Lecture 3 ( 3): April 20 and 22, 2004 Chapter 4 Demand, Supply, and rice Stiglitz: pp. 71-95. Key Terms: demand curve substitutes complements demographic effects supply curve equilibrium price excess supply excess demand 1. The Law of Supply and Demand In competitive market economies actual prices tend to be the equilibrium prices, at which demand equals supply. rice the market supply curve E at point E * Demand = Supply the market demand curve 0 Q* Quantity of good X *: the equilibrium price Q*: the equilibrium quantity rice The price of a good or service is what must be given in exchange for the good. rice measures scarcity. 1
2. Market Demand 1. What is the Demand Curve? The market demand curve gives the total quantity of the good or service demanded at each price. As decreases, the movement takes place along (or, on) the demand curve. the market demand 0 Good X the Market of good X That is, we say that as the price of good X falls, the quantity of good X demanded increases. Note that there are no changes in other factors other than a change in the price (per unit) of good X. When the price of good rises, a movement on the demand curve occurs. That is, the quantity of good demanded decreases. 2. Factors shift market demand curves. A Change in 1. income 2. the price of substitute 3. the price of a complement 4. the composition of the population 5. tastes 6. information 7. the availability of credit 8. expectations 3. Demand curve vs. quantity of good X demanded The demand curve (of good X) means the whole demand curve. The quantity of good X demanded means a point on the demand curve. 4. The demand curve shifts to the right or left as changes in any of the items in 2. The demand for good X increases. This is the same as saying that the demand curve shifts to the right. 2
The demand for good X increases (or rises). D0 D1 0 Good X/time The demand for good X decreases. This is the same as saying that the demand curve shifts to the left. D2 D0 0 Good X/time 3
3. Market Supply 1. What is the Supply Curve? The market supply of a good is simply the total quantity of that all the firms in the economy are willing to supply at a give price. 2. Factors shift market supply curves. A Change in 1. the prices of inputs, 2. technology 3. the natural environment 4. the availability of credit 5. expectations Changes in these factors will shift the supply curve either to the right or left. The supply of good X increases. This is the same as saying that the supply curve shifts to the right. S0 S1 0 Good X/time The supply of good X decreases. This is the same as saying that the supplu curve shifts to the left. S2 S0 0 Good X/time 4
Equilibrium: Demand = Supply at * Excess demand: Demand>Supply at 1 Excess Supply: Demand<Supply at 0 rice the market supply curve 0 A B E at point E * Demand = Supply 1 C D the market demand curve 0 Q* Quantity of good X At the price of 0 the quantity supplied at B exceeds the quantity demanded at A. This means the excess supply exists. Hence, there is a tendency for the price to decrease from 0 to *. On the other hand, at the price of 1, the quantity demanded at D exceeds the quantity supplied at C. Thus, the price tends to rise from 1 to * until the price becomes * at point E, where the demand equals the supply. At the price * and Q* in equilibrium, unless either the demand or supply curve (or both curves) shifts, there will be no changes for * and Q*. The Important Note: rices In competitive markets, prices are determined by the law of supply and demand. Shifts in the demand and supply curves lead to changes in the equilibrium price. Similar principles apply to the labor and capital markets. The price for labor is the wage, and the price for capital is the interest rate. 5
Lecture 3 ( 3): April 20 and 22, 2004 Chapter 5 Using Demand and Supply Stiglitz: pp. 96-121 Key Terms: price elasticity of demand infinite elasticity zero elasticity price elasticity of supply market clearing price ceilings price floors sticky prices 1. rice Elasticity rice elasticity measures responsiveness in quantity (either demanded or supplied) due to one percent change in price. 1-1 rice elasticity of demand (for good X, e.g., apples, oranges or cars) The price elasticity of demand is defined as the percentage change in the quantity demanded divided by the percentage change in price. rice elasticity of demand = ercentage change in quantity demanded ercentage change in price rice/ unit Figure 1 Market demand for ice cream 2.10 2.00 E F D 0 90 100 Good X 6
In figure 1, suppose we draw the market demand curve of ice cream. Note that we take the price of ice cream on the Y-axis and the quantity of ice cream demanded per period on the X-axis. As you know, as the price falls from $2.10 per unit to $2.00, the quantity of ice cream demanded increases from 90 to 100. Then, we can calculate the price elasticity of demand for ice cream in the market as, % changes in the quantity demanded The price elasticity of demand for ice cream = % changes in the price Let ε stands for the price elasticity of demand so that we can define it as, 1 X % inx X ε = = = X,.. (1) % in X The above definition is used when changes in price is infinitely small. Therefore, it is used to measure the price elasticity of demand at a point on the demand curve. However, our example in Figure 1 is not at a point on the demand curve but the example shows the range from points from E to F. In this case, we use, as an approximation, an arc price elasticity of demand, defined as follows: X 10 X 0 + X 1 90 + 100 10 2 2 arc ε = = = 95 = 2.15789 2.16.. (2) 0.10 0.10 0 + 1 2.10 + 2.00 2.05 2 2 The above value of -2.16 means that when the price of ice cream increases by 1 This price elasticity is called own price elasticity of demand in a strict sense. The ln X price elasticity of equation (1) is expressed also as ε =. ln 7
one percent, the quantity of ice cream demanded decreases by 2.16 percent. Note that the minus sign shows the relationship between the price and the quantity of good X (here, ice cream) demanded is inverse. This is the law of demand. 1-2 Various values of the price elasticity of demand Some examples of the value of the price elasticity of demand are as follows: Figure 2 Figure 3 ε = 0 ε = 0 Good X 0 Good Y a vertical demand curve a horizontal demand curve Figure 4 < ε < 0 0 Good Z In the case of figure 4, the values of price elasticity are grouped into three such as, (1) 1 < ε < 0 : inelastic (2) ε = 1: unitary, and (3) ε < 1: elastic. 8
1-3 Why is the price elasticity important? What kind of information can we get by knowing the values of price elasticity of demand for various goods and services? Now, suppose that the manager in a store is considering to raise the price of good sold in the store and he (or she) know the price elasticity of demand for the good. Let say the price elasticity of demand for the good is -2.0. What will happen to the revenues to the store after raising the price of good? Can the store increase the revenue? Answer 1: No. It reduces the total revenue to the store. WHY? Note that the price elasticity if the measure of changes in consumption of good in response to changes in the price. As said, the price elasticity is -2.0, it means when the price increases by one percent, the consumption (that is, the quantity of the good demanded) decreases by 2 percent. Total Revenue = times X = >( increases by 1%) x (X decreases by 2%) What will be the total revenue? Of course, it decreases. Answer 2: By using some mathematics, we have, Total Revenue = X log TR = log + log X d log TR = d log + d log X d logtr d log d log X = 1+ = 1+ ε, where d log d log X ε =. d log Since ε is always negative except for the cases of 0 and, we can write as follows: 9
d logtr = 1 ε... (3) d log Then, in equation (3), if the value of the price elasticity is -2.0, we have: d logtr d log = 1 ε = 1 2 = 1 < 0. This means that when the price of the good increases by 1 percent, the total revenue decreases by 1 percent. So, if we want to simply know the total revenue increase or decrease, all we have to know the value of the price elasticity of demand. Exercise 1: Indicate if the total revenue in a market as a whole increases, decreases or does not change, when the price of the product increases by 2%? 1) 0 > ε > 1: 2) ε = 1: 3) ε < 1 Exercise 2: Find the price elasticity of demand at point E. Figure 5 10 5 E A linear market demand curve 0 Good X 10 20 10
2 rice elasticity of Supply The price elasticity of supply is defined as the percentage change in quantity supplied divided by the percentage change in price. rice elasticity of supply = ercentage change in quantity supplied ercentage change in price rice/ unit Figure 6 Market supply of ice cream 2.10 2.00 F E D 0 80 100 Good X 2-1 Arc-price elasticity of supply arc X X 0 + X 2 e = 0 + 1 2 1 20 80 + 100 2 = = 0.10 2.10 + 2.00 2 20 90 0.10 2.05 = 4.4444 4.4 That is, when the price of good X increases by 1%, the quantity of good X supplied increases by 4.4%. 11
In the case of the price elasticity of supply (of goods and services), the value is positive. Therefore, the relationship between the price and quantity supplied is positive, as rises, X supplied increases. 2-2 the (point) price elasticity of supply % inx e = % in X = X = X X Figure 7 8 E A linear market supply curve 5 0 Good X 10 the price elasticity of supply at point E is: % inx e = % in X = X 1 = 3 5 8 10 = 8 6 = 1.333 1.3 As the price increases by 1%, the quantity of good X supplied increases by 1.3%. 12
3 Short and long run supply curves In economics, we often separate our analysis into two ways such as a short run and a long run. The meanings of those are as follows: (1) In the short run: The time is not long enough for firms to adjust their production processes by changing, say, sizes of capital in the firms and technology. In the technical way, there are at least one or more fixed factors of production. (2) In the long run: (2-1) the time is long enough for firms to adjust their production processes by adjusting factors of productions, but not technology of productions. (2-2) all changes, including all factors of production as well as technologies in the production. Therefore, when we consider the demand curve of a typical market in the short and long runs, the slope of their corresponding supply curves will differ. That is, in the long run, since all factors of production and technology changes (that means, firms can find more efficient ways to produce their goods and services at lower costs), the supply curve will be flatter (or technically, more elastic) that the short-run supply curve. Figure 8 Short-run S Long-run S 0 Good X 13
4 rice Ceiling and rice Floor (in the short run) In a competitive product market (that means, all consumers and producers are freely joining the market with no costs) with no government interventions, the price of product per unit is determined by the demand and supply curves such as, Figure 9 S 0 E D 0 X0 Good X In Figure 9, the demand curve intersects the supply curve at point E. Therefore, at point E, we say D=S. The resulting price, 0, and the quantity, X 0, are called the equilibrium price and the equilibrium quantity of good X. Note, we use the word equilibrium to indicate the demand equals the supply. In fact, we economist consider the equilibrium point E is the most preferable point in the society since the welfare in the market is maximized. How do we know that the market welfare is maximized. (1) The market demand curve shows the maximum willingness to pay in exchange for good per unit. (2) The market supply curve shows the least cost (that is, in a most efficient way) to produce output at different levels of output. (3) At any output level below X 0 the consumer s willingness to pay exceeds the least cost of production in the market. That is, there will be gain to produce more. 14
(4) At any output level above X 0, the cost of production in the market (or the cost to supply the good to the market) exceeds the willingness to pay by consumers in the market. That is, the good is too expensive or costly to meet the consumer s demand. (5) Hence, at point E, the willingness by consumers in the market as a whole is exactly equal to the least cost to produce the good per unit. Therefore, there will be no loss at all. By the way, the consumer s willingness pay is in fact the maximum price that the consumers can pay or the monetary evaluation of good per unit. 4-1 rice Ceiling rice ceilings are maximum prices legally allowed in markets by government. That is, no price is allowed above the price ceilings. The regulation looks like this. Figure 10 S 0 rice ceiling E D 0 Sc X0 Dc Good X In Figure 10, if government sets the regulated price (that is, price ceiling) as the horizontal line, what will happen to the consumers and producers in the market? At the ceiling price, the quantity of good X demanded is given at D c, while the supply is at S c. Hence, the demand exceeds the supply, i.e., D>S. There will be the excess demand by the amount of the difference between D c and S c. This phenomenon will result in the situation that many consumers in the 15
market make lines to purchase good X since there is a shortage of good X in the market. Then, what will be? One of the possible results is that there will be black markets. In the black markets, some producers or people who can get good X by probably illegal ways will try to sell good X at very high prices, which will be well above 0. Then, who gets good X? I believe they are the people who can afford paying the high prices. As another sequence, since the price of good X is regulated well below the competitive price, producers in the market are normally willing to supply only as much as S c. Therefore, we know there will be fewer consumers in the market who are able to buy good X. Hence, the regulated price, i.e., the price ceiling, distorts the market and lower the market welfare, whose result is certainly not preferable, since we know resources in the society are scarce. Example of price ceiling: rent control and usury law (maximum interest rate charged) 4-1 rice Floor rice floor is a minimum price legally allowed in a market by government. That is, no price is allowed below the price floor. The regulation looks like this. Figure 11 S rice floor 0 E D 0 DF X0 SF Good X 16
In Figure 11, the price floor is set above the equilibrium price so that there will be excess supply by the amount of S F minus D F. This will result in that more good X is unsold and accumulated in warehouses of firms in the market. Or, if government guarantees its purchase of the excess amount of good X, then now the government will pile the goods in its warehouse, like rise. In the market, consumers must pay at the price floor and consequently reduce their consumption from X 0 at the competitive market equilibrium. So, the total consumption at the price floor is smaller than the equilibrium amount of consumption at 0. Hence, the market is worse at the price floor than at the competitive equilibrium. Example of price floor: minimum wage law and government price support for rise. 17
Lecture 4 ( 4): April 20 and 22, 2004 Chapter 6 Time and Risk Stigliz: pp. 122-142 Key Terms interest principal present discounted value intertemporal trades 2 real rate of interest nominal rate of interest assets expectations myopic expectations adaptive expectations rational expectations risk averse adverse selection moral hazard entrepreneurs 1. Time Value of Money If you are asked which you would prefer either having one dollar now or one dollar a year from now, most of you will say a dollar now rather than receiving the same amount a year later. That is, one dollar now is worth more than one dollar a year later. This is called the time value of money. Now, how much do you think the worth now of one dollar received next year? We use the concept of present discounted value. 1-1 resent Discounted Value (DV): In order to calculate the present discounted value of one dollar next year, we divide one dollar by 1 + interest rate, i.e., ( 1+ r). Thus, we have 1 DV =. (1+ r) Now, suppose the interest rate is 1 percent, i.e., r = 0.01, the DV is, 1 DV = = 0.99. (1+ 0.01) This means, one dollar next year is the value of 99 cents now. This is the reason why you choose one dollar now rather than one dollar next year. 2 Intertemporal 18
[Exercise] How much worth of 2 dollars to get paid at the end of two years is now, if the interest rate is 2 percents? 2 DV = 1.96078 2 (1 + 0.02) =. 1-2 Interest Rate The interest rate r is a price. It tells how many dollars next period we can get if we give up one dollar today. Therefore, the higher the interest rate, the higher the price is for consumption today. If you consume by one dollar today, you are giving up the opportunity to receive the interest by the amount of r 1.00 next period. Real Interest Rate and Nominal Interest rate: First, it is easy to see what the nominal interest rate ( ) is. The nominal interest rate is one you may see rates posted at banks and in the newspaper. For example, when you go to a bank and ask tellers how much the interest rate is now for your savings account. It is surely less than one percent now, as of January 2004. the interest rate told by a teller is the nominal rate of interest (or the nominal interest rate). Real interest rate is the difference between the nominal interest rate and rate of inflation. Real Interest Rate = Nominal Interest Rate Rate of Inflation Now, let us define r : real interest rate, i : nominal interest rate, and : expected inflation rate. We will have, r = i - or 19
i = r +, which means that the nominal interest rate = the real interest rate + the expected rate of inflation. [Exercise] How much is the today s worth of 2 dollars next year? Assume that the nominal interest rate rate of inflation i is 3%, of which the real interest rate is 2%. r is 1% and the expected DV = 2 [1+ = i] 2 [1+ (0.01+ 0.02)] = 2 [1+ 0.03] = 1.9417 [Story] Suppose you are considering to buy a good X now and it costs 100 yen per unit. But, you are asked to lend 100 yen at the same time by your friend. Your friend promised to pay an interest for borrowing 100yen in addition to 100 yen tomorrow. She is very clever and says the interest rate is 10% for borrowing 100 yen from you. You finally decide to lent 100 yen to her rather than buying the good X now. Now, let us assume the inflation rate is 10% per day and will be so tomorrow. rice of a good ( = 0. 10 ) money in yen Today t=0 100 (assumed) 100 (you lend to your friend) Tomorrow 110 110 (you get paid from your friend) In the above example, are you making any gains or loss? You might say you are happy because your friend appreciates your kindness for lending 100 yen today. But, think it again. You are making some loss under the above contract, although you can buy one unit of good X tomorrow, while you can buy it today too if you do not lend 100 yen to her. What you are making the loss is the sacrificed consumption today for tomorrow. Which is happier either the today s consumption or tomorrow s? Therefore, in general, if you lend some money and give up today s (or current) consumption for tomorrow (or future), you must charge more than the expected rate of 20
inflation. The charged interest rate is the nominal interest rate. Thus, the extra charge over the expected rate of inflation is the real interest rate. In other way, your willingness to give up today s consumption for tomorrow is, say, 3%. The rate is called your rate of time preference. Thus, if the (expected) inflation rate is 10% and your rate of time preference is 3%, then the nominal interest rate should be 3%+10%=13%. Then, you net gain is 3% when you get paid from your friend tomorrow. Otherwise, if you get paid only 10% under the inflation rate is 10%, you are forcing yourself to give up your current consumption, which is your psychic loss. 1-3 Supply and Demand for Loan-able Funds When there is no inflation, the real interest rate is equal to the nominal interest rate. But, if the rate of inflation is not 0 but some positive value, then the nominal interest rate is the price of loan-able funds. No Inflation Case: = 0 The real interest rate = the nominal interest rate r = i Figure 12 r Supply of loan-able funds r* Demand for loan-able funds 0 M* Quantity of Money Loan-able and Borrowed 21
Non-zero Inflation Case: 0 The real interest rate = the nominal interest rate the rate of inflation, which implies The nominal interest rate = the real interest rate + the rate of inflation i = r + Figure 13 i Supply of loan-able funds i** Demand for loan-able funds 0 M** Quantity of Money Loan-able and Borrowed In the case of non-zero rate of inflation, if you lend one dollar now, you should take the rate of inflation into account for the interest rate. Suppose, = 0. 02 and you say the (nominal) rate of interest i is also 0.02. Let us see how much you get next period. The amount you receive next period: one dollar (1+ i) = 1 1.02 = 1.02. During the period, the rate of inflation is 2%. Hence, the value of money decreases by 2%. That is, you lose the real value by the amount of 0.02 dollars. Note, inflation always reduces the value of purchasing power since the price of goods rises, while the goods are the same in quantity as the period before inflation. 22
Suppose the good in question costs one dollar now. If the inflation rate is 2 percents, the price of the good next period is 1.02 dollars. Now, you see. You get 1.02 dollars next period, when you led one dollar today. But at the same time the price of goods rises by 2 percent, which is the rate of inflation. Hence, the price next period is 1.02 dollars. Hence, by lending one dollar today you do not get any benefits, but rather you make loss by sacrificing the current consumption today for the sake of the consumption next period. Therefore, to avoid your loss, when you lend your money, your charge for the interest should include the rate of inflation. In our above example, if you want to have the real interest rate to be 2 percents, your interest rate (that is, the nominal interest rate) should be the sum of the real interest rate and the rate of inflation: i = r + = 0.02 + 0.02 = 0. 04. That is, the money interest rate is 4%. 2. The Market for Assets eople usually save money in the form of assets such as stocks, bonds, other financial securities, gold and so on. In order to buy these assets, people sacrifice current consumptions for the sake of future consumption. For giving up the current consumption, people get paid interest payments in return in the future. Hence, what important is present discounted values of those assets. Since DV over the n period is defined as DV = n Future Asset' s r ice( t) t= 0 t (1 + no min al int erest rate), t = 0,..., n, any changes in present discounted values will affect the demand for those financial assets. 23
Therefore, if you expect an increase in the interest rate (usually, we observe the nominal interest rates), DV of dollars you expect to receive in the future falls. This implies, the financial assets become less attractive. This will cause people to reduce the demand for financial assets. If we consider the financial asset in question now is stocks, i.e., financial securities, the price of shares on the stock market will fall. This is shown by the arrows in the figure below: Figure 14 price of share of stock Supply of stocks p* 1 Demand for stocks 0 S1 S* Quantity of Stock sold and bought Lesson 1: the nominal interest rate moves inversely with the prices of assets. Lesson 2: the real interest rate may be related with the expected rate of inflation. Note: Lesson 2 has may in the statement since I am not quite confident with this statement since I have no evidences with me. In fact, I am stating Lesson 2 from my memory of 30 years ago. Of course, if there is an increase in expected rate of inflation while the money rate of interest does not change, the real rate of interest must decrease. It depends on how fast the money rate of interest can adjust with the expected rate of inflation. On the other hand, if there is an increase in the expected rate of inflation, this increase may cause an increase in production of output such as GN, if the wage contracts are fixed between employers and employees during relevant terms. This implies that the real wage rate may fall in the future and, hence, the employers are more willing to hire unemployed people and to produce out put. Then, if the nominal interest 24
rate is staggered (that is, not flexible), then an increase in real output must lower the real rate of interest. 3 3. The Market for Risk In our daily life, we are seldom free from risk. What I mean by risk is an occurrence of unexpected events, while the term of risk is usually used rather in a negative way. There is another word to express the similar meaning as risk. That is the term of uncertainty. In some formal texts, risk is defined differently from uncertainty. We are not differentiating these terms here, while I am always using the term of risk. 4 Our text says that psychologists study risk-avoidance behavior of individuals by focusing on the anxiety to which uncertainty gives rise. We economists refer to this risk-avoidance behavior by saying that individuals are risk averse (rinciples of Micro-Economics by J. E. Stiglitz (1997) p.130). Note. risk averse: 3-1 Responding to Risk Various ways to avoid and mitigate risk simply avoid risk. In other words, don t get closer to any events with risk to keep one s option open. That is, don t leave you with only one choice, but rather with many choices. Diversifying risk. Don t put all of your eggs in one basket. That is, when you buy some financial securities, do not buy one company s stock only but buy different companies stocks. Transferring and sharing risks. Buy some insurances against an occurrence of unexpected event such as fire, sickness and so forth. 3-2 Limits on Insurance as protecting against risk Adverse Selection and Moral Hazard Adverse Selection ( ) The adverse selection problem arises when insurance companies try to raise their premiums and the best risks (persons) stop buying insurance but the worst risks 3 Sorry to say, but, since I am not a macro economist, please check this with macro economists. 4 I believe, the term of uncertainty is used when an unexpected event has a known probability distribution to the individual (or firm) in question. 25
(persons) buy insurance. Note. remium: the risk premium is the extra payment an individual or firm must receive to be willing to bear risks. For example, an insurance company promises to pay some amount of money if an individual buy an insurance policy against fire burning her own house. Suppose the value of her house is $100 and the probability of fire is 0.01. The expected loss = $100 times 0.01 = $1 This one dollar is the expected payment she can make to the insurance company. However, the insurance company will never sell an insurance policy promising the $100 payment for the loss of house due to fire, since there is no gain for the company at all. Then, if she pays $1.10 rather than $1 to the insurance company and the latter sells the insurance policy, the extra payment, i.e., 0.10 dollars (= 10 cents), is the risk premium. [A Small Talk] When you travel by air, you may want to buy an insurance against any accidents during your travel. If the probability of accident during travel is 0.01%, i.e., 0.0001, and the loss if accidents take place is 30,000,000 yen, the expected loss (or payment) is, the expected loss = 0.0001 x 30,000,000=3,000 Then, the fair price is 3,000 yen for the insurance. But, since the individual is usually risk averse, she may willing to buy the insurance by paying more than 3,000 yen and suppose she buys an insurance for 5,000 yen to receive 30,000,000 yen. The difference is, 5,000-3,000=2,000 yen, which is the risk premium for her. Moral Hazard Insurance reduces the individual s incentives to avoid the insured-against accident. For example, when you have an car insurance against car accidents, you may become less careless or more aggressive in driving your car. This sort of individual s behavior may take place by knowing damages due to car accident are covered by the insurance policy she buys. 5 5 lease do not risk your life when you drive your car. You are not taking into account the psychic values attached to you by your boy- or girl-friend. More importantly, do not, 26
please, forget your parents, sisters and brothers. 27