Microeconomics (2008) PDF

1 Krister Ahlersten Microeconomics Download free books at BookBooN.com 2 Microeconomics © 2008 Krister Ahlersten & Ventus Publishing ApS ISBN 978-87-7681-410-6 Download free books at BookBooN.com...

1 Krister Ahlersten Microeconomics Download free books at BookBooN.com 2 Microeconomics © 2008 Krister Ahlersten & Ventus Publishing ApS ISBN 978-87-7681-410-6 Download free books at BookBooN.com 3  Microeconomics Contents Contents 1 Introduction 10 1.1 Plan 11 2 Supply, Demand, and Market Equilibrium 12 2.1 Demand 12 2.1.1 The Demand Curve 12 2.1.2 When do We Move along the Demand Curve, and When Does It Shift? 13 2.2 Supply 14 2.2.1 The Supply Curve 14 2.3 Equilibrium 16 2.3.1 How to Find the Equilibrium Point Mathematically 17 2.4 Price and Quantity Regulations 17 2.4.1 Minimum Prices 17 2.4.2 Maximum Prices 19 2.4.3 Quantity Regulations 19 3 Consumer Theory 21 3.1 Baskets of Goods and the Budget Line 22 3.2 Preferences 25 3.3 Indifference Curves 26 3.4 Indifference Maps 27 3.5 The Marginal Rate of Substitution 28 Please click the advert Download free books at BookBooN.com 4  Microeconomics Contents 3.6 Indifference Curves for Perfect Substitutes and Complementary Goods 29 3.7 Utility Maximization: Optimal Consumer Choice 31 3.8 More than Two Goods 32 4 Demand 34 4.1 Individual Demand 34 4.1.1 The Individual Demand Curve 34 4.1.2 The Engel Curve 35 4.2 Market Demand 36 4.3 Elasticity 38 4.3.1 Price Elasticity 38 4.3.2 Income Elasticity 39 4.3.3 Cross-Price Elasticity 40 5 Income and Substitution Effects 41 5.1 Normal Good 42 5.2 Inferior Good 43 6 Choice under Uncertainty 46 6.1 Expected Value 46 6.2 Expected Utility 46 6.3 Risk Preferences 48 6.4 Certainty Equivalence and the Risk Premium 49 6.5 Risk Reduction 50 7 Production 51 7.1 The Profit Function 51 7.2 The Production Function 52 Please click the advert We have ambitions. 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Look for opportunities at www.simcorp.com/careers www.simcorp.com Download free books at BookBooN.com 5  Microeconomics Contents 7.2.1 Average and Marginal Product 52 7.2.2 The Law of Diminishing Marginal Returns 53 7.3 Production in the Short Run 54 7.3.1 The Product Curve in the Short Run 54 7.4 Production in the Long Run 57 7.4.1 The Marginal Rate of Technical Substitution 58 7.4.2 The Marginal Rate of Technical Substitution and the Marginal Products 58 7.4.3 Returns to Scale 59 8 Costs 60 8.1 Production Costs in the Short Run 61 8.2 Production Cost in the Long Run 63 8.3 The Relation between Long-Run and Short-Run Average Costs 66 9 Perfect Competition 68 9.1 Introduction 68 9.2 Conditions for Perfect Competition 68 9.3 Profit Maximizing Production in the Short Run 69 9.3.1 Strategy to Find the Optimal Short-Run Quantity 71 9.3.2 The Firm’s Short-Run Supply Curve 71 9.3.3 The Market’s Short-Run Supply Curve 72 9.4 Short-Run Equilibrium 72 9.5 Long-Run Production 73 9.6 The Long-Run Supply Curve 75 9.7 Properties of the Equilibrium of a Perfectly Competitive Market 76 10 Market Interventions and Welfare Effects 77 10.1 Welfare Analysis 79 what‘s missing in this equation? 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Moller - Maersk. www.maersk.com/mitas Download free books at BookBooN.com 6  Microeconomics Contents 11 Monopoly 80 11.1 Barriers to Entry 80 11.2 Demand and Marginal Revenue 80 11.3 Profit Maximum 81 11.4 The Deadweight Loss of a Monopoly 83 11.5 Ways to Reduce Market Power 84 12 Price Discrimination 85 12.1 First Degree Price Discrimination 85 12.2 Second Degree Price Discrimination 87 12.3 Third Degree Price Discrimination 87 13 Game Theory 88 13.1 The Basics of Game Theory 88 13.2 The Prisoner’s Dilemma 89 13.3 Nash Equilibrium 91 13.3.1 Finding the Nash Equilibrium in a Game in Matrix Form 91 13.4 A Monopoly with No Barriers to Entry 92 13.4.1 Finding the Nash Equilibrium for a Game Tree 93 13.5 Backward Induction 94 14 Oligopoly 96 14.1 Kinked Demand Curve 96 14.1.1 How does the Price in the Kinked Demand Curve Arise? 97 14.2 Cournot Duopoly 98 14.3 Stackelberg Duopoly 99 14.4 Bertrand Duopoly 100 it’s an interesting world Where it’s Please click the advert Student and Graduate opportunities in IT, Internet & Engineering Cheltenham | £competitive + benefits Part of the UK’s intelligence services, our role is to counter threats that compromise national and global security. 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Download free books at BookBooN.com 7  Microeconomics Contents 15 Monopolistic Competition 102 15.1 Conditions for Monopolistic Competition 102 15.2 Market Equilibrium 102 15.2.1 Short Run 102 15.2.2 Long Run 102 16 Labor 104 16.1 The Supply of Labor 105 16.2 The Marginal Revenue Product of Labor 106 16.3 The Firm’s Short-Run Demand for Labor 107 16.3.1 Perfect Competition in both the Input and Output Market 107 16.3.2 Monopoly in the Output Market 108 16.3.3 Monopsony in the Input Market 109 16.3.4 Bilateral Monopoly 110 17 Capital 111 17.1 Present Value 112 17.1.1 Bonds 112 17.1.2 Stocks 113 17.2 Correction for Risk 113 17.2.1 Diversifiable and Nondiversifiable Risk 113 17.3 CAPM: Pricing Assets 115 17.4 Pricing Business Projects 115 18 General Equilibrium 117 18.1 A “Robinson Crusoe” Economy 117 18.2 Efficiency 117 DIVERSE - INNOVATIVE - INTERNATIONAL Are you considering a European business degree? 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Please visit Copenhagen Business School at www.cbs.dk Diversity creating knowledge Download free books at BookBooN.com 8  Microeconomics Contents 18.3 The Edgeworth Box 117 18.4 Efficient Consumption in an Exchange Economy 119 18.5 The Two Theorems of Welfare Economics 120 18.6 Efficient Production 120 18.7 The Transformation Curve 121 18.8 Pareto Optimal Welfare 123 18.8.1 A Definition of Pareto Optimal Welfare 124 19 Externalities 125 19.1 Definition 126 19.2 The Effect of a Negative Externality 126 19.3 Regulations of Markets with Externalities 127 20 Public Goods 128 20.1 Definition of Public and Private Goods 128 20.2 The Aggregate Willingness to Pay 128 20.3 Free Riding 129 21 Asymmetric Information 130 21.1 Adverse selection 130 21.1.1 Insurance 130 21.1.2 Used Cars 130 21.1.3 Signaling and How to Reduce Problems with Adverse Selection 131 21.2 Moral hazard 131 21.2.1 How to Reduce Problems with Moral Hazard 132 22 Key Words 133 wanted: ambitious people At NNE Pharmaplan we need ambitious people to help us achieve the challenging goals which have been laid down for the company. 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Download free books at BookBooN.com 9 Microeconomics Introduction 1 Introduction Economics is often defined as something along the lines of “the study of how Economics: The study of society manages its scarce resources.” The starting point of most such studies how society manages its is that individuals allocate their resources such that they themselves will get scarce resources the highest possible level of utility. An individual has an idea of what the con- sequences of different actions will be, and she chooses that action she believes will produce the best result for her. She is, in other words, selfish and rational. Note that she is also forward-looking. She acts so that she in the future will get the highest possible level of utility, independently of what she has already done. That she is selfish does not have to mean that she is an egoist. However, it does mean that she will only voluntarily share with others if she believes that she thereby will maximize her own utility. We often call this simplification of human beings Homo Economicus. Homo Economicus: A model of human beings. She The resources that we are talking about here could be labor, capital (such as is assumed to maximize her machines), and raw materials. That they are scarce means there are not enough own utility. resources to produce everything we want. That, in turn, means that one has to Resources: Labor, capital and raw materials. The weight different things against each other. To get more of one thing, one has to things we use to produce give up something else. If you, e.g., want to sleep an extra hour, it is impossi- goods and services. ble to do so without giving up something else, such as an hour of studying. There is, consequently, a sort of a hidden cost to sleeping longer. This type of cost is called opportunity cost (or alternative cost). A classical saying in Opportunity/alternative economics is that “there is no such thing as a free lunch.” This means that, cost: The (hidden) cost of even if you do not actually pay for the lunch, you always have to give up at choosing one alternative instead of another. least the time when you could have done something else. That is, you always have to pay the opportunity cost. When we study microeconomics, it is primarily individual human beings and Microeconomics: The study of the economic individual firms, agents, that we study. This is in contrast to macroeconomics, behavior of individual where one studies whole economies, and questions such as unemployment and human beings and firms. Agent: An entity that is inflation. capable of making a deci- sion, e.g. a human being or Roughly speaking, there are three types of decisions that need to be made in an a firm. economy: Which goods and services to produce, how to produce them, and Macroeconomics: The study of whole economies. who should get them. Often in economic models, the prices of goods (or ser- vices, labor, capital, etc.) automatically coordinate these decisions in a market. A market is any mechanism where buyers and sellers meet. That could be, for Market: Meeting place example, a market square, a stock exchange, or a computer network where one where buyers and sellers are can buy and sell things. able to trade with each other. Microeconomics if often based on models. We try to describe a real phenome- Model: A simplified non as simply as possible by only highlighting a few central features. Many description of reality. economic models can be used for predictions and can therefore be tested against reality. Such models are called positive. The opposite kind of models, Positive economics: A models that are about values, is called normative. For example, to decide testable economic model. Normative economics: An about an economic policy one would first use positive economics to make as- economic model that sessments about the consequences of different alternatives. Then one would includes values (and there- fore is not testable). use one’s opinions about what is desirable and what is not to choose between the different alternatives. That is then a normative decision. Download free books at BookBooN.com 10 Microeconomics Introduction 1.1 Plan Before we begin, it is probably wise to make it clear where we are trying to go. We want to develop a number of models that together can describe how an economy works. They should be able to produce clear and testable predictions and be as simple as possible. x In a market, products and/or services are being bought and sold (or traded). We begin by looking at consumers and producers, and their respective demand and supply in a market. That way, we will see an example of how the market price of a good is determined. x Consumers and producers, however, have difficult problems to solve before they arrive at their respective demand and supply. First, we look at a consumer’s problem in a very simple case: She has to choose between two different goods for which she has different preferences. We show how it is possible to go from her preferences and income to her demand for one of the goods. Then we show how one can derive the demand for the whole market. x Then we change perspectives and study a producer’s problem. We will then discover that the model looks very similar to that of the con- sumer. The producer has to produce the good with the help of labor and capital, and different combinations of the two will lead to differ- ent quantities of the good. She also has to think about the fact that, different combinations will have different costs. The results will help us to show how the market supply is determined. x There are usually quite many consumers but substantially fewer pro- ducers. This has a large impact on how the market operates, and we therefore continue to study different market forms. We will differenti- ate between cases where there are one, two, some, and many produc- ers. We also study the welfare effects of different market forms. x The producers have a demand for labor and the workers supply it. The labor market has some odd features that we will treat separately. x Equilibrium is a central concept in economics. We show how con- sumer and producer markets, as well as the market for goods, simul- taneously reach equilibrium in a simple and stylized economy. x Lastly, we relax some of the assumptions we have made so far. We show how undesirable results can arise because of so-called market failures, e.g. because different agents have different amounts of in- formation about a good, or because it is difficult to keep out users who do not pay. Download free books at BookBooN.com 11  Microeconomics Supply, Demand, and Market Equilibrium 2 Supply, Demand, and Market Demand curve: Shows how much the buyers are willing Equilibrium to buy at different prices of a good. We begin our study of microeconomics by looking at a market with many buy- ers and sellers, i.e. a market where there is a large amount of competition. We Ceteris paribus: Latin for “with other things the will study such a market in more depth in Chapter 9, as well as other market same”. types, but starting here makes it easy to get a feel for how the subject works. 2.1 Demand Complementary goods: Goods that are typically consumed together 2.1.1 The Demand Curve Substitute goods: Goods that can be used instead of The demand curve shows how large quantities of a good buyers are willing to each other. buy at different prices. Note the expression “are willing.” It is not about how much they actually buy, but about how much they would want to buy if a cer- tain price was offered. A demand curve is only valid if all other relevant factors are held constant (ce- teris paribus: with other things the same). The most important other factors Preferences: What an that can affect demand are: individual prefers; her taste. Sharp Minds - Bright Ideas! 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Dedicated Analytical Solutions FOSS Slangerupgade 69 3400 Hillerød Tel. +45 70103370 www.foss.dk Download free books at BookBooN.com 12 Microeconomics Supply, Demand, and Market Equilibrium x The buyers’ income. x Prices and price changes on other goods. We will make a distinction between complementary goods and substitute goods. An example of complementary goods is right and left shoes. If the price of right shoes rises then the demand for right shoes will typically decrease. However, the demand for left shoes will also typically decrease. Con- sequently, the demand for left shoes partly depends on the price of another good: right shoes. Substitute goods work in the opposite way. An example could be blue and green pens: If one cannot use blue, one can often use green in- stead. If the price of green pens rises, the demand for green pens typi- cally decreases. However, if the price of blue pens is unchanged one can use these instead of the green ones, and then the demand for blue pens increases. Consequently, the demand for blue pens depends on the price of another good: green pens. Note that for substitute goods, a rise in the price of the other good leads to an increase in the demand for the good we are analyzing, whereas for complementary goods it is the other way around; a rise in the price of the other good leads to a decrease in the demand for the good analyzed. x Preferences. What consumers demand is largely a matter of taste. If there is a change in taste, there is usually also a change in demand. Taste can change for many different, underlying, reasons. For exam- ple, changes in moral perception or in fashion. If these factors are held constant, then the demand curve is valid and it usually slopes downwards. In other words, the lower the price is the higher is the de- mand, and vice versa. Demand is defined for a certain period. One can for ex- ample think of it as defined over a month, corresponding to a monthly salary. When drawing a demand curve in a diagram, the quantity demanded is on the X-axis and the price is on the Y-axis. This is slightly odd, since we often think of the quantity demanded as a function of the price, not the other way around. There are historical reasons for drawing it this way. 2.1.2 When do We Move along the Demand Curve, and When Does It Shift? The relation between price and quantity that is described by the demand curve is valid only if it is the price of the good itself that changes. Look at Figure 2.1 and the demand curve D1. If, in the beginning, the price is p1, then the quantity demanded is Q1 (point A). If the price of the good falls to p2, then the quantity demanded changes to Q2 (point B). We, consequently, move along the demand curve when the price of the good changes. Download free books at BookBooN.com 13 Microeconomics Supply, Demand, and Market Equilibrium Figure 2.1: The Demand Curve p A C p1 B p2 D1 D2 Q Q1 Q2 Q3 If, instead, something else changes (e.g. income, the prices of other goods, consumer preferences, or anything that affects the demand on the good), then the demand curve shifts. Assume again that the price is p1 so that the quantity demanded is Q1 (point A). If the consumer’s income increases, she can buy more of the good than she could before. Consequently, the whole demand curve shifts from D1 to D2. If the price is still p1, the quantity demanded in- creases to Q3 (point C). 2.2 Supply 2.2.1 The Supply Curve The producer counterpart to the demand curve is the supply curve. It shows how large quantities the producers are willing to sell at different prices, given that other factors that can affects supply are held constant. The supply curve is typically upward sloping or horizontal (but it could also be downward sloping). The demand curve is also valid over a certain period. Later, we will distinguish between two time periods: short and long horizons. The most important factors, beside the price, that affect supply are: x Factor prices, i.e. wages, prices of machines and compensation to owners and lenders. In other words, changes in the cost of production. x Laws and regulations that apply to the production. x Prices of other goods the firm produces or could potentially produce. Perhaps the producer is producing blue and green pens. If the price of green pens rises, she is likely to shift over resources (workers and ma- chines) to that production and there is less left with which to produce Supply curve: Shows how much the sellers are pre- blue pens. Consequently, the supply of blue pens decreases, even pared to sell at different though the price of blue pens is unchanged. prices of a good. Download free books at BookBooN.com 14 Microeconomics Supply, Demand, and Market Equilibrium Figure 2.2: The Supply Curve p S2 S1 C A p1 B p2 Q Q3 Q2 Q1 The supply curve behaves in a way that is similar to that of the demand curve. Look at Figure 2.2 and the supply curve S1. If the price is p1, then the produc- ers are willing to sell the quantity Q1 (point A). If the price of the good falls to p2, we move along S1 to point B, where the quantity is Q2. If, instead, some other factor changes, e.g. if wages increase so that it becomes more expensive to produce the good, the whole supply curve shifts. For instance from S1 to S2. If the price is still p1, then the quantity supplied changes from Q1 to Q3 (point C). www.job.oticon.dk Download free books at BookBooN.com 15 Microeconomics Supply, Demand, and Market Equilibrium Factor prices: The prices of 2.3 Equilibrium the factors of production. A market is in equilibrium when both of these conditions are fulfilled: 1. No agent wants to change her decision or strategy. 2. The decisions of all agents are compatible with each other, so that they can all be carried out simultaneously. If we join the supply and demand curves in one diagram, we get an equilibrium point where the two curves intersect. At this point, the price the consumers are willing to pay is the same as the price the producers demand. In Figure 2.3, the equilibrium price (market-clearing price) is p* and the equilibrium quantity is Q*. Figure 2.3: Equilibrium p S p2 p* p3 D Q Q4 Q2 Q* Q1 Q3 The equilibrium point has two important properties in that it is most often (but not always) stable and self-correcting. That it is stable means that, if the market is in equilibrium there is no tendency to move away from it. That it is self- correcting means that, if the market is not in equilibrium then there is a ten- dency to move towards it. To see more clearly what this means, suppose the price is higher than in equi- librium, e.g. that it is p2. At that price, producers are willing to supply the quantity Q1 whereas the consumers are only willing to buy the quantity Q2. Therefore, there is an excess supply of the good. To get rid of the extra units the producers are prepared to lower the price. This will push the price down- Equilibrium: A situation in which no agent wants to wards, closer to p*. At p*, there is no excess supply and the downward push on change her decision and all the price ends. decisions are compatible. Then assume, instead, that the price is lower than p*, e.g. that it is p3. At this Equilibrium price: The price, the consumers demand the quantity Q3 whereas the producers are only price that arises when there willing to supply the quantity Q4. Consequently, there will be a shortage of the is an equilibrium in the market. good, and the consumers will be prepared to bid up the price to get more units. Equilibrium quantity: The This will tend to push the price upwards, closer to p* where, again, the push quantity that is bought and will end. sold when there is an equilibrium in the market. Download free books at BookBooN.com 16 Microeconomics Supply, Demand, and Market Equilibrium 2.3.1 How to Find the Equilibrium Point Mathematically Supply and demand can be written as mathematical functions, and in simple examples, they are often straight lines. They could, for instance, be: ­QS 85  30 p ® ¯QD 185  20 p. Here, QD is the quantity demanded, QS is the quantity supplied, and p is the price. We now want to find the price, p*, that makes QD = QS. If the left-hand sides above are equal, the right-hand sides must also be so. Therefore, substitute p* for p and set the right-hand sides equal to each other: 85  30 p* 185  20 p* To get p* alone on the left-hand side, we add 20 p* on both sides and subtract 85 from both sides. Then we have that 50 p* 100. Dividing by 50 on both sides yields the result that p* 2. If we then want to know the equilibrium quantity, Q*, we substitute the result Regulation: Laws that influence prices and/or we got for p* into either the supply or the demand function above. (Note that quantities in a market. they must yield the same quantity, since p*, by definition, is the price that makes QD = QS.) Secondary effect: An unintended side effect of, for instance, a law. ­QS* 85  30 p * 85  30 * 2 145 Q* ® * ¯QD 185  20 p * 185  20 * 2 145 Consequently, we have the equilibrium price, p* = 2, and the equilibrium quan- Minimum price/price floor: The lowest price a tity, Q* = 145. regulation allows. 2.4 Price and Quantity Regulations Many markets are, for a number of reasons, regulated. The government could for instance decide about prices that the market is not allowed to go above or below, or about maximum quantities. Such regulations will benefit certain groups of people, but often have unintended negative side effects. These are often called secondary effects. 2.4.1 Minimum Prices Minimum prices (also called price floors) are often used for wages (the price of labor) and for certain types of goods such as agricultural goods. The mini- mum price is usually chosen above the equilibrium price, as in the opposite case it would not have any effect. (The market participants would then choose p* instead.) Consumers and producers are consequently prevented from reach- ing the equilibrium price p*. Download free books at BookBooN.com 17  Microeconomics Supply, Demand, and Market Equilibrium Look at Figure 2.4. The effect of the minimum price is that the consumers only demand the quantity Q2 whereas the producers supply the quantity Q1. There- fore, we get an excess supply of the good. Note that consumers and producers are allowed to buy and sell at any price above the minimum price. A price higher then pmin will however result in an even larger excess supply, so typically the minimum price is chosen. The situation described is not an equilibrium. To see that, note that point 2 in the definition of an equilibrium (see Section 2.3) is not satisfied: Given the price pmin producers want to sell the quantity Q1, but that is not possible since the consumers only want to buy the quantity Q2. Figure 2.4: The Effect of a Minimum Price p S pmin p* D Q Q2 Q* Q1 wanted: ambitious people At NNE Pharmaplan we need ambitious people to help us achieve the challenging goals which have been laid down for the company. Kim Visby is an example of one of our many ambitious co-workers. Besides being a manager in the Manufacturing IT department, Kim performs triathlon at a professional level. Please click the advert ‘NNE Pharmaplan offers me freedom with responsibility as well as the opportunity to plan my own time. This enables me to perform triath- lon at a competitive level, something I would not have the possibility of doing otherwise.’ ‘By balancing my work and personal life, I obtain the energy to perform my best, both at work and in triathlon.’ If you are ambitious and want to join our world of opportunities, go to nnepharmaplan.com NNE Pharmaplan is the world’s leading engineering and consultancy company focused exclusively on the pharma and biotech industries. NNE Pharmaplan is a company in the Novo Group. Download free books at BookBooN.com 18 Microeconomics Supply, Demand, and Market Equilibrium 2.4.2 Maximum Prices Maximum prices (also called price ceilings) are in several countries used for apartment rentals. For a maximum price to have any effect, it has to be below the equilibrium price, and the effects are the opposite to those of a minimum price. In Figure 2.5, pmax is the maximum price. It causes the consumers to de- mand the quantity Q1 whereas the producers only want to supply Q2, and, con- sequently, there is a shortage. A typical consequence of a maximum price is that the search time to find an appropriate good is increased since the supply is too small to meet the demand. Figure 2.5: The Effect of a Maximum Price p S Maximum price/price ceiling: The highest price a regulation allows. p* pmax D Q Q2 Q* Q1 2.4.3 Quantity Regulations The effects of quantity regulations are similar to those of price regulations. As- sume for instance that there is a restriction stating that one may only import the quantity Qmax of a certain good, say Asian textiles. Download free books at BookBooN.com 19 Microeconomics Supply, Demand, and Market Equilibrium Figure 2.6: The Effect of a Quantity Regulation p S pD p* pS D Q* Q Qmax Q1 Producers would have been willing to supply the quantity Qmax at a price of pS, whereas the consumers would have been willing to buy that quantity at a price of pD. Since the quantity is not allowed to increase, there is excess demand at all prices other than pD. When there is excess demand, consumers are likely to bid up the price, so the price that this market is likely to arrive at is pD. Note that at the price pD, producers are willing to supply a much larger quan- tity, Q1, but that they are prevented from doing so by the regulation. The con- sumers have to pay a price that is larger than the equilibrium price (pD instead of p*) and they get fewer units of the good, so they typically are made worse off by a quantity regulation. Download free books at BookBooN.com 20  Microeconomics Consumer Theory 3 Consumer Theory Where does the demand curve come from? In order to explain why individuals choose different quantities at different prices, we will use a model with three components: x Consumers have certain restrictions on how they can choose. Most importantly, they have a budget, but there can also be other restric- tions. x Individual preferences (or tastes) determine how satisfied an individ- ual will be with different combinations of goods and/or services. We measure the level of satisfaction in terms of utility. x Given preferences and restrictions, the individual maximizes her util- ity of consumption. We will now discuss these three components.      Please click the advert     Download free books at BookBooN.com 21 Microeconomics Consumer Theory 3.1 Baskets of Goods and the Budget Line As a consumer, one can choose between several different goods and services. A certain combination of goods and services is called a basket of goods (a bundle of goods, or a market basket). The consumer’s problem can therefore Budget: The amount of be described as having to choose between different baskets, given the restric- money, or wealth, a con- tions she faces, such that she maximizes her utility. sumer has access to. We begin by looking at a simple case where we have just two goods, good 1 and 2, with prices p1 and p2. A basket that consists of the quantity q1 of good 1 and q2 of good 2 is written (q1,q2). For example, (4,3) means that we have 4 Utility: A measure of how satisfied a consumer is. units (or kilos, liters, etc) of good 1 and 3 units of good 2. The price of the bas- Maximize: Choose in such ket (q1,q2) is then: a way that one gets as much as possible of something else. p 1 * q1  p 2 * q 2. If we have a limited amount of money to buy these goods for, this will impose a restriction on how much we can buy of each good. Letting m denote the amount of money available, the price of the basket chosen must not exceed m. The different combinations of good 1 and 2 that cost exactly m can be written Basket / bundle of goods: A combination of goods and services. p1 * q1  p 2 * q 2 m. Solving this expression for q2, we get the function of the budget line: m  p1 * q1 m p1 q2  * q1 p2 p2 p2 This function is a straight line that intercepts the Y-axis at m/p2 and has the slope p1/p2 (see Figure 3.1). All the points on the budget line cost exactly m. The points in the grey area be- low the budget line cost less than m whereas the points above cost more than m. The baskets that a consumer with wealth m can buy are, consequently, the ones on and below the budget line. There is a simple strategy for finding the budget line: If we only buy good 2, the maximum quantity that we can buy is m/p2, whereas if we buy only good 1, the maximum quantity that we can buy is m/p1. Indicate the first point on the Y-axis and the second on the X-axis, and then draw a straight line between Budget line: A graphical them. The line you have drawn is the budget line, and it will automatically description of the baskets a have the slope -p1/p2. consumer can buy, given a certain budget. Download free books at BookBooN.com 22 Microeconomics Consumer Theory Figure 3.1: The Budget Line q2 The Budget Line m/p2 1 -p1/p2 q1 m/p1 The slope of the budget line is called the marginal rate of transformation (MRT). We consequently have that p1 MRT  p2 Suppose, for instance, that the two goods are ice cream (price 10) and pizza Marginal rate of trans- (price 20). MRT will then be -10/20 = -0.5. We can interpret this such that you formation: The slope of the budget line. have to give up half a pizza if you want to have one more ice cream (or, vice versa, that you have to give up two ice creams, -20/10, to get one more pizza). To transform your basket into another basket with one more ice cream, you have to give up half a pizza. Note that this means that the price of ice cream measured in pizzas (instead of money) is half a pizza. If income or prices change, the budget line will also change. Look at Figure 3.2 and the budget line B1. If the price of good 1 rises from p1 to p'1, we can only buy a maximum of m/p'1 of that good, but we can still buy m/p2 of good 2. Consequently, the budget line rotates about the intercept with the Y-axis to B2. If, instead, the price of good 2 rises from p2 to p'2, then B1 rotates about the in- tercept with the X-axis to B3. When a price changes, MRT also changes since the slope of the budget line changes. If the price of ice cream rises from 10 to 20, MRT will be -20/20 = -1. Now, you have to give up a whole pizza to get one more ice cream. Note that this also means that the pizza has become cheaper, relatively speaking: You can now get one more pizza for just one ice cream, even though the price of pizza is unchanged. Assume now that the prices are p1 and p2, as they were originally, but that the income increases to m'. We can then buy a maximum of m'/p2 of good 2 and a maximum of m'/p1 of good 1. B1 consequently shifts to B4. Note that the slope of B4 is exactly the same as the slope of B1, since the prices are unchanged: You have more money, but you still have to give up half a pizza if you want to have one more ice cream. Download free books at BookBooN.com 23 Microeconomics Consumer Theory 3.2 Preferences The theory of preferences belongs to the most difficult parts of basic micro- economics, so take your time with this section. It is very important to both un- derstand and be able to use preference-theory in the rest of the material. You have probably heard the expression that “one should not compare apples and oranges,” or something similar. The point here is precisely that one should do that, and even to compare anything with anything else. This is done through a preference order. We will assume that an individual always knows what she prefers: she prefers basket A to basket B, she prefers B to A, or she is indiffer- ent between them. If all baskets are ordered accordingly, we have a preference order and such an order is valid for a certain individual. Transaction costs: Any Usually, the following four assumptions are made about preference orders: cost, apart from the price of the good, that is associated x Complete. The individual can order all conceivable baskets of goods. with buying or selling it. x Transitive. If the individual prefers A to B, and B to C, she also pre- fers A to C. In other words, there are no “circles” in preferences. x Non-satiation. An individual always prefers more of a good to less. This assumption is a bit tricky. Suppose we think of pollution as a good. Is more pollution usually preferred to less pollution? No, obvi- ously not. To get around this type of problem, we have to define the good in the opposite way: Instead of pollution, we define clean air to be the good. More clean air is better than less. x Convexity. Suppose we have two baskets that an individual is indif- ferent between, A and B. She will then always prefer (or at least be indifferent between) baskets that lie between these two baskets. Say Indifference curve: A that she is indifferent between a basket consisting of (2 apples, curve showing different 4 bananas) and (4 apples, 2 bananas). She will then, according to the combinations of two goods between which a consumer assumption, prefer a basket of (3 apples, 3 bananas) to the other two is indifferent. Similar to (or, at least, be indifferent between all of them). elevation contours on a map. Are these assumptions true? Many people have debated the reasonableness of them. Are you, for instance, non-satiable? Which do you prefer: 2 liters of milk or 10,000 liters? Probably 2 liters. The rest will not fit into the refrigerator and will soon start to smell. It will also require a lot of work to get rid of them. Preference order: A In many models, however, it is also assumed that there are no transaction complete “list” of which costs. This means that, there are no costs to trading, except for the price of the things a certain individual prefers to other things. goods. Examples of transaction costs are the cost of a stamp if you mail in an Indifferent: It does not order, the effort it takes to go to the market where you can buy things, or the matter which of the things she gets. cost to hire a lawyer to go through a contract before you sign it. Models that include transaction costs become much more complicated, but, on the other hand, they also become more realistic. In the example, you would probably prefer 10,000 liters of milk if it would not cost you anything to sell them and immediately get rid of them. In a worst-case scenario, you would sell then at a price of 0, which should make you indifferent between 2 and 10,000 liters of milk. Download free books at BookBooN.com 24  Microeconomics Consumer Theory pensate for the loss of that one unit. We, consequently, have to increase q2 more and more, the lower q1 is, to ensure that the individual has the same util- ity. And as we need larger and larger amounts of good 2 to keep the individual indifferent after having lost one more unit of good 1, the slope of the indiffer- ence curve will increase as we move to the left (i.e. as we reduce good 1), and vice versa when we move to the right. 3.4 Indifference Maps Since the preferences are complete, some indifference curve must run through each point, i.e. each basket. If we randomly choose four baskets, A, B, C, and D, there will be some indifference curve that runs through each point (see Fig- ure 3.4). If we move to the northeast in the diagram, the level of utility increases. Label- ing the indifference curves I1, I2, I3, and I4, they must therefore represent higher and higher levels of utility. A collection of several indifference curves in one figure is called an indifference map. It is common to compare indifference maps to elevation contours on a regular map: It is like walking up or down a hill when one moves from one indifference curve to another. Brain power By 2020, wind could provide one-tenth of our planet’s electricity needs. Already today, SKF’s innovative know- how is crucial to running a large proportion of the world’s wind turbines. Up to 25 % of the generating costs relate to mainte- nance. These can be reduced dramatically thanks to our systems for on-line condition monitoring and automatic lubrication. 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A C B Indifference curve q1 After having made the four assumptions above, we can say a lot about what an in- difference curve must look like. All points in the diagram (i.e. all possible combi- Indifference curve: A nations of good 1 and 2) correspond to a basket. Since the preferences are com- curve that shows all combi- nations of goods that an plete, there must be some preference curve that runs through any point in the dia- individual is indifferent gram. Another way to say the same thing: Pick any point in the diagram; which- between. ever point you picked, there is an indifference curve running through that point. We now randomly select a point in the diagram, say point A. Since the indi- vidual is non-satiable, all points where she gets more of either good 1, or good 2, or of both are better for her. This corresponds to the grey area north- east of point A. Similarly, all points where she gets less, the grey area south- west to A, must be worse for her. Consequently, she cannot be indifferent be- tween basket A and any point in the grey areas. Therefore, a preference curve that runs through A cannot also run through any point in the two grey areas. This means that an indifference curve will slope downwards. (See, however, the case of complementary goods in Section 3.6) The assumption of convexity implies that the slope will become smaller and smaller as we move to the right. Convexity means that, if we randomly choose any other point on the indifference curve that runs through A, say point B, and then choose a point in between them, say point C, then point C must be better Indifference map: A collection of indifference than (or at least as good as) A and B. C must therefore lie on a higher indiffer- curves in a diagram. ence curve than the one that runs through A and B. If this is true for any choices of A, B, and C, then the curve must slope less and less the farther to the right we get. An economic interpretation of this criterion is that, the less one has of a certain good, e.g. the lower q1 is, the less inclined one is to give up one more unit of that good. If that is so, then one will demand more of the other good to com- Download free books at BookBooN.com 26  Microeconomics Consumer Theory pensate for the loss of that one unit. We, consequently, have to increase q2 more and more, the lower q1 is, to ensure that the individual has the same util- ity. And as we need larger and larger amounts of good 2 to keep the individual indifferent after having lost one more unit of good 1, the slope of the indiffer- ence curve will increase as we move to the left (i.e. as we reduce good 1), and vice versa when we move to the right. 3.4 Indifference Maps Since the preferences are complete, some indifference curve must run through each point, i.e. each basket. If we randomly choose four baskets, A, B, C, and D, there will be some indifference curve that runs through each point (see Fig- ure 3.4). If we move to the northeast in the diagram, the level of utility increases. Label- ing the indifference curves I1, I2, I3, and I4, they must therefore represent higher and higher levels of utility. A collection of several indifference curves in one figure is called an indifference map. It is common to compare indifference maps to elevation contours on a regular map: It is like walking up or down a hill when one moves from one indifference curve to another. Please click the advert Download free books at BookBooN.com 27 Microeconomics Consumer Theory After we have drawn the indifference curves, we can also compare points that do not lie to the northeast or southwest of each other. In the figure, point B is not to the northeast of point A, but it does lie on an indifference curve that is “higher” than the one that runs through A. Consequently, point B represents a basket that is better than the one represented by point A. We can also see this in the following way: Note that there are points on I2 that lie to the northeast of point A (between the two dotted lines that originate at A). Those points must therefore be better than A. Moreover, all points on I2 are equally good for the individual (since she, by definition, is indifferent between all of them). Conse- quently, point B represents a level of utility that is exactly the same as the points on I2 that are to the northeast of A. Therefore, B must be better than A is. Note that if we argue that way, we have used the assumption of transitivity. Figure 3.4: An Indifference Map q2 D C I4 A I3 Impossible B indifference curve I2 q1 I1 The indifference curves have the following four important properties: x Baskets that are further away from the origin (the point (0,0) in the graph) are better than the ones closer to the origin. x Every point has an indifference curve that runs through it, since the preferences are complete. x Indifference curves cannot cross each other. This follows from the as- sumptions of transitivity and non-satiation. x The indifference curves slope downwards. If they would slope up- wards, we would violate the assumption of non-satiation. 3.5 The Marginal Rate of Substitution Look at one of the indifference curves in Figure 3.4. The slope of the curves is of central importance. Think about what the slope means: If you choose some basket on one of the curves, how much would you be willing to give up of good 2 to get one more unit of good 1? If you would be willing to give up only a small quantity of good 2, the magnitude of the slope would be small, whereas if you were willing to give up a lot, it would be large. Download free books at BookBooN.com 28 Microeconomics Consumer Theory Imagine that we have two individuals who each have 5 apples (good 1) and 5 bananas (good 2). To get one more apple, the first is willing to give up one Marginal rate of substitu- tion: How much an individ- banana, whereas the other is willing to give up two bananas. The first individ- ual is willing to pay for an ual’s indifference curve running through the point (5,5) will then slope less additional unit of a good in terms of another good than the second individual’s indifference curve. These two individuals have (rather than money). It different tastes regarding apples and bananas. corresponds to the slope of an indifference curve. The numerical value of the slope of an indifference curve, the magnitude of the slope, is called the marginal rate of substitution (MRS), and it can approxi- mately be calculated as 'q2 MRS 'q1 Here, 'q1 and 'q2 are the changes in quantity for good 1 and good 2, respec- tively. Individual 2 above was willing to give up 2 bananas to get one more apple. Then 'q2 = -2, 'q1 = 1, and MRS = -2/1 = -2. The fact that the indiffer- ence curves slope less and less to the right implies that MRS is decreasing. Often, one does not keep the minus sign in MRS. It is then implicitly under- stood that one gets less (minus) of one good to get more (plus) of the other. Note that, if one leaves out the minus in MRS, one typically does so for MRT Marginal: An infinitely small change. Usually, one as well (see Section 3.1). speaks of a change of one unit. The expression for MRS above is only approximate. The smaller one chooses 'q1, the better the approximation will be. For it to become completely exact, 'q1 must be chosen infinitely small. This, in turn, makes it necessary to use de- rivatives. That, however, lies outside the scope of this book. Note that the word "marginal" means "infinitely small.” You will hear that word many times in economics. Perfect substitutes: Two goods that are possible to use interchangeably, so that a consumer is indifferent 3.6 Indifference Curves for Perfect Substitutes and between them. This causes the indifference curves to be Complementary Goods straight lines. An example of (almost) perfect substitutes we have already seen is green and blue pens. Perfect substitutes have the property that, instead of decreasing MRS, they have constant MRS. This means that they have the same slope eve- rywhere, i.e. they are straight lines sloping downwards to the right (see Fig- ure 3.5). In the case of the pens we have that MRS = 1/1 = 1 (where we have dropped the minus sign), but MRS could be any number. The defining criterion for perfect substitutes is that MRS is constant. Download free books at BookBooN.com 29  Microeconomics Consumer Theory Figure 3.5: Perfect Substitutes and Complementary Goods q2 q2 Complementary goods Perfect substitutes q1 q1 The example of complementary goods we saw before was right and left shoes. One has no use for one without the other. This fact causes the indiffer- ence curves to become L-shaped (see Figure 3.5). Assume we have two left shoes and two right shoes. Even if we get many more right shoes, we will still have the same utility as before. The indifference curves are therefore vertical along q2 and horizontal along q1, and the only way to reach a higher level of utility is to get more of both good 1 and good 2. Please click the advert We have ambitions. Also for you. SimCorp is a global leader in financial software. At SimCorp, you will be part of a large network of competent and skilled colleagues who all aspire to reach common goals with dedication and team spirit. We invest in our employees to ensure that you can meet your ambitions on a personal as well as on a professional level. SimCorp employs the best qualified people within economics, finance and IT, and the majority of our colleagues have a university or business degree within these fields. Ambitious? Look for opportunities at www.simcorp.com/careers www.simcorp.com Download free books at BookBooN.com 30 Microeconomics Consumer Theory