Mathematical Economics
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Course Introduction
Mathematical Economics is a course that explores the application of mathematical methods to represent, analyze, and solve economic problems. It introduces students to key mathematical tools such as calculus, linear algebra, and optimization techniques, which are essential for modeling economic theories and analyzing quantitative relationships. The course covers topics such as comparative statics, constrained optimization, game theory, and economic dynamics, equipping students with the skills to rigorously approach complex economic phenomena. Through a blend of theoretical instruction and practical problem-solving, students develop the analytical foundation necessary for advanced study and research in economics.
Recommended Textbook
Microeconomic Theory Basic Principles and Extensions 10th Edition by Walter Nicholson
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334 Verified Questions
334 Flashcards
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Chapter 1: Preferences and Utility
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Sample Questions
Q1) 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
Q2) For this utility function,the MRS
A)depends on the values of x and y.
B)is always 0.
C)is always 2.
D)is always 4.
Answer: C
Q3) If an individual's utility function is quasi-concave,his or her MRS will
A)diminish as x is substituted for y.
B)increase as x is substituted for y.
C)be undefined except in special cases.
D)always depend only on the ratio of x to y.
Answer: A
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Chapter 2: Utility Maximization and Choice
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Sample Questions
Q1) If the price of x falls,the budget constraint
A)shifts outward in a parallel fashion.
B)shifts inward in a parallel fashion.
C)rotates outward about the x?intercept.
D)rotates outward about the y?intercept.
Q2) Suppose that at current consumption levels an individual's marginal utility of consuming an extra hot dog is 10 whereas the marginal utility of consuming an extra soft drink is 2.Then the MRS (of soft drinks for hot dogs)-- that is,the number of hot dogs the individual is willing to give up to get one more soft drink-is A)5.
B)2.
C)1/2.
D)1/5.
Q3) If an individual's utility function for coffee (x)and cream (y)is given by U(x,y)= min (x,5y),the demand function for coffee is given by
A)X = I/2p<sub>x</sub> .
B)X = I/(p<sub>x</sub> + p<sub>y</sub>).
C)X = I/(p<sub>x</sub> + 0.2p<sub>y</sub>).
D)X = I/(p<sub>x</sub> + p<sub>y</sub>)<sup>2</sup>.
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Page 4
Chapter 3: Income and Substitution Effects
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Sample Questions
Q1) If the prices of all goods increase by the same proportion as income,the quantity demanded of good x will A)decrease.
B)increase.
C)remain unchanged.
D)change in a way that cannot be determined from the information given.
Q2) The price elasticity of demand for a vertical demand curve is A)0.
B)1
C)1. D)infinity.
Q3) The price elasticity of demand for a horizontal demand curve is A)0. B)-1.
C)1. D)-infinity.
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Chapter 4: Demand Relationships Among Goods
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Sample Questions
Q1) "Hicks' Second Law of Demand" states that "most" goods must be
A)gross substitutes.
B)gross complements.
C)net substitutes.
D)net complements.
Q2) If utility is separable in a three-good utility function \(\left[ U \left( x _ { 1 } , x _ { 2 } , x _ { 3 } \right) = U _ { 1 } \left( x _ { 1 } \right) + U _ { 2 } \left( x _ { 2 } \right) + U _ { 3 } \left( x _ { 3 } \right) , U _ { i } ^ { \prime } > 0 \quad U _ { i } ^ { \prime } < 0 \right]\) then for changes in \(p _ { 1 } , x _ { 2 } \text { and } x _ { 3 } \text { must }\)
A)both be gross substitutes for x<sub>1</sub> .
B)both be gross complements for x<sub>1</sub> .
C)be such that if one is a gross substitute for x<sub>1</sub> ,the other is a gross complement for x<sub>1</sub> .
D)both be gross substitutes or both be gross complements for x.
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Chapter 5: Uncertainty and Information
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Sample Questions
Q1) 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.
Q2) The condition for optimal portfolio choice can be represented by:
A) \(E \left[ U ^ { \prime } / \left( 1 + r _ { f } \right) \right] = 0\) .
B) \(E \left[ U ^ { \prime } \left( r - r _ { f } \right) \right] = 0\) .
C) \(E \left[ U ^ { \prime } r / \left( 1 + r _ { f } \right) \right] = 0\) .
D) \(E \left[ U ^ { \prime } ( 1 + r ) \right] = 0\) .
Q3) Suppose a person's utility of wealth is given by \(U ( W ) = \sqrt { W }\) and his or her initial wealth is 10,000.What is the maximum amount he or she would pay for insurance against a 50 percent chance of losing 3,600?
A)1,800.
B)1,900.
C)2,000.
D)2,100.
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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 difference between a Nash equilibrium and a subgame-perfect equilibrium is A)the former requires rational play both on and off the equilibrium path but the latter requires rational play only on the equilibrium path.
B)the former requires rational play only on the equilibrium path but the latter requires rational play both on and off the equilibrium path.
C)Nash equilibria are a subset of the subgame-perfect equilibria.
D)nothing; they are synonyms.
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Chapter 7: Production Functions
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Sample Questions
Q1) The <u>average</u> productivity of labor reaches its maximum
A)at the point of inflection of the total product curve.
B)where the slope of the total product curve is steepest.
C)where the slope of the total product curve is zero.
D)where marginal and average productivity are equal.
Q2) If more and more labor is employed while keeping all other inputs constant,the marginal physical productivity of labor will eventually A)increase.
B)decrease.
C)remain constant.
D)We cannot tell from the information provided.
Q3) The marginal physical productivity of labor is
A)the slope of the total output curve at the relevant point.
B)the negative of the slope of the total output curve at the relevant point.
C)the slope of the line connecting the origin with the relevant point on the total output curve.
D)the negative of the slope of the line connecting the origin with the relevant point on the total output curve.
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Chapter 8: Cost Functions
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Sample Questions
Q1) 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.
Q2) An increase in the wage rate will have a greater effect on average costs
A)the larger the proportion labor costs are of total costs and the easier it is to substitute capital for labor.
B)the larger the proportion labor costs are of total costs and the harder it is to substitute capital for labor.
C)the greater is the diminishing marginal product of labor.
D)the greater are returns to scale.
Q3) A linear total cost curve which passes through the origin implies that
A)average cost is constant and marginal cost is variable.
B)average cost is variable and marginal cost is constant.
C)average and marginal costs are constant and equal.
D)We need more information to answer question.
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Page 10
Chapter 9: Profit Maximization
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Sample Questions
Q1) If the demand faced by a firm is inelastic,selling one more unit of output will
A)increase revenues.
B)decrease revenues.
C)keep revenues constant.
D)increase profits.
Q2) If the demand faced by a firm is elastic,selling one less unit of output will
A)increase revenue.
B)decrease revenue.
C)keep revenues constant.
D)decrease price.
Q3) If a firm's marginal revenue is below its marginal cost,an increase in production will usually
A)increase profits.
B)leave profits unchanged.
C)decrease profits.
D)increase marginal revenue.
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Chapter 10: The Partial Equilibrium Competitive Model
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Sample Questions
Q1) 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.
Q2) A change in the distribution of income that leaves total income constant will not shift the market demand curve for a product providing
A)everyone has an income elasticity of demand of zero for the product.
B)everyone has the same income elasticity of demand for the product.
C)individuals have differing income elasticities for the product,but the average income elasticity for income gainers is equal to the average income elasticity for income losers.
D)any of these conditions occur.
Q3) Price controls
A)are always popular with consumers because they lower prices.
B)create shortages.
C)increase producer surplus because firms can now sell a greater quantity of a good at a lower price.
D)are necessary to preserve equity.
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Chapter 11: General Equilibrium and Welfare
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Sample Questions
Q1) 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.
Q2) A market characterized by imperfect information will have an equilibrium price if at that price
A)quantity demanded equals quantity supplied when all participants have the same information.
B)quantity demanded equals quantity supplied given prevailing information levels.
C)quantity demanded equals quantity supplied under perfect information.
D)quantity demanded exceeds quantity supplied if suppliers are better informed (and vice-versa).
Q3) If markets are perfect,a rational actor may reasonably conclude from the high price of a good that the good
A)is produced by a monopoly.
B)is of better quality.
C)has a greater demand for it.
D)is not known about by other consumers.
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Page 13
Chapter 12: Monopoly
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Sample Questions
Q1) The supply curve for a monopoly is given by
A)the firm's marginal cost curve above the average variable cost curve.
B)the one point on the demand curve that corresponds to the quantity for which price is equal to MC.
C)the one point on the demand curve that corresponds to the quantity for which MR equals MC.
D)the entire demand curve above the point where price is equal to average cost.
Q2) 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.
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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Chapter 13: Imperfect Competition
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Sample Questions
Q1) 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.
Q2) In a Cournot equilibrium each firm chooses an output level which
A)maximizes joint profits.
B)maximizes the price received.
C)maximizes profits given what the other firms produce.
D)maximizes revenue given what the other firms produce.
Q3) 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.
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15
Chapter 14: Labor Markets
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Sample Questions
Q1) 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.
Q2) If an individual's supply of labor curve is positively sloped throughout,then
A)the substitution effect always dominates the income effect.
B)the income effect always dominates the substitution effect.
C)the substitution effect dominates at low real wage levels and the income effect dominates at high real wage levels.
D)the income effect dominates at low real wage levels and the substitution effect dominates at high real wage levels.
Q3) When an individual's wage rises,the income effect tends to
A)increase hours worked.
B)decrease hours worked.
C)leave hours worked unchanged.
D)it is impossible to predict what will happen to hours worked.
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Chapter 15: Capital and Time
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Sample Questions
Q1) If the interest rate rises,the present discounted value of a stream of payments owed in the future
A)rises.
B)stays constant.
C)falls.
D)may rise or fall depending on the shape of the stream.
Q2) Adding uncertainty to future consumption will tend to increase savings providing:
A) \(U ^ { \prime \prime } > 0\) .
B) \(U ^ { \prime \prime } / U ^ { t } > 0\) .
C) \(U ^ { \prime \prime } / U ^ { t } < 0\) .
D) \(U ^ { \prime\prime\prime} > 0\) .
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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17
Chapter 16: Asymmetric Information
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Sample Questions
Q1) Which statement is true if the monopolist can observe the consumer's type in the nonlinear-pricing application?
A)The monopolist supplies the consumer with as much of the good as if it were competitively priced.
B)The monopolist's profit approaches the upper bound from the simple linear pricing problem.
C)The monopolist extracts all of the surplus from the low type but not the high type.
D)The monopolist extracts all of the surplus from the high type but not the low type.
Q2) Which of the following is not a straightforward example of a (principal \(\rightarrow\) agent)relationship?
A)Homeowner \(\rightarrow\) real estate agent.
B)Shareholder \(\rightarrow\) manager.
C)Manager \(\rightarrow\) line employee.
D)Doctor \(\rightarrow\) patient.
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Chapter 17: Externalities and Public Goods
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Sample Questions
Q1) Each of the following provides incentives to reduce a negative externality except
A)merger with affected firms.
B)subsidizing consumption of the good being produced.
C)bargaining among firms.
D)taxation of the externality.
Q2) Special interest groups often
A)represent broad questions of public interest.
B)pursue rent seeking behavior.
C)do not use lobbying techniques.
D)have no effect on the political process.
Q3) To reach an economically efficient output level,the size of an excise tax imposed on a firm generating a negative externality should be
A)the firm's marginal cost.
B)the social marginal cost.
C)the difference between the social marginal cost and the firm's marginal cost.
D)the sum of the social marginal cost and the firm's marginal cost.
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