Mathematical Economics Exam
Bank
Course Introduction
Mathematical Economics focuses on the application of mathematical methods to represent economic theories, analyze economic problems, and solve decision-making issues in economics. The course covers fundamental mathematical concepts including calculus, linear algebra, and optimization, emphasizing their use in modeling consumer behavior, production processes, market equilibrium, and other economic phenomena. Students will learn how to formulate and solve problems analytically, interpret mathematical results within an economic context, and utilize these tools to gain deeper insights into both microeconomic and macroeconomic issues. Mathematical Economics is designed to enhance students quantitative reasoning and prepare them for advanced studies or professional careers that require rigorous economic analysis.
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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Sample Questions
Q1) 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
Q2) 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
Q3) If utility is given by \(U ( x , y ) = \sqrt { x y }\) ,then the person's MRS at the point x = 5,y = 2 is given by A)0.4.
B)1.0.
C)2.5.
D)5.0.
Answer: A
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Chapter 2: Utility Maximization and Choice
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Sample Questions
Q1) 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.
Q2) 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>.
Q3) 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.
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4
Chapter 3: Income and Substitution Effects
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Sample Questions
Q1) If the demand for a product is elastic,then a rise in price will
A)cause total spending on the good to increase.
B)cause total spending on the good to decrease.
C)keep total spending the same,but reduce the quantity demanded.
D)keep total spending the same,but increase the quantity demanded
Q2) Assume x and y are the only two goods a person consumes.If after a rise in p<sub>x</sub> the quantity demanded of y increases,one could say
A)the income effect dominates the substitution effect.
B)the substitution effect dominates the income effect.
C)it is still impossible to determine whether the substitution or income effect dominates.
D)none of these answers is correct.
Q3) An individual's demand curve
A)represents the various quantities that a consumer is willing to purchase of a good at various price levels.
B)is derived from an individual's indifference curve map.
C)will shift if preferences,prices of other goods,or income change.
D)all of these answers are correct.
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Chapter 4: Demand Relationships Among Goods
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Sample Questions
Q1) In the Slutsky equation for \(\partial x _ { i } / \partial p _ { j }\) ,the income effect is given by
A)\(x _ { i } \partial x _ { i } / \partial I\) .
B)\(x _ { j } \partial x _ { i } / \partial I\) .
C)\(x _ { i } \partial x _ { j } / \partial I\) .
D)\(x _ { j } \partial x _ { j } / \partial I\) .
Q2) If the demand for x is given by \(x = k p _ { x } ^ { - 1.2 } p _ { y } ^ { 0.5 } I ^ { 0.7 }\) ,which of parameter values hold?
A)\(e _ { x , p _ { x } } = 1.2 e _ { x , I } = .7 e _ { y , p _ { x } } = .5\) .
B)\(e _ { x , p _ { x } } = - 1.2 e _ { x , p _ { y } } = .5 e _ { x , 1 } = .7\) .
C)\(e _ { x , p _ { k } } = - 1.2 \quad e _ { y , p _ { y } } = .7 \quad e _ { x , I } = .5\) .
D)None of these relations hold since the demand function is not homogeneous of degree zero in \(p _ { x } , p _ { y } , \text { and I. }\)
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Chapter 5: Uncertainty and Information
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Sample Questions
Q1) 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) \(E \left[ U ^ { \prime } ( 1 + r ) \right] = 0\) .
Q2) The option to delay the choice of portfolio allocation is valuable because
A)interest costs are positive.
B)volatility of returns is lower.
C)more can be placed into high return,risky assets.
D)the allocation can be based on new information.
Q3) A risk averse individual is offered a gamble that promises a gain of $1000 with probability 0 .25 and a loss of $300 with probability 0.75 .Given this situation,he or she will
A)definitely take the gamble.
B)definitely not take the gamble.
C)definitely take the gamble if his or her income is high enough.
D)take an action that cannot be determined given the information available.
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Chapter 6: Strategy and Game Theory
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Sample Questions
Q1) Cheap talk
A)has no bearing on games; only "real" actions matter.
B)can transmit information in certain equilibria,but only if players' interests are sufficiently distinct.
C)can transmit information in certain equilibria,but only if players' incentives are sufficiently aligned.
D)always leads to the best equilibrium for the "talker".
Q2) A game of incomplete information is distinct from one of complete information in that players
A)do not observe each others' actions.
B)do not know each others' payoff functions.
C)do not know the timing of moves.
D)use mixed strategies.
Q3) Nash equilibria
A)always exist in pure strategies.
B)generally come in even numbers.
C)always exist in finite games.
D)All of these answers are correct.
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8
Chapter 7: Production Functions
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Sample Questions
Q1) A firm's isoquant shows
A)the amount of labor needed to produce a given level of output with capital held constant.
B)the amount of capital needed to produce a given level of output with labor held constant.
C)the various combinations of capital and labor that will produce a given amount of output.
D)none of these answers is correct.
Q2) Suppose the production function for good q is given by \(q = 3 k + 2 l\) where k and l are capital and labor inputs.Consider three statements about this function:
I.The function exhibits constant returns to scale.
II.The function exhibits diminishing marginal productivities to all inputs.
III.The function has a constant rate of technical substitution. Which of these statements is true?
A)All of them.
B)None of them.
C)I and II but not III.
D)I and III but not II.
E)only I.
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9
Chapter 8: Cost Functions
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Sample Questions
Q1) The input demand functions that can be derived from cost functions are referred to as "contingent" demand functions because the functions:
A)assume input costs are constant.
B)express input demand as a function of output.
C)depend on the assumption of profit maximization.
D)assume constant returns to scale in production.
Q2) Technical progress will
A)shift a firm's production function and its related cost curves.
B)not affect the production function,but may shift cost curves.
C)shift a firm's production function and alter its marginal revenue curve.
D)shift a firm's production function and cause more capital (and less labor)to be hired.
Q3) For a constant returns to scale production function
A)marginal costs are constant but the average cost curve has a U-shape.
B)both average and marginal costs are constant.
C)marginal cost has a U-shape; average costs are constant.
D)both average and marginal cost curves are U-shaped.
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Chapter 9: Profit Maximization
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Sample Questions
Q1) The substitution effect of a change in wage rate on a firm's demand for labor input will be more significant
A)the greater the change in output.
B)the more sharply curved are the firm's isoquants.
C)the flatter are the firm's isoquants.
D)the larger the quantity of labor employed.
Q2) The size of the reduction in quantity of labor hired by a firm due to an increase in the wage rate depends upon all of the following except
A)what percentage of total costs are made up of labor costs.
B)how much quantity demanded in the output market will be reduced by a higher price.
C)the capital to labor ratio before the wage increase.
D)how easily other inputs can be substituted for labor.
Q3) Profit functions are homogeneous of degree
A)zero in input and output prices
B)zero in input prices.
C)one in input and output prices.
D)one in input prices.
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11
Chapter 10: The Partial Equilibrium Competitive Model
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Sample Questions
Q1) For an increasing cost industry,the long-run supply curve has a(n)_____________ elasticity of supply
A)infinite.
B)negative.
C)positive.
D)zero.
Q2) "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.
Q3) Long-run producer surplus in a perfectly competitive industry accrues mainly to
A)suppliers of inputs with inelastic supply curves.
B)suppliers of inputs with elastic supply curves.
C)firms' owners.
D)marginal consumers.
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Chapter 11: General Equilibrium and Welfare
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Sample Questions
Q1) In order to assure allocative efficiency,
A)people's marginal rate of substitution must equal the economy's rate of product transformation.
B)people's marginal rate of substitution must equal the firm's rate of technical substitution among inputs.
C)a firm's rate of technical substitution must equal the economy's rate of product transformation.
D)all of the other answers are correct.
Q2) The slope of the production possibility frontier shows
A)the marginal rate of substitution between the two goods.
B)the relative marginal costs of the two goods.
C)the efficient combination of outputs possible using fixed amounts of input.
D)the relative marginal productivities of the two goods.
Q3) The reason externalities distort the allocation of resources is that A)too few goods are usually produced.
B)firms often go out of business because of the externality.
C)a firm's private costs do not reflect the social cost of production.
D)regulating externalities uses scarce resources.
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Chapter 12: Monopoly
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Sample Questions
Q1) A monopoly's economic profits are represented by
A)(price minus marginal cost)times number of units sold.
B)(price minus average cost)times number of units sold.
C)(marginal revenue minus price)times number of units sold.
D)(marginal cost minus price)times number of units sold.
Q2) All monopolies exist because of
A)firms' desire to maximize profits.
B)failure of antitrust laws.
C)barriers to entry.
D)natural selection.
Q3) In the real world,a monopolist's costs will often be
A)lower than for a firm in a competitive industry.
B)equal to the costs of a firm in a competitive industry.
C)higher than for a firm in a competitive industry.
D)almost zero.
Q4) Relative to single price policy third degree price discrimination
A)always reduces welfare.
B)always increases welfare.
C)may increase welfare if total output falls.
D)may increase welfare if total output rises.
Page 14
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Chapter 13: Imperfect Competition
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Sample Questions
Q1) Suppose n identical firms engage in Bertrand competition in a stage game repeated infinitely often.What condition on the discount factor \(\delta\) is required for firms to be able to tacitly collude on the monopoly industry output?
A) \(\delta \geq 1 / 2\) .
B) \(\delta \leq 1 / n\) .
C) \(\delta \geq 1 / n ^ { 2 }\) .
D) \(\delta \geq 1 - ( 1 / n )\) .
Q2) 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.
Q3) In the Hotelling model of spatial competition,profits arise from
A)monopoly power.
B)rents based on locational advantage.
C)the ability to price discriminate.
D)increasing returns to scale.
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Page 15
Chapter 14: Labor Markets
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Sample Questions
Q1) For a monopsonistic hirer of labor the gap between labor's marginal revenue product and its wage rate will be greater
A)the more elastic the supply curve for labor.
B)the more inelastic the supply curve for labor.
C)the more elastic the firm's demand for labor.
D)the more inelastic the firm's demand for labor.
Q2) "Compensating wage differentials" arise because
A)workers possess different skills.
B)workers prefer some jobs to others.
C)firms pay higher wages for workers with higher marginal productivities.
D)firms discriminate in hiring.
Q3) 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.
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Chapter 15: Capital and Time
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Sample Questions
Q1) The annual rental rate for a machine is
A)the yearly depreciation and maintenance costs for the machine.
B)the yearly interest costs associated with owning the machine.
C)the initial purchase price of the machine divided by the number of years the machine is expected to last.
D)the sum of the yearly depreciation,maintenance,and interest costs associated with owning the machine.
Q2) An increase in the corporate profits tax will most likely lead to
A)a decrease in the rental rate of capital in the corporate sector.
B)no change in the rental rate of capital in the corporate sector.
C)no change in the rental rate of capital in the non-corporate sector.
D)an increase in the rental rate of capital in the corporate sector.
Q3) A fall in interest rates leads to
A)an increase in the rental rate on a machine.
B)a decrease in the rental rate on a machine.
C)no change in the rental rate on a machine.
D)a fall in the marginal productivity of capital.
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Page 17
Chapter 16: Asymmetric Information
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Sample Questions
Q1) Which of the following illustrates adverse selection?
A)Individuals sometimes mistakenly buy defective cameras.
B)Individuals will not search for bargains for low cost items.
C)Individuals know a lot about their family health history when they buy insurance.
D)Individuals can choose whether to drive safely or not.
Q2) Let \(s ( \pi ) = a + b \pi\) be the manager's salary in an owner-manager version of the principal-agent problem.Which of the following is characteristic of a "powerful" incentive scheme?
A)a close to 0.
B)a close to 1.
C)b close to 0.
D)b close to 1.
Q3) Suppose that you were again competing in a sealed-bid auction for the Vermeer painting which you value at $100,000,but now it is a first-price auction.What bid should you submit?
A)Exactly $100,000.
B)Somewhat lower than $100,000 depending on the number of other bidders.
C)Somewhat higher than $100,000 depending on the number of other bidders.
D)Cannot say which of a),b),or c)is right without further information.
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Page 18
Chapter 17: Externalities and Public Goods
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Sample Questions
Q1) de Condorcet's Paradox occurs when
A)majority rule voting cycles among alternatives.
B)majority rule voting results in decisions that are not Pareto optimal.
C)point voting yields indeterminate results.
D)point voting results in decisions that are not Pareto optimal.
Q2) 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.
Q3) The "free-rider problem" of public goods refers to
A)individuals' refusal to pay taxes.
B)individuals' attempts to hide their preferences for collective goods and to avoid paying for them.
C)individuals' over?use of collective goods.
D)the inelasticity of individuals' demands for public goods.
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