Mathematical Economics
Final Exam
Course Introduction
Mathematical Economics is a course designed to apply mathematical methods and techniques to analyze and solve problems in economic theory and practice. The course covers fundamental mathematical tools such as calculus, linear algebra, and optimization, and demonstrates their use in formulating and interpreting economic models involving consumer and producer behavior, market equilibrium, and welfare analysis. Students will learn to translate economic problems into mathematical expressions, analyze the results, and interpret economic implications, providing a rigorous foundation for advanced study and research in economics.
Recommended Textbook
Microeconomic Theory Basic Principles and Extensions 10th Edition by Walter Nicholson
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17 Chapters
334 Verified Questions
334 Flashcards
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Page 2
Chapter 1: Preferences and Utility
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12 Verified Questions
12 Flashcards
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Sample Questions
Q1) Which of the following utility functions best represents the idea that two goods,x and y,are perfect complements?
A) \(U ( x , y ) = \sqrt { x y }\)
B)U(x,y)= x + y.
C) \(U ( x , y ) = | x - y |\) .
D)U(x,y)= min (x,y).
Answer: D
Q2) Which of the following utility functions represent the same preferences as \(U ( x , y ) = \sqrt { x \cdot y }\)
A) \(U ( x , y ) = 10 \sqrt { x y }\) .
B)U(x,y)= x . y.
C)U(x,y)= ln x + ln y.
D)All of these represent the same preferences.
Answer: D
Q3) Indifference curves
A)are non-intersecting.
B)are contour lines of a utility function.
C)are negatively sloped.
D)all of these are correct.
Answer: D
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Chapter 2: Utility Maximization and Choice
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13 Verified Questions
13 Flashcards
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Sample Questions
Q1) If an individual's utility function is given by \(U ( x , y ) = \sqrt { x y }\) and I = 100, p<sub>x</sub> = 1,p<sub>y</sub> = 4,his or her preferred consumption bundle will be: A)(20,20).
B)(50,12.5).
C)(40,15).
D)(30,15).
Q2) The slope of the budget constraint line is
A)the ratio of the prices (p<sub>x</sub>/p<sub>y</sub>).
B)the negative of the ratio of the prices (p<sub>x</sub>/p<sub>y</sub>).
C)the ratio of income divided by price of y (I/p<sub>y</sub>).
D)none of these is correct.
Q3) Suppose utility is given by U(x,y)= ln x + ln y and p<sub>x</sub> = 1,I = 10.If y must be purchased in whole units,what is the maximum price this person would pay for that good?
A)1.
B)5.
C)10.
D)20.
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Chapter 3: Income and Substitution Effects
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19 Verified Questions
19 Flashcards
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Sample Questions
Q1) If there are only two goods and these are consumed in fixed proportions,the price elasticities of demand for these two goods will sum to
A)0.0
B)-0.5
C)-1.0
D)a number between 0 and -1.
Q2) The price elasticity of demand for a linear demand curve follows the pattern (moving from high prices to low prices)
A)elastic,unit elastic,inelastic.
B)unit elastic,inelastic,elastic.
C)inelastic,unit elastic,elastic.
D)elastic,inelastic,unit elastic.
Q3) A decrease in demand is represented by
A)a shift outward of the entire demand curve.
B)a shift inward of the entire demand curve.
C)a movement along the demand curve in a southeasterly direction.
D)a movement along the demand curve in a northwesterly direction.
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5
Chapter 4: Demand Relationships Among Goods
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18 Flashcards
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Sample Questions
Q1) The primary additional insight provided by expanding the theory of choice from two to three goods is that a pair of goods may now be
A)gross substitutes.
B)gross complements.
C)net substitutes.
D)net complements.
Q2) If a rise in the price x causes less y to be demanded,
A)x and y are gross complements.
B)x and y are gross substitutes.
C)x and y are net complements.
D)x and y are net substitutes.
Q3) A generalization of Engel's Law is given by
A)\(e _ { x , p _ { y } } + e _ { y , x } + e _ { x , 1 } = 1\) .
B)\(s _
C)\(e _
D)\(s _ { x } + s _ { y } = l\) .
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6
Chapter 5: Uncertainty and Information
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16 Flashcards
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Sample Questions
Q1) An option may add value to a transaction because:
A)interest charges are reduced.
B)the price of the good is reduced.
C)additional information may become available.
D)options provide buyers with monopsony power.
Q2) Risk-averse individuals will diversify their investments because this will
A)increase their expected returns.
B)provide them with some much-needed variety.
C)reduce the variability of their returns.
D)reduce their transactions costs.
Q3) People who always choose not to participate in fair games are called A)risk takers.
B)risk averse.
C)risk neutral.
D)broke.
Q4) An individual will never buy complete insurance if
A)he or she is risk averse.
B)insurance premiums are unfair.
C)he or she is a risk taker.
D)insurance premiums are fair.
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Chapter 6: Strategy and Game Theory
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Sample Questions
Q1) Which of the following is a true statement about signaling games?
A)In a separating equilibrium,the second mover's posterior beliefs are the same as his priors.
B)In a separating equilibrium,Bayes' rule cannot be used to compute posterior beliefs (because it produces an undefined answer).
C)In a pooling equilibrium,both the first and second movers choose the same action.
D)In a pooling equilibrium,the second mover learns nothing from the first mover's action.
Q2) The strategy profile in which both players remain silent in the Prisoners' Dilemma can be described as
A)non-Pareto optimal and unstable.
B)Pareto optimal and unstable.
C)non?Pareto optimal and stable.
D)Pareto optimal and stable.
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8
Chapter 7: Production Functions
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14 Flashcards
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Sample Questions
Q1) A production function may exhibit
A)constant returns to scale and diminishing marginal productivities to all inputs.
B)constant returns to scale and diminishing marginal productivities to all but one input,but at least one input must have a constant marginal productivity.
C)constant returns to scale and diminishing marginal productivity to at most one input.
D)constant returns to scale and diminishing marginal productivities for no inputs.
Q2) The marginal rate of technical substitution (RTS)of labor for capital measures
A)the amount by which capital input can be reduced while holding quantity produced constant when one more unit of labor is used.
B)the amount by which labor input can be reduced while holding quantity produced constant when one more unit of capital is used.
C)the ratio of total labor to total capital.
D)the ratio of total capital to total labor. .
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Chapter 8: Cost Functions
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20 Verified Questions
20 Flashcards
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Sample Questions
Q1) The average fixed cost curve always has a negative slope because
A)marginal costs are below average fixed costs.
B)average variable costs exceed marginal costs.
C)total fixed costs always decrease.
D)total fixed costs do not change as output increases.
Q2) The shape of a firm's long-run average cost curve is determined by
A)the degree to which each input encounters diminishing marginal productivity.
B)the underlying nature of the firm's production function when all inputs are able to be varied.
C)how much the firm decides to produce.
D)the way in which the firm's expansion path reacts to changes in the rental rate on capital.
Q3) The firm's expansion path records
A)profit-maximizing output choices for every possible price.
B)cost-minimizing input choices for all possible output levels for when input rental rates expand along with production.
C)cost-minimizing input choices for all possible output levels for a fixed set of input prices.
D)cost-minimizing input choices for profit-maximizing output levels.
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Page 10
Chapter 9: Profit Maximization
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32 Verified Questions
32 Flashcards
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Sample Questions
Q1) If a price-taking firm's production function is given by \(q = \sqrt { l }\) ,its profit function is given by
A) \(p / 2 w\) .
B) \(p ^ { 2 } / 2 w\) .
C) \(p / 2 w ^ { 2 }\) .
D) \(p ^ { 2 } / 4 w\) .
Q2) Suppose capital and labor must be used in fixed proportions to produce widgets and that the price elasticity of demand for widgets is zero.Then the wage elasticity of demand for labor by widget makers will be A)+1. B)-1.
C)0.
D)infinite.
Q3) A profit-maximizing firm will never hire that quantity of a factor of production for which that factor has an increasing marginal productivity because A)it would not be maximizing output.
B)it would not be maximizing the productivity of labor.
C)it would not be minimizing costs.
D)it would not be maximizing profits.
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Page 11
Chapter 10: The Partial Equilibrium Competitive Model
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31 Verified Questions
31 Flashcards
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Sample Questions
Q1) In the long run,the greater burden of a specific tax will usually be absorbed by A)consumers.
B)the party -- consumers or producers -- with the more elastic demand/supply curve.
C)the party with the least elastic demand/supply curve.
D)shareholders and employees of the firm in the form of reduced dividends and wages.
Q2) One way to minimize the excess burden resulting from a specific tax is to
A)tax only wealthy firms and individuals.
B)spread the tax over many goods and services.
C)tax goods for which either supply or demand is inelastic.
D)tax luxury items such as yachts and sports cars.
Q3) "Missing markets" result from
A)high costs of the establishment of such markets.
B)strict price controls.
C)the inability of producers to gain economies of scale.
D)foreign countries dominating a domestic market for a product.
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Chapter 11: General Equilibrium and Welfare
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Sample Questions
Q1) Consider three ways of allocating two goods in a two-person exchange economy.
I.Both individuals take prices as given and equilibrium prices are established by an impartial auctioneer.
II.One individual can act as a perfect price discriminator and force the other individual to pay a different price for each unit of a good that is traded.
III.One individual is a monopolist and can charge the other individual a single,utility-maximizing price.
Which of these situations is efficient?
A)None of them.
B)Only I.
C)I and II,but not III.
D)I and III,but not II.
E)All of them.
Q2) The "Classical Dichotomy" refers to
A)a distinction between "value in use" and "value in exchange."
B)separate theories of demand and supply.
C)the possibility of Giffen's Paradox
D)determination of relative prices independent of the nominal price level.
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Chapter 12: Monopoly
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Sample Questions
Q1) All of the following might explain a firm offering quantity discounts except:
A)lower costs of handling large orders.
B)an inelastic demand for the good.
C)monopoly power in this market.
D)adoption of a sales maximization strategy.
Q2) If the government requires a natural monopoly to price at marginal cost,
A)monopoly firms will earn zero economic profits because the price of the good equals the cost of producing that good.
B)monopoly firms will operate at a loss because P < AC.
C)more firms will be able to enter the market.
D)producer surplus will increase because quantity supplied is greater.
Q3) All monopolies exist because of
A)firms' desire to maximize profits.
B)failure of antitrust laws.
C)barriers to entry.
D)natural selection.
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14
Chapter 13: Imperfect Competition
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21 Flashcards
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Sample Questions
Q1) The subgame-perfect equilibrium of a two-stage game in which firms first choose capacities and then engage in a Bertrand price setting game resembles the equilibrium in
A)the competitive model.
B)the Cournot model.
C)the cartel model.
D)the price leadership model.
Q2) Product differentiation complicates the study of oligopolies because such markets may not
A)be efficient.
B)have prices equal to marginal cost.
C)have free entry and exit.
D)obey the law of one price.
Q3) A profit-maximizing firm should spend an additional dollar on advertising so long as this expenditure results in more than one dollar of:
A)additional sales.
B)reduced costs.
C)increased profits.
D)demand.
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Page 15
Chapter 14: Labor Markets
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Sample Questions
Q1) If an individual is maximizing his or her utility,his or her marginal rate of substitution of leisure hours for consumption will be
A)equal to one divided by his or her wage rate.
B)greater than one divided by his or her wage rate.
C)equal to his or her wage rate.
D)less than his or her wage rate.
Q2) A price discriminating monopsonist could increase its profits by
A)paying the minimum wages possible.
B)hiring as little capital as possible.
C)paying lower wages to workers with inelastic supply of labor curves than to workers with elastic curves.
D)paying lower wages to workers with elastic supply of labor curves than to workers with inelastic curves.
Q3) The opportunity cost of leisure is approximated by A)the price of leisure activities (such as theater tickets).
B)an individual's hourly real wage rate.
C)commuting expense.
D)an individual's total income.
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Chapter 15: Capital and Time
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17 Flashcards
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Sample Questions
Q1) In a perfectly competitive market a firm's rental rate for a machine (v)will be given by: v = p(r + d)where r is the prevailing rate of interest and d is the depreciation rate.In this formula p represents
A)the present market price of the machine.
B)the initial purchase price of the machine (assuming this differs from its present market price.
C)the price of the firm's product.
D)the depreciated value of the machine.
Q2) In Fisher's model of the determination of the rate of return,the price of a "future good" is
A)less than the price of a current good if the interest rate is negative.
B)equal to the price of a current good if the interest rate is positive.
C)greater than the price of a current good if the interest rate is positive.
D)less than the price of a current good if the interest rate is positive.
Q3) The present value of $1 payable in the future decreases
A)the higher r is and the sooner it is to be paid.
B)the lower r is and the sooner it is to be paid.
C)the higher r is and the longer time until it is paid.
D)the lower r is and the longer time until it is paid.
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Page 17
Chapter 16: Asymmetric Information
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Sample Questions
Q1) Which contracting party gains from the use of a more sophisticated contract?
A)The principal,who offers the contract.
B)The agent,who accepts the contract.
C)Both parties may lose.
D)Both parties gain equally.
Q2) What tradeoffs are present in the moral-hazard-in-insurance problem?
A)Full insurance benefits the risk-averse customer but gives him excessive incentives to take care to avoid harm.
B)Full insurance benefits the risk-averse customer but provides him with no incentive to take care to avoid harm.
C)Full insurance benefits the risk-averse consumers but does not allow the insurer to extract as much surplus from all types.
D)Full insurance is beneficial for all consumers,but if sold at an actuarially fair price for the population will draw only the riskiest types.
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Chapter 17: Externalities and Public Goods
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Sample Questions
Q1) In probabilistic voting models, may result in social welfare maximizing decisions.(Which phrase best completes the sentence?)
A)logrolling.
B)bribes.
C)point voting.
D)competition among candidates.
Q2) Some economists have hypothesized that government bureaucracies seek to maximize
A)social well being.
B)gross national product.
C)fringe benefits for bureaucrats.
D)their own budgets.
Q3) Efficient production of a public good requires
A)that individuals pay for such goods according to benefits received.
B)that each individual's MRS be equal to the RPT of public goods for private goods.
C)that the sum of individuals' MRSs be equal to the RPT of public goods for private goods.
D)that governments produce at the low point of the average cost curve for the public good.
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