, linear algebra, and optimization to formulate and solve models of consumer behavior, producer theory, market equilibrium, and other economic phenomena. The course emphasizes logical reasoning and rigorous analysis, enhancing students ability to interpret complex economic relationships quantitatively and to apply mathematical tools in both microeconomic and macroeconomic contexts.
Recommended Textbook
Microeconomics An Intuitive Approach with Calculus 2nd Edition by Thomas Nechyba
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713 Verified Questions
713 Flashcards
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Page 2
Chapter 1: Introduction
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Sample Questions
Q1) Suppose two economic models give the same predictions --- but one is simplistic and unrealistic in its assumptions while the other is rich in detail and resembles the real world more closely.If the sole goal of the economist is to predict, then the economist should use the simple and unrealistic model.
A)True
B)False
Answer: True
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) To say that one policy is better than another because it is more efficient is a normative, not a positive, statement.
A)True
B)False
Answer: True
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Chapter 2: A Consumers Economic Circumstances
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Q1) Regardless of which consumption bundle in her choice set a consumer chooses, she will spend all of her available income.
A)True
B)False
Answer: False
Q2) The budget line on a graph represents choices which exhaust all resources.
A)True
B)False
Answer: True
Q3) Derive the budget line equation for the case where good 2 is a composite good.What is the vertical intercept and what is the slope?
Answer: Since p<sub>2</sub> = 1, the usual budget line equation x<sub>2</sub>=I/p<sub>2</sub> - (p<sub>1</sub>/p<sub>2</sub>)x<sub>1</sub> becomes x<sub>2</sub>=I - p<sub>1</sub>x<sub>1</sub>, an equation with a vertical intercept of I and a slope of - p<sub>1</sub>.
Q4) If a consumer's fixed income increases, his opportunity cost also increases.
A)True
B)False
Answer: False
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Chapter 3: Economic Circumstances in Labor and Financial Markets
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Sample Questions
Q1) An "endowment" is something whose value is unknown. A)True
B)False Answer: False
Q2) In the typical leisure/consumption model, an increase in the wage is equivalent to a decrease in the price of the composite consumption good.
A)True
B)False
Answer: True
Q3) 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: 11ea67b0_0517_9d87_8b3b_8fd11fa1ef66_TB5129_11 Choice Set: 11ea67b0_0517_9d88_8b3b_fd7001be6fe5_TB5129_11
Q4) In choice sets, intertemporal budget constraints illustrate consumption trade-offs over time.
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) Suppose bundle A is better than bundle B for a consumer, and bundle C is an average of bundles A and B.
a.Use the continuity, convexity and monotonicity assumptions to formally prove that this implies that bundle C is better than bundle B.
b.Did you also -- implicitly or explicitly -- use the rationality axioms?
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) When the price of beer goes up, our model of tastes would typically require tastes to change.
A)True
B)False
Q4) Explain the following statement: For the same individual, tastes over goods may vary at the margin as we move from one bundle to another.
Q5) Prove formally that the rationality axioms alone rule out the possibility of indifference curves crossing.
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Chapter 5: Different Types of Tastes
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Q1) Tastes for perfect substitutes are both homothetic and quasilinear.
A)True
B)False
Q2) Homothetic tastes are always tastes over essential goods.
A)True
B)False
Q3) There are no quasilinear tastes that have constant elasticity of substitution.
A)True
B)False
Q4) In the case of perfect complements, more is not necessarily better.
A)True
B)False
Q5) All homogeneous functions (of any degree) are homothetic but not all homothetic functions are homogeneous (of some degree).
A)True
B)False
Q6) There is no elasticity of substitution that is inconsistent with tastes being homothetic. A)True
B)False
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Chapter
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Sample Questions
Q1) Which of the following is correct about a consumer's optimization problem:
A)In order for a consumer to not be optimizing at a corner solution, it is necessary for us to assume that all goods are essential.
B)In order for a consumer to not be optimizing at a corner solution, it is sufficient for us to assume that all goods are essential.
C)In order for a consumer to not be optimizing at a corner solution, it is necessary and sufficient for us to assume that all goods are essential.
D)None of the above.
Q2) Suppose that choice sets are convex but we tastes may or may not be convex.(Assume all our other usual assumptions about tastes hold.) The first order conditions of the constrained utility maximization problem are then
A)necessary conditions for a true optimum.
B)sufficient conditions for a true optimum.
C)necessary and sufficient conditions for a true optimum.
D)none of the above.
Q3) If all goods are essential, a consumer will optimize at an interior solution.
A)True
B)False
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8
Chapter 7: Income and Substitution Effects in Consumer
Goods Markets
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Sample Questions
Q1) Bottles of Coca-Cola and equally-sized bottles of Pepsi Cola are perfect substitutes for a consumer, but a bottle of Coke costs 10 cents less than bottles of Pepsi.The income effect of a 15 cent increase in the price of Pepsi will be for the consumer to drink less cola. A)True
B)False
Q2) Income effects are negative for normal goods, and positive for inferior goods. A)True
B)False
Q3) The price of peaches goes up and I observe you buying fewer strawberries.This implies strawberries must be a normal good.
A)True
B)False
Q4) The price of peaches goes up and I observe you buying more strawberries.This implies that strawberries must be an inferior good. A)True
B)False
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Chapter 8: Wealth and Substitution Effects in Labor and Capital Markets
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Q1) In the U.S., everyone has to pay social security taxes on labor income until pre-tax income reaches a certain amount after which no additional taxes are due.Consider the case of workers A, B and C who have 60 hours of leisure per week and who earn an hourly wage of $40.Suppose the social security tax is 50% up to a pre-tax weekly income of $1,200 and then falls to zero for any income above $1,200 per week.Assume tastes are homothetic.
a.Worker A is observed to work 40 hours per week under this tax system.Is he working more or less than he would if the system were abolished?
b.Worker B is observed to work 30 hours a week under this tax system.Is he working more or less than he would if the system were abolished?
c.Worker C is observed to work 20 hours per week under this system.Is he working more or less than he would if the system were abolished?
d.Could any of the three workers above share exactly the same tastes?
e.For which of these workers is there no deadweight loss from the tax?
Q2) If leisure is an inferior good, then an increase in wages will cause workers to work more.
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) Leisure being a normal good is neither necessary nor sufficient for labor supply to slope up.
A)True
B)False
Q2) For the same sized substitution effect, own-price demand curves for inferior goods are steeper than own price demand curves for normal goods.
A)True
B)False
Q3) If a good is quasilinear, its own-price demand curve is vertical.
A)True
B)False
Q4) If tastes are homothetic in leisure and consumption, labor supply curves slope up.
A)True
B)False
Q5) Assuming the same sized substitution effect, normal goods have steeper cross-price demand curves than inferior goods.
A)True
B)False
11
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Chapter 10: Consumer Surplus and Deadweight Loss
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Sample Questions
Q1) There is a compensated demand (or MWTP) curve for every indifference curve just as there is an uncompensated demand curve for every income level.
A)True
B)False
Q2) Why is the following statement incorrect: "A tax on all consumption goods is efficient because it equally taxes all goods and therefore does not distort their prices."
Q3) A policy which gains the winners more than the losers lose, in principle, could never result in unanimous approval of the policy.
A)True
B)False
Q4) When tastes are not quasilinear, the positive economist will introduce error into the analysis if he uses the uncompensated (rather than the compensated) demand curve to analyze changes in consumer surplus.
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) Suppose a single-input production function has initially increasing but eventually decreasing marginal product -- and suppose we know that an interior solution is profit maximizing.In this case, the first order condition for the profit maximization problem
A)is necessary for identifying the profit maximizing production plan.
B)is sufficient for identifying the profit maximizing production plan.
C)is both necessary and sufficient for identifying the profit maximizing production plan.
D)is neither necessary nor sufficient for identifying the profit maximizing production plan.
Q2) An increase in the wage will cause the output supply curve in the one-input model to shift in unless labor is an inferior input.
A)True
B)False
Q3) With all other inputs held fixed, the marginal product of any input must eventually increase as more of that input is hired.
A)True
B)False
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13
Chapter 12: Production With Multiple Inputs
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Sample Questions
Q1) Increasing returns to scale production technologies cannot give rise to convex producer choice sets.
A)True
B)False
Q2) Conditional input demands are homogeneous of degree zero in input prices.
A)True
B)False
Q3) Assuming an interior solution, a production plan is profit maximizing if and only if all marginal revenue products are equal to input prices.
A)True
B)False
Q4) Technologically efficient production plans are also economically efficient.
A)True
B)False
Q5) All economically efficient production plans are technologically efficient. A)True
B)False
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Page 14
Chapter 13: Production Decisions in the Short and Long Run
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Sample Questions
Q1) Output price changes cause substitution effects and scale effects.
A)True
B)False
Q2) Output supply is more responsive to price in the short run than in the long run.
A)True
B)False
Q3) If the wage falls, we know for sure that the firm will produce more in the long run but we cannot be sure whether it will use more or less capital.
A)True
B)False
Q4) Conditional input demand curves always slope down, but unconditional input demand curves can slope up.
A)True
B)False
Q5) Short run average expenditure curves are tangent at their lowest point to the long run average cost curve.
A)True
B)False
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Chapter 14: Competitive Market Equilibrium
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Sample Questions
Q1) Whenever a firm is making positive economic profit, there is nothing it can do to make more profit.
A)True B)False
Q2) An increase in license fees -- a long run recurring fixed cost -- will lead to a drop in the number of firms competing in a competitive industry.
A)True B)False
Q3) If a firm makes negative short run profits, it will exit the industry in the long run.
A)True B)False
Q4) Suppose a firm is making zero long run profit.Then it's short run profit cannot be negative.
A)True B)False
Q5) Equilibrium prices coordinate the actions of producers and consumers. 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 market production level of a good will be the same as that chosen by a social planner whose goal includes (but is not necessarily limited to) efficiency.
A)True B)False
Q2) Both successful market-processes and central planning rely on self-interested behavior.
A)True B)False
Q3) 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
Q4) Explain how prices in a competitive market form --- and how they take the place of almost limitless information that a social planner would need if he tried to mimic the market outcome.
17
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Chapter 16: General Equilibrium
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Sample Questions
Q1) Comment on the following: "The second welfare theorem says that we can get any efficient allocation to be an equilibrium allocation.If endowments are inequitably distributed in an economy, we can therefore redistribute among people and still get an efficient outcome.As a result, there is no policy trade-off between equity and efficiency."
Q2) If the two goods in an Edgeworth Box are perfect complements for one person and perfect substitutes for the other, then all efficient allocations are such that the first person has the same amount of good 1 as of good 2.
A)True
B)False
Q3) A "pure exchange economy" is one in which producers and consumers are evenly divided.
A)True
B)False
Q4) Any allocation resulting from a mutually beneficial trade is efficient.
A)True
B)False
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Page 18
Chapter 17: Choice and Markets in the Presence of Risk
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Sample Questions
Q1) When tastes are risk averse, an individual will always choose less risk over more risk.
A)True
B)False
Q2) Actuarily fair insurance reduces risk without changing the expected value of a gamble.
A)True
B)False
Q3) Suppose that individuals with state-independent and risk-averse tastes insure each other through state-contingent trades.The competitive equilibrium price will then result in actuarily fair insurance terms.
A)True
B)False
Q4) Risk averse individuals will fully insure to avoid risk.
A)True
B)False
Q5) The certainty equivalent is less than the expected value of a gamble when tastes are risk averse.
A)True
B)False
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Chapter 18: Elasticities, Price-Distorting Policies, and Non-Price Rationing
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Q1) The equilibrium increase in marginal costs for firms resulting from the imposition of a price floor will be larger the more inelastic the price elasticity of demand is.
A)True
B)False
Q2) Suppose a consumer has the following rule of thumb: Regardless of how gasoline prices fluctuate, she will always buy $20 of gasoline per week and then adjust her driving patterns accordingly.We can then conclude the following:
A)Her own-price elasticity of demand is equal to -1.
B)Her income-elasticity of demand is 0.
C)Her own-price elasticity is 0.
D)Her income elasticity of demand is -1.
E)Both (a) and (b).
F)Both (a) and (d).
G)Both (c) and (d)
H)None of the above.
Q3) When price elasticity is less than -1, consumer spending increases as price falls.
A)True
B)False
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Chapter 19: Distortionary Taxes and Subsidies
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Q1) 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
Q2) Under which of the following scenarios does an increase in the wage tax cause a drop in employment but no deadweight loss?
A)When the wealth effect for workers is larger than the substitution effect.
B)When the wealth effect for workers is smaller than the substitution effect.
C)When the wealth effect for workers is equal to the substitution effect.
D)It is possible under any of these scenarios.
E)There is no scenario under which this is possible.
Q3) In most cases, the fact that one of the market curves is perfectly inelastic is not sufficient to conclude that a per-unit tax in that market is efficient.A tax on land rents is an exception.Can you explain why?
Q4) A wage tax in a labor market with a perfectly inelastic labor supply curve is efficient.
A)True
B)False
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21
Chapter 20: Prices and Distortions Across Markets
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Q1) Explain how an import quota might be more inefficient than an import tariff that has the same impact on prices.
Q2) When tariffs on imports are eliminated, everyone benefits.
A)True
B)False
Q3) Explain the impact of speculators on markets is similar and how it may be different from the impact of exporters and importers.
Q4) While some countries might be better off (in terms of social surplus) from the imposition of a tariff, the world overall is always worse off (in terms of social surplus) when import tariffs are imposed.
A)True
B)False
Q5) Quality of life indexes produced in popular magazines often place a heavy emphasis on the cost of housing in different cities -- with a lower housing cost entering the index as a positive feature of the city.Why might such quality of life indeces be misleading?
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22
Chapter 21: Externalities in Competitive Markets
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Q1) In the absence of the negative externality from each individual's contribution to road congestion, roads would not be congested (aside from congestion caused by accidents).
A)True
B)False
Q2) Explain how any cap-and-trade system can be made to be equivalent to a pollution tax and vice versa.
Q3) Explain why many fishermen on a commonly owned lake continue to fish until the revenue from the average catch is equal to the marginal cost of fishing -- and why the same is not true for a firm that employs fishermen to fish on a privately owned lake.
Q4) Whether or not production is accompanied by an externality, a social planner who aims to maximize social surplus will always produce (assuming he does produce) where marginal social cost is equal to marginal social benefit.
A)True
B)False
Q5) Explain how the introduction of an additional competitive market can always solve the efficiency problem that emerges from a negative externality.
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Page 23
Chapter 22: Asymmetric Information in Competitive Markets
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Q1) Universal health insurance policies fall into three categories: single payer/single provider systems, single payer systems, and regulated insurance markets.The United States has elements of two of these.
A)True
B)False
Q2) Whenever there is adverse selection, there will be missing market.
A)True
B)False
Q3) In the presence of asymmetric information, high-cost and low-cost customers are charged asymmetric prices.
A)True
B)False
Q4) In equilibrium, consumers will incur costs to signal their type (in markets with adverse selection) only if this results in a price that is lower than the pooling equilibrium price.
A)True B)False
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Chapter 23: Monopoly
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Q1) In the absence of recurring fixed costs, a monopolist will always produce a positive output quantity.
A)True
B)False
Q2) Explain why the deadweight loss from monopoly power may be exacerbated if the barrier to entry that creates monopoly power is created through exclusive government granting of a monopoly.For what types of government grants of monopoly power might this not be the case?
Q3) 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
Q4) The more profit a monopolist makes, the more inefficient is the monopoly outcome. A)True
B)False
Q5) Explain what the Saudi oil minister meant when he warned OPEC of using its market power too much by saying "Remember, the Stone Age did not end because we ran out of stones."
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Chapter 24: Strategic Thinking and Game Theory
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Q1) If a pooling equilibrium is played in a signaling game, the receiver will update her beliefs about the sender before settling on her best option.
A)True
B)False
Q2) A Prisoner's Dilemma game is one in which not cooperating is a dominant strategy despite cooperation making everyone better off.
A)True
B)False
Q3) If a player's strategy in a sequential game is to choose an action that stops the game early on, it is unnecessary to specify that player's plans for moves later on in the game when it would have been his turn to move again.
A)True
B)False
Q4) Suppose a player can play 2 possible actions and has 5 possible decision nodes in a sequential game.Then he has 10 possible strategies he can play.
A)True
B)False
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Chapter 25: Oligopoly
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Q1) Two firms in an oligopoly can always do better if one firm buys the other.
A)True
B)False
Q2) Explain why firms in a cartel might lobby for government regulation.
Q3) Suppose two Bertrand price competitors have different constant marginal costs.In any simultaneous move Nash equilibrium, only the lower cost firm will produce.
A)True
B)False
Q4) 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 entrant will enter the market and force the incumbent to compete.
A)True
B)False
Q5) We showed that, when demand is linear and marginal cost is constant, the Stackelberg leader produces the monopoly output while the Stackelberg follower produces half the monopoly output.If the leader and follower now enter a simultaneous quantity setting game, why can't the leader maintain the same equilibrium?
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Chapter 26: Product Differentiation and Innovation in Markets
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Q1) Since firms within a monopolistically competitive industry set output where marginal revenue is equal to marginal cost, the size of the fixed entry cost does not impact the equilibrium price.
A)True
B)False
Q2) Government may actually establish temporary monopolies by the issuance of patents and copyrights.
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) In the circle model with constant marginal cost, each point on the circle will contain a firm in equilibrium if fixed entry costs are zero.
A)True
B)False
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Chapter 27: Public Goods
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Q1) If everyone has identical preferences over public goods, Lindahl prices for providing the efficient level of the public good will be the same for everyone.
A)True
B)False
Q2) If giving to public goods is subsidized through deductions under a progressive income tax, the government subsidizes public goods consumed by higher income individuals at greater rates than public goods consumed by lower income individuals.
A)True
B)False
Q3) Public goods arise because of externalities.
A)True
B)False
Q4) Our free-rider model of voluntary giving suggests that, when the government subsidizes private giving to charity, it's contribution will simply "crowd out" the private contributions so long as no one is at a corner solution.
A)True
B)False
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Chapter 28: Governments and Politics
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Q1) Median voters in settings where the policy space is single dimensional and everyone has single peaked preferences are Arrow Dictators.
A)True
B)False
Q2) A democratic (majority rule) decision over a multi-dimensional issue can be manipulated by an agenda setter only if voter tastes are not single-peaked.
A)True
B)False
Q3) The Pareto Unanimity axiom in Arrow's theorem implies that Arrow believes social choice processes should choose only pareto efficient outcomes.
A)True
B)False
Q4) It is possible to come up with a democratic social choice process that satisfies Arrow's axioms as long as we are willing to let go of the No Dictatorship axiom.
A)True
B)False
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Page 30
Chapter 29: What Is Good Challenges From Psychology and Philosophy
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Q1) Suppose $100 invested next year results in a return of b two years from now.If individuals do not discount the future but have a beta of 0.5 (in the beta-delta model), for what range of b will an individual plan to make the investment but then reverse course next year?
Q2) Any consequentialist approach to normative economics that uses standard indifference maps as social indifference maps (over utilities or consumption) will choose efficient outcomes in the first-best case.
A)True
B)False
Q3) In a society in which everyone lives at the subsistence level, the Gini coefficient is 0. A)True B)False
Q4) Social preferences chosen from behind the veil of ignorance are likely to value efficient outcomes and are likely to treat individuals symmetrically. A)True
B)False
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