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MICROECONOMICS I
PROGRAM AND SET OF PROBLEMS
Universitat de València
Year 2004-05
PROGRAM
MICROECONOMICS I (12146)
This course concentrates on microeconomic theory at an intermediate level. Students should have completed a course on introductory economics. The program includes topics that cover half the material normally treated in micro courses. The other half is included in Microeconomics II. Roughly, the program covers consumer theory and extensions, and an introduction to welfare and general equilibrium economics.
The main text used in the course will be:
Intermediate Microeconomics. A Modern Approach. By Hal R. Varian. Fourth Edition. Norton International Student Edition. New York, 1996. A Spanish translation exists under the title Microeconomía Intermedia (Second Edition). Editorial A. Bosch. Barcelona.
Other texts which cover the same material are:
Microeconomics and Behavior. By Robert A. Frank. Third Edition. Mc Graw-Hill. New York, 1997
Microeconomics. By Michael L. Katz and Harvey S. Rosen. Mc Graw-Hill. New York, 1998
The reference to chapters given below each lesson, corresponds to Varian’s book.
LESSION 1: BASIC IDEAS
The concept of a model
Optimization and equilibrium
Demand, Supply and Market Equilibrium
Practical applications
Chapter: 1
LESSION 2: CONSUMER THEORY (I): BUDGET CONSTRAINT
The budget constraint
Changes in the budget constraint
Taxes, subsidies and rationing
Examples
Chapter: 2
LESSON 3: CONSUMER THEORY (II): PREFERENCES
Consumer preferences
Indifference curves
Examples of preferences
The Marginal Rate of Substitution
Chapter: 3
LESSON 4: CONSUMER THEORY (III): UTILITY
Cardinal utility
Constructing a utility function
Examples of utility functions
Marginal utility and the Marginal Rate of Substitution
Chapter: 4
LESSON 5: CONSUMER THEORY (IV): CONSUMER EQUILIBRIUM
Optimal choice
The Substitution effect
The Income effect
Consumer demand
Perfect Substitutes and Perfect Complements
Implications of the Marginal Rate of Substitution conditions
Chapters: 4, 6 and 8
LESSON 6: EXTENSIONS AND APPLICATIONS OF CONSUMER THEORY
The approach of revealed preference
Budget constraints with fixed and changing endowments
The application of consumer theory to labour supply
Budget constraints and preferences over time
Choice and the interest rate
Chapters: 7, 9 and 10
LESSON 7: CONSUMER’S SURPLUS
The concept of consumer’s surplus
Interpretation of changes in consumer surplus
Compensating and Equivalent Variations
Calculating Gains and Losses
Chapter: 14
LESSON 8: MARKET DEMAND
From individual to market demand
The inverse demand function
The concept of elasticity
Elasticity and marginal revenue
Income elasticity
Chapter: 15
LESSON 9: MARKET EQUILIBRIUM
Market equilibrium
Comparative statistics
Taxes. The deadweight loss of taxation
Pareto efficiency
Chapter: 16
LESSON 10: EXCHANGE
The Edgeworth Box
Pareto efficient allocations
Equilibrium and efficiency
The two welfare theorems
Chapter: 28
LESSON 11: WELFARE
Aggregation of preferences
Social welfare functions
Welfare maximization
Chapter: 30
LESSON 12: MARKET FAILURES
Externalities. The Coase theorem
Public Goods. Public and private provision of public goods
Asymmetric information
Chapters: 31, 34 and 35
MICROECONOMICS I
Problems
Lesson 1: Basic Ideas
- Say whether you agree or disagree with the following statements and explain why:
a)The economic character of a problem appears only when the three following elements -diversity of objectives, transferability of resources and scarcity of resources- are present at the same time.
b)The Robbins’ definition of economics -“the study of the allocation of scarce means to satisfy competing ends”- incorporates the three elements mentioned in question a) above.
c)The model of supply and demand is a way of simplifying the world. It is a classification scheme, by means of which we decide which variables matter in demand, supply of both.
d)The “ceteris paribus” clause is just an indication of the variables that are held constant in the particular analysis of a problem.
e)In the normal terminology used by economists, a “change in the quantity demanded” means the same as a “change in the demand curve”.
2.Suppose that the market for butter and margarine can be represented by the following implicit functions
Butter Margarine
Supply
Demand
a)What other relevant variables could be considered in each of these four functions?
b)How would you represent in each of these two markets the respective conditions of equilibrium?
c)If you had to represent graphically the market for butter, what variables would you include in the “ceteris paribus” clause? Why?
d)If you had to represent graphically the market for margarine, what variables would you include in the “ceteris paribus” clause? Why?
e)Represent graphically these two markets. (Put prices in the vertical axis and quantities in the horizontal axis).
f)Show the direction of the effect of each of the variables on the corresponding dependent variable by means of a plus (+) or minus (-) sign below the variable in question. Suppose, in carrying out this exercise, that butter and margarine are substitute goods.
g)Suppose that because of a change in technology, the production of margarine becomes significantly cheaper. What effect will this event have on the price and quantity of margarine? Will the market for butter be affected?
h)Suppose that because of the entry of a group of vegetarian tourists during the summer there is an increase in the demand for margarine. What effect will this event have on the markets of margarine and butter?
3.Suppose you are given by an econometrician the explicit parameters that define the functions considered in the previous exercise.
a)Represent graphically the two markets. (Put prices in the vertical axis and quantities in the horizontal axis).
b)Find out the equilibrium price and quantity of both butter and margarine.
c)Suppose that because of an adverse change in technology, the supply function of margarine becomes . All other functions remain the same. How will this event affect the equilibrium of both markets?
d)Return to the original specification. Suppose now that because of a change in tastes, the demand function for butter becomes . All other functions remain the same. How will this event affect the equilibrium of both markets?
Lesson 2: Budget constraint
1.Say whether you agree or disagree with the following statements and explain why:
a)The budget constraint permits to identify those bundles of goods which are affordable by a given consumer from those bundles which are not affordable.
b)The budget line is the set of bundles goods which are affordable by the consumer.
c)If the prices of goods increase by the same proportion as income, the budget constraint remains unchanged.
d)If, other things equal, the prices of goods double, the slope of the budget line will also double.
e)If the price of one good doubles and income also doubles, the slope of the budget line will remain the same.
f)If the consumer’s income increases with no change in relative prices, the budget line will move parallel to itself.
g)If the consumer’s income increases by 10% and the prices of goods x and y both increase by 10%, the consumer will buy 10% more of each of the two goods. (Exam, July 04)
2.You have an income of € 40 to spend on two commodities. Commodity x costs € 10 per unit and commodity y costs € 5 per unit.
a)Write down your budget equation and represent it graphically. (Put commodity x on the horizontal axis and commodity y on the vertical axis). Call this budget A.
b)Suppose that the price of commodity x falls to € 5 while everything else stays the same. Write down and represent graphically your new budget equations. Call this budget B.
c)Suppose the amount you are allowed to spend falls to € 30, while the price of both commodities remain at € 5. Write down your budget equation and represent it graphically. Call this budget C.
d)Which of the three budgets gives the consumer the largest set of consumption opportunities?
e)Compare budgets A and C. At which bundle of commodities do they cross? Shade the area representing commodity bundles affordable with budget C but not affordable with budget A. Shade the area of commodity bundles affordable with budget A but not affordable with budget C.
3.Your budget is such that if you spent your entire income, you could afford either 4 units of x and 6 units of y or 12 units of x and 2 units of y.
a)Draw this budget line.
b)What is the ratio of the price of x to the price of y?
c)If you spent all your income on x, how many units of x could you buy?
d)If you spent all your income on y, how many units of y could you buy?
e)You are told that the price of x is € 1. Write down the budget equation that gives you the budget line of this problem.
f)You are told that the price of x is € 3. Write down the budget equation that gives you the same budget line.
4.Rosa was consuming 100 units of x and 50 units of y. The price of x rose from € 2 to € 3. How much would Rosa’s income have to rise so that she can still exactly afford 100 units of x and 50 units of y?
5.If Pepe spent his entire allowance, he could afford 8 units of x and 8 units of y a week. He could also afford 10 units of x and 4 units of y a week. The price of x is € 0.50. What is the price of y and Pepe’s weekly allowance?
- Marta is preparing for the only two exams left to finish her degree in economics: Microeconomics and Econometrics. She has time to read 40 pages of Microeconomics and 30 pages of Econometrics. In the same amount of time she could also read 30 pages of Microeconomics and 60 pages of Econometrics.
a)Assuming that the number of pages per hour that she can read of either subject does not depend on how she allocates her time, how many pages of Econometrics could she read if she decided to spend all her time on this subject and none on Microeconomics?
b)How many pages of Microeconomics could she read if she decided to spend all her time reading Microeconomics?
7.A consumer’s weekly income is € 200, and the prices of commodities x1 and x2 are respectively p1 = € 4 and p2 = € 2. Additionally, a law prohibits people to buy more than 30 units of x1 per week. What is the budget set of this consumer? What is the equation of his budget line?
8.The government wants to promote the consumption of x and penalize the consumption of y. To this end, it passes a law according to which consumers, to obtain goods, in addition to the payment of the corresponding nominal prices of each good in money (), will have to pay a coupon price for each good (). A consumer has a nominal weekly income of € 200 () and the government gives him 200 non transferable coupons every week.
a)Draw the budget constraint of this consumer and derive the equation of the budget line.
b)Suppose that at the equilibrium position, the consumer buys 40 units of x and 20 units of y. What will the new equilibrium be if the number of weekly coupons that the government gives him rises to 400? (Suppose the weekly income of the consumer remains the same at ).
c)Return to the original situation, with and 200 coupons, and suppose that the equilibrium position is units of x and units of y ( = 33.333...). Suppose now that the nominal weakly income of the consumer rises to , while the government maintains unchanged at 200 the number of weekly coupons. As a result of this increase in income, the consumption of x goes up to and the consumption of y goes down to . This shows that y is an inferior good for this consumer. Do you agree? Explain.
(Exam, January 03)
9.A consumer spends all his weekly income of € 200 (m = 200) in two goods x and y. While y can be bought at a constant price, x is sold under a discount system if the purchase is high. Specifically, the price of y is € 2 (py = 2); and the price of x is 4 (px = 4) for the first 10 units of x and 2 (px = 2) for units in excess of 10. Draw the budget set of this consumer and derive the budget equation.
10.A consumer spends all his weekly income of € 200 (m = 200) in two goods x and y, the prices of which are respectively € 2 and € 4 (px = 4 and py = 2).
a)Draw the budget set and derive the budget equation.
b)How is the budget set modified if the consumer receives a weekly subsidy of € 50 which is non-transferable and can only be spent in good x.
c)Return to the initial budget. How is it modified if the government imposes a tax of € 1 per unit of commodity y bought?
Lesson 3: Preferences
1.Say whether you agree or disagree with the following statements and explain why:
a)The set of bundles weakly preferred is convex if a line segment connecting any two points in that set, lies entirely in the set.
b)Convex preferences is just one way of saying that people prefer a bundle that mixes commodities to a bundle that concentrates on one commodity.
c)The assumption of convexity is reasonable because people, when consuming, do not specialize in only one good.
d)A computer “hacker” is offered a choice between 10 floppy disks and 5 software manuals, or 9 floppy disks and 20 software manuals. If this individual’s preferences satisfy the usual assumptions, we can safety predict that he will choose the second option.
e)Perfect complements are goods that have to be consumed in fixed proportions.
f)The downward slope of indifference curves is a consequence of the diminishing marginal rate of substitution.
2.Carlos likes both apples xa and bananas xb. In fact, he consumes nothing else. We know he is indifferent between the bundle formed by 20 apples and 5 bananas (20, 5) and any other bundle such that xaxb = 100. We also know that if we place him in the bundle (10, 15), he will show that he is indifferent between this bundle and any other such that xaxb = 150.
a)Graph the indifference curve that passes through point (20, 5), and the indifference curve that passes through point (10, 15).
b)Say whether the following four statements are correct or incorrect:
~
c)Is the set of bundles that Carlos weakly prefers to (20, 5) a convex set?
d)Is the set of bundles that Carlos considers inferior to (20, 5) a convex set?
e)Find Carlos’ marginal rate of substitution around the bundle (10, 10).
f)Find Carlos’ marginal rate of substitution around the bundle (5, 20) and around the bundle (20, 5). Do Carlos’s preferences exhibit diminishing marginal rate of substitution? What is the meaning of this result?
3.For Alex, coffee and tea are substitutes, but not perfect substitutes. Likewise, he regards butter and toast as complements, but not perfect complements.
a)Draw Alex’s indifference curves between coffee and tea.
b)Draw Alex’s indifference curves between butter and toast.
c)With the information given, is it possible to identify any significant difference between the two set of curves in a) and b)?
4.Eva likes apples but hates pears. If apples and pears are the only two goods available, draw her indifference curves.
5.Juan likes food but dislikes cigarette smoke. The more food he has, the more food he would be willing to give up to achieve a given reduction in cigarette smoke. If food and cigarette smoke are the only two goods, draw Juan’s indifference curves.
Lesson 4: Utility
1.Say whether you agree or disagree with the following statements and explain why:
a)A utility function that represents a person’s preferences is a function that assigns a utility number to each commodity bundle.
b)Once preferences are represented by utility functions, it is very easy to find the marginal rate of substitution because the slope of an indifference curve is minus the ratio of the marginal utility of one good to the marginal utility of the other.
c)If two consumer’s utility functions are monotonic increasing transformations of each other, then these consumers must have the same map of indifference curves.
2.Complete the following table:
U = (x1, x2)MU1 (x1, x2)MU2 (x1, x2)MRS (x1, x2)
2x1 + 3x2---
ax1 + bx2---
lnx1 + x2---
x1x2---
---
3.Carlos’ utility function is U = xaxb, where xa are the number of apples and xb the number of bananas.
a)Carlos has 40 apples and 5 bananas. Find the equation of the indifference curve that passes through the bundle (40, 5).
b)Berta offers to give Carlos 15 bananas if he will give her 25 apples. Would Carlos have a bundle that he likes better than (40, 5) if he makes this trade? What is the largest number of apples that Berta could demand from Carlos in return for 15 bananas if she expects him to be willing to trade or at least to be indifferent about trading?
4.Out of the whole map of preferences of a consumer, we know the formulas of two of them: x2 = 40 – 4, and x2 = 24 – 4.
a) Find out the utility function of this consumer. Is this a quasilinear utility function?
b)The consumer’s initial consumption is 9 units of x1, and 10 units of x2. If his consumption of x1 is reduced to 4 units, how many units of x2 will he have to consume to be as well-off as before.
c)The consumer is indifferent between the bundle (9, 10) and the bundle (25, 2). If you double the amount of each in each bundle, you would have bundle (18, 20) and bundle (50, 4). Are those two bundles on the same indifference curve?
d)What is the marginal rate of substitution (MRS) when he is consuming the bundle (9, 10)? And when he is consuming the bundle (9, 20)?
e)Can you write a general expression for the consumer’s MRS? Does it depend on the variables x1 and x2? What significance has this fact?
5.Lucia’s utility function is U = max{x, 2y}.
a)Graph the function x = 10 and also the function 2y = 10.
b)Find the value of U if x = 10 and 2y<10. Find the value of U if x>10 and 2y = 10.
c)Now draw the indifference curve along which U = 10.
d)Does Lucia have convex preferences?
6.Antonio’s utility functions is , where x1 is the number of apples and x2 the number of bananas consumed.
a)Fund out the slope of Antonio’s indifference curve through the bundle (4, 6).
b)Three bundles that belong to this indifference curve are: (-, 0); (7, -); and (2, -). Complete the blanks.
c)Find out the equation for the indifference curve through (4, 6).
d)Juana offers Antonio 9 bananas in exchange for 3 apples. Will Antonio accept the offer?
e)Juana says to Antonio “Antonio, I do not understand you. Your MRS is –2. That means that an extra apple is worth only twice as much to you as an extra banana. I offered you 3 bananas for every apple you gave me. If I offer to give you more than your MRS you should want to trade with me”. Is Juana right?