1

3. Supply and Demand In this chapter you will learn:

Determinants of demand Determinants of Supply How supply and demand respond to price, income, cost, and other variables Normal and inferior goods Elasticites Price controls: short and long run effects Tax incidence: who bears the burden of a tax – the answer may surprise you! Foreign exchange markets

3.1 Introduction We can define a competitive market for an output in the following way: the supply of the good is determined by firms producing the good while the demand for the good is determined by consumers who wish to consume it. Each economic agent (firm or consumer) acts in his or her own best interest and no one has any market power. When a transaction takes place, the property right involving the ownership of the product is transferred from the seller to the buyer and is protected by law. The price of the good is determined in the marketplace through the interaction of hundreds, if not thousands, of market participants. Firms choose how much to produce and how to produce it. They try to maximize their profit subject to their technology and the way they are organized. Consumers choose how much to buy and maximize their utility or happiness by spending their income but they are subject to a constraint involving their budget. The key to understanding how the market works is figuring out how supply and demand are determined. For an input market, e.g., labor, the roles are reversed; consumers supply the input while firms demand it.

Many markets are competitive in the sense we have described. So the model of a "competitive market" that we will develop can be widely used to make predictions involving price and quantity and how these variables might respond to other variables like income, taxes, government regulations, new competition entering the market, and even bad weather. Keep in mind that it is a model of a perfectly functioning market. We develop confidence in the model if its predictions are confirmed by the data.

3.2 Demand Let’s consider a particular market, the market for movies shown in the theater. What does the demand for movies depend on? The price of a movie ticket, income, the prices of related goods like popcorn or streaming videos that are related to movies, and advertising. Demand is then given by X = D(p, q, r, I, Ads), where X is quantity demanded, p is the price of a movie ticket, q is the price of popcorn, r is the price of some other good that is related to movies like streaming video rentals on iTunes, or DVD/Bluray disks, I is income, and Ads represents advertising. The notation "D( )" means that the quantity demanded, X, is a "function of," or "depends on," the variables listed inside the parentheses, e.g., p, q, I, and Ads in this case. So, quantity demanded is a function of price, the prices of related goods, income, and advertising.

Since X is related to p, q, r, I, and Ads by the demand function D( ), we can graph X versus any of the variables p, q, r, I, or Ads. Traditionally, the "demand curve" depicts a graph of the relationship between quantity and price, X and p. Suppose we pick a high price and calculate quantity demanded such as point A in the Figure. If the law of demand holds, then as the price falls more quantity is demanded and we move along the curve from A to B. Notice that quantity

2

increases as the price falls; the variables move in the opposite direction of one another. On the other hand, if we start at B and raise the price, people economize on the good and buy less so quantity falls and we move from B to A. Once again the price and quantity are moving in the opposite direction. Whenever two variables, X and Y, move in the opposite direction of one another, we say there is a negative correlation between the two variables and denote it as corr(X, Y) < 0. Thus, when the law of demand holds, corr(X, p) < 0, and "the demand curve" slopes downward.

Furthermore, the slope of the demand curve is defined as Δp/Δx, the rise over the run, which

is negative if the law of demand holds. The larger the slope is in magnitude, the steeper the demand curve. The smaller the slope is in magnitude, the flatter the curve is. For example, the demand for new cars might have a slope of - 0.53 and be fairly shallow, while the demand for cigarettes might exhibit a slope of - 1.7 and be very steep. A small increase in price will reduce the quantity demanded for a good with a shallow demand curve more than it will for a good with a demand curve that is relatively steep. So a small price increase will lower the quantity demanded of cars more than cigarettes. (The magnitude of a number is measured by absolute value. The absolute value of the slope is |Δp/ΔX| and it is always a positive number. The larger it is, the steeper the slope.)

We say that there has been a change in the quantity demanded whenever there is a move

along the demand curve, e.g., a move from A to B in the diagram above. However, when the entire curve shifts out or in, we say there has been a change in demand. A change in price will induce a move along the demand curve, while a change in any of the other variables (q, I, Ads) will cause the demand curve in the previous diagrams to shift, either out or in.

Since the demand function D(p, q, I, Ads) tells us how the quantity of the good demanded, X, is related to other variables like income, we can also study what happens when one of these other

p

X

Law of Demand

•

•

A

B

p

Cars

p

cigarettesD D

flat curve - small slope steep curve - large slope

3

variables changes. A change in income, for example, will cause a change in demand and the entire demand curve will shift. We can then graph this relationship, e.g., X versus I.

In general, income is a prime candidate for a variable that influences demand and there are three cases to consider. First, if people buy more of the good when income rises, or buy less when income falls, there is a positive correlation between X and I, corr(X, I) > 0.1 This is the case of a normal good and the graph of X versus I will slope upward, as in the move from A to B in the Figure on the left below. On the other hand, if people buy less of the good when income rises, or buy more of the good when income falls, there is a negative correlation between X and I, corr(X, I) < 0. We can depict this with a downward sloping curve when we graph income versus quantity demanded, a move from A to B in the Figure on the right. This is the case of an inferior good. Finally, if income and demand are unrelated, a change in income will produce no response in the quantity demanded. The correlation is zero in that case. The graph that relates income and quantity demanded is called the Engel Curve after the 19th century German statistician Ernst Engel.

Engel Curves

In general, the correlation between two variables tells us about their relationship. If two

variables are positively related to one another, the correlation is positive. If two variables are inversely related to one another, the correlation is negative. Remember: when two variables, say X and Y, always move in the same direction, then corr(X, Y) > 0, and the graph of the relationship is upward sloping. If they always move in the opposite direction, then corr(X, Y) < 0 and the graph is downward sloping.

3.3 Example: Graphing demand. Suppose demand only depends on price and income and is given by the equation

X = 100 - 2p + (1/4)I, where X is the quantity demanded, p is price, and I is income. How do we graph this equation? It has three variables, X, p, and I. Pick one and fix it. This allows you to choose values for the other two variables so you can graph their relationship. For example, to obtain the traditional demand curve, fix income, and then adjust the price and see what happens to quantity. Fix I = 100. Then substituting I = 100 into the demand equation, we obtain X = 100 - 2p + (1/4)100 = 125 - 2p. The two intercepts are (125, 0) and (0, 62.5) and the line connects them as depicted.

1 When two variables move in the same direction, either up together or down together, they are positively correlated. Let X = magnitude of an earthquake, Z = damage caused by the earthquake, corr(X, Z) > 0. When two variables move in opposite directions, one is up while the other is down, and vice versa, they are negatively related. Let X = beer consumed, Z = ability to drive a car, corr(Z, X) < 0.

X X

normalgood

inferior good

incomeincome

X X

normalgood

inferior good

incomeincome

A

B B

A

4

Also, notice that if income increases to 200, the demand curve will shift out for each price. This is the case of a normal good. The demand for a normal good will always shift out with an increase in income and shift back with a decrease in income.2

We can also graph X versus I by picking a value for p, the market price. Set p = 10. Then graph: X = 100 – 20 + (1/4)I = 80 +(1/4)I for different values of income. The Engel curve in this case will be upward sloping. What happens to the Engel curve when p increases to p = 20?

3.4 Shifts in Demand: Income What happens to the demand curve for movies when q, I, or Ads changes? It will either shift out or shift in. Consider income. The thought experiment is to hold the other variables p, q, and Ads constant, then change income and see what happens to the quantity of movies demanded. Consider the demand for movies and suppose that at the going price of $5 per movie, you are willing to go see two movies per month. Then suppose that you receive an increase in your income. If you are willing to go to a third movie, your demand for movies at $5 per movie has increased as a result of receiving more income and you will move from point A in the Figure to point B. This is also true at prices of $1, $2, $3, $4, $6, $7, so the entire demand curve will shift out as a result of the increase in income. A decrease in income will cause you to reduce the number of movies you go to each month. In that case, the commodity "movies in the theater" is a normal good.3

Many commodities appear to be normal goods, e.g., watches, high fashion items like blue

jeans, hybrid cars, houses, laptops, smart phones, meals in restaurants, liposuction, ManiPedi’s, and travel. It is interesting to observe an economy as it develops. In the 2000s, we are seeing demand for some of these items increase in developing countries like India as income increases.

2 You should try this. Set I = 200 and graph the new demand curve. What are the intercepts? What is the relationship of the new demand curve to the original demand curve? How does the demand curve shift when income increases from 100 to 200? Is it a parallel shift or does the curve swivel? 3 The word "normal" carries no ethical or moral connotation, nor does it carry a connotation about the quality of the good. It is simply a definition involving the relationship between quantity demanded and income.

p

X

62.5

125

p

X

D

•$5

2

A

p

X

D

•$5

2

A

3

• B

p

X

D

•

2

A

3

• B$5

5

For example, people who earn higher incomes in India are choosing to eat more meat products. This has implications for agriculture policy in other food exporting countries and will tend to raise the price of meat. Energy also appears to be a normal good, which has implications for energy prices worldwide. Economic development in China and India, that increases the demand for energy, will keep oil prices permanently higher in a long run sense as their economies continue to develop. This has implications for the standard of living in other countries like the US, Japan, and Europe that consume energy and will now have to compete in the energy market.

We have depicted the case of a normal good in the diagram below where we have graphed the traditional demand curve for movies on the left and income versus the quantity demanded of movies on the right. Suppose we start at point A in both diagrams and suppose there is an increase in income. This causes the demand for movies to shift to the right and we obtain point B in both diagrams (since price has not changed). Thus, if we know that the law of demand holds so the traditional demand curve is downward sloping, and we also know that the good is a normal good, i.e., corr(X, I) > 0, then an increase in income will cause the traditional demand curve to shift out and this will correspond to an upward sloping Engel curve.

Normal good

For an inferior good, an increase in income causes the consumer to spend less on the good,

while a decrease in income causes the consumer to spend more. Examples include milk, hamburger, macaroni and cheese, rental apartments, used cars, shoes purchased at Payless or Wal-Mart, and Keystone beer. For some, movies might be an inferior good, especially if they prefer watching shows on a big screen tv at home. Suppose the good "movies" is an inferior good. Start at point A in both diagrams and suppose income increases. The demand curve will shift back and pick up point B at the same price level (because price is fixed) in the left hand diagram. This corresponds to point B in the right hand diagram because income has gone up but quantity demanded has gone down as we move from point A to B. So the Engel curve is downward sloping in this case. Note that the traditional demand curve is still downward sloping because the law of demand will still hold for an inferior good.

Example: Is education a "normal" good? Wealthy societies choose to spend more resources on education than poor societies. So education is considered a "normal" good; as the wealth of a country increases, it spends more resources on education.

Example: Are children an "inferior" good? Wealthy people tend to produce fewer children than poor people. And people in developed countries where average income is high tend to produce fewer children than in poor countries where average income is low.

p

Movies

D

•

2

A

3

• B$5

I

Movies

•

•

A

B

The Demand Curve The Engel Curve

6

Inferior good

Japan has one of the world's lowest birth rates in the world. The average woman in Japan

produced about 1.8 children in 1975 and only about 1.38 children in 2010, the lowest ever in Japan and one of the lowest birth rates in the world. In 2014, the population shrank by about 268,000 people.4 Demographers estimate that Japan's population will fall from its current level of 125 million to 105 million by 2050. If there are fewer young people coming along, the demand for products on average will fall and this may have serious consequences for the economy. The Bandai Corporation, that makes toys such as the Power Rangers and Tomagochis, a popular electronic pet, started paying any employee having a third child one million yen (about $10,000) in 2004.

Research: Nobel Laureate Gary Becker combined these two facts about education and children. He argued that parents care about the quantity of children they produce and the quality of each child in the sense of how educated the child is. In wealthier societies parents apparently want fewer children, but of higher “quality,” i.e., more educated, than parents in poorer societies. In comparisons across countries, and in a particular country over time, the "quantity" of children tends to be an "inferior" good and “quality per child” tends to be a “normal” good.5

Application: Is government spending a normal good? There tends to be a positive correlation between total government spending and GDP, lending credence to the notion that government activities are a normal good. A measure of the income elasticity, defined below, of government spending and income or GDP is 0.313. This means a ten percent increase in national income leads to an increase in government spending of 3.13%, using quarterly data for the US, 1947 – 2014.6 This is actually known as Wagner’s Law, i.e., government spending is a normal good, and seems to have widespread empirical support across many countries.

3.5 Substitutes and Complements in Demand Other variables may also affect the demand for movies. For example, streaming video rentals and watching a movie in a theatre are probably substitutes so the price of a video rental may affect the demand for movies. Let q be the price of a video rental and suppose movies and videos 4 See http://www.washingtonpost.com/blogs/wonkblog/wp/2015/01/07/japans-birth-rate-problem-is-way-worse-than-anyone-imagined/ 5 Parents have two reasons for producing a lot of children in developing countries like India or in Sub-Saharan Africa. First, children constitute an important source of labor and hence income for the family. Second, children are the prime means of taking care of the parents when the parents are too old to produce for themselves. In developed countries like the US, children are banned from work at an early age by law and other means are available for financing the parent's retirement consumption, e.g., social security and private capital markets. 6 Formally, this estimate stems from the regression equation,

Ln(Govt) – Ln(Govt-1) = 0.313[Ln(GDPt) – Ln(GDPt-1)], with a t-stat of 9.3 and an R2 of 49.6%. (Data Source: FRED.)

p

Movies

D

•B • A

I

Movies

•

•

The Demand Curve The Engel Curve

A

B

7

are substitutes. Consider what happens to the demand for videos and the demand for movies when there is an increase in the price of videos, q. Suppose q doubles. Assuming that the law of demand holds for video rentals, this will lead to a lower quantity of videos being rented. Demand will shift toward substitutes so there will be an increase in demand for movies seen in the theater. Thus, higher q leads to lower video demand, corr(videos, q) < 0, because of the law of demand, and greater demand for movies, corr(movies, q) > 0, because they are substitutes. So higher q will cause the demand for movies to shift out when the two goods, movies and videos, are substitutes. This also works in reverse; lower q leads to greater quantity demanded of videos (because the law of demand holds for videos) and lower movie demand so the demand curve for movies would shift back.

The case of substitutes

Just the opposite happens for the case of complements. For example, q might represent

the price of popcorn. Higher q might lead to lower demand for popcorn, because of the law of demand, and might also lead to lower demand for movies if movies and popcorn are complements. In that case an increase in q would cause the demand for movies to shift back while lower q would cause the demand for movies to shift out. Notice that in the case of substitutes, the quantity demanded for the two goods moves in opposite directions when q increases. For the case of complements, they move in the same direction when q increases. (The same is true when q falls; they move in the same direction when they are complements.)

The case of complements

Advertising plays a large role in the movie industry. Movie producers must believe that it

increases demand or else they wouldn't advertise. In fact, billions of dollars are spent advertising the latest blockbusters. Thus, producers must believe corr(A, X) > 0. Draw the graphs of the demand curve and the relationship between advertising and quantity of movies demanded. What

8

should a movie distribution company do in a recession if corr(X, P) < 0, corr(X, I) > 0, corr(X, A) > 0, and income falls in a recession?

Application: Pharmaceutical drug prices have been increasing gradually throughout the early 1990s. Then in 1998 they began increasing dramatically. Coincidentally, in 1998 Congress changed the law to allow drug companies to advertise on television. Now we are inundated with commercials for these products. Drug companies must believe that the advertising increases demand for their product. Several recent studies indicate that the top thirty drugs whose prices have risen the most in the last decade are also the drugs that are most heavily advertised.7 One can reasonably conclude that Americans are paying higher drug prices to essentially pay for ads for those drugs on television!

3.6 Supply Supply will also depend on a variety of variables. For example, the supply of movies will depend on the going market price of a movie ticket because this generates revenue to the movie production and distribution companies. It may also depend on production costs like the salaries of the movie stars, location shooting, special effects, the film crew, and so on. Suppose Y is quantity supplied, and w represents the salaries of the movie stars to keep things simple. Then, Y = S(p, w), is the supply function; supply is a function of the price and the salaries of the movie stars. Typically, suppliers of a product will supply more of the good when the price is high than when it is low. So we typically expect supply to slope upward, i.e., corr(Y, p) > 0. We can label this the "law of supply." A movement along the supply curve is said to be a "change in the quantity supplied." A shift of the entire supply curve is said to be a "change in supply."

The interesting question is: how will supply respond to a change in w? We would imagine that fewer movies would be made if the salaries of the stars increase. In that case, an increase in w will cause the supply curve for movies to shift back. A decrease in w, a somewhat unlikely event, would cause the supply curve to shift out. Thus, corr(Y, w) < 0.

Application: It is interesting to note that movie stars today rarely make more than one movie per year now. In the 1930's and 1940's during the golden era of Hollywood, movie stars like Clark Gable, Cary Grant, Spencer Tracy, Katherine Hepburn, William Powell, and Myrna Loy would make three or four movies per year at the peak of their careers. Interestingly enough, the real income of movie stars has increased dramatically since the 1970s. Now it is not unheard of for an A-list star to make $20 million or more per movie. At the height of his fame, Clark Gable, the so-called King of Hollywood in the late 1930's and 1940's, made about $7000 per week or about $360,000 per year. If he made four movies in a year, this comes to about $90,000 per movie. Prices have increased about ten-fold since 1939. So Clark Gable made much less per movie than the stars make today, which is probably why there are fewer movies made today featuring stars than eighty years ago; it costs too much. This is exactly what our theory would predict.

3.7 Equilibrium In a competitive market the price is determined through the interaction of a large number of participants. This is depicted below. Thus, for the movie market we might posit the following model: X = D(p, q, I, Ads) is demand, Y = S(p, w) is supply, p = price of a movie ticket, q = price of popcorn, I = average income, Ads = a measure of advertising, and w = salary of the stars. In equilibrium S = D and the equilibrium price and quantity are given geometrically by the 7 See http://www.dailyfinance.com/2009/11/24/drug-ads-do-nothing-but-boost-prices-for-taxpayers/ and http://www.npr.org/templates/story/story.php?storyId=113675737

9

intersection of the two curves; pe is the equilibrium price and Qe is the equilibrium quantity transacted.

The model can be used to make predictions about what will happen in this industry if any of the variables (q, I, Ads, w) change. In order to make predictions we need to know how X is related to q, I, and A, and how Y is related to w. Our assumptions are: corr(X, I) > 0, corr(X, q) < 0, corr(X, Ads) > 0, and corr(Y, w) < 0. These are assumptions, not predictions. A prediction is about what happens to the market price and quantity when q, I, Ads, or w change. The test condition is to observe a change in one of the variables, (q, I, Ads, w). The prediction is what happen to the price p.

For example, an increase in income, say from economic growth, would cause the demand to

shift out if the good "movies" is a normal good. Only the demand curve will shift out because income does not enter the supply equation; income only enters the demand equation. Our model would predict that the price of a movie ticket will increase and the quantity transacted will also increase if income increases.8 On the other hand, an increase in the salaries of the stars w would probably cause the supply curve to shift back as costs go up. This in turn will cause the price of a movie ticket to rise and the quantity transacted to fall. So an increase in w would lead to fewer movies being made and the price of a movie ticket would be higher.

An individual market tends to be remarkably stable. When something changes like income there will be a change in the behavior of consumers and firms that causes the market to move to a new equilibrium point. One can think of these strong market forces as a natural mechanism that eventually finds the correct market price. Suppose the price is too high for some reason. What would we actually observe in a real market setting? A firm would have trouble making sales, its inventory would start to build up, orders would slow down, and this would create a surplus. The firm would have to cut back production and cut its price to increase sales. This naturally causes the price to fall until it reaches the equilibrium price once again. On the other hand, if the price is too low, we would observe consumers buying more than they usually do, the firm’s inventory would fall dramatically, and shortages would occur. The firm would realize it is running out of the good more quickly than usual and begin to produce more while raising their price. Eventually, the price would increase to its equilibrium level once again. The market tends to be very stable because of this natural mechanism.

3.8 Examples where price is not used to allocate the resource There is a flourishing black market in body parts, morbid as that sounds. KSFM 1025 reported (2012) that a kidney was going for $262,000, a liver was $157,000, and a heart was $119,000.

8 Recall from Chapter 1, A + TC --> P. In the movie market, A = corr(X, I) > 0, corr(X, q) < 0, corr(X, Ads) > 0, and corr(Y, w) < 0, TC = income increases, P = price of a movie ticket will increase.

p

X, Y

S

D

pe

Qe

10

Why is the price so high? Because there is a shortage of donors. And price is not used to allocate the resource, e.g., livers, for legal transplants. In that case, how is the good allocated? Typically, a medical protocol is used to determine if the patient is eligible for a transplant and this differs by organ. Once a patient passes the protocol they are put on a waiting list. Unfortunately, 18 people waiting for a transplant die every day in the US. Of course, the purchase of body parts is illegal in most countries, however, that does not stop the black market from operating (Pun intended.).9

You can typically drive on the roads, streets, highways, and bridges in the US for free. So when the price of something is zero, what does our theory imply? The theory tells us that people will use too much of the good and not economize. Since prices are not generally charged for use of public infrastructure, people will tend to drive too much and this will cause more damage to the roads and highways, and so on. In addition, companies will use trucking as a method of transporting goods across country rather than rail, which will also cause more damage to the infrastructure. However, for a variety of reasons the US is not taking care of its infrastructure. This has led to some high profile bridge collapses. For example, the I 35W bridge near the university of Minnesota in Minneapolis collapsed in 2007 killing 13 people, and injuring over 100 others. The Mount Vernon bridge in Washington State collapsed in 2013 when a truck struck the bridge. In fact, there are over 70,000 bridges that are under restricted use in the US, or about 11% of all bridges. The problem is that people do not economize when they are charged a zero price for something like driving on the roads.

3.9 Price Controls. Prices equilibrate markets and provide investors with information they can use to allocate their investments. When prices are fixed they will not perform these functions. More to the point, the natural mechanism described earlier in this chapter requires that prices be flexible. If prices are fixed, this mechanism will not work. In addition to equilibrating the market, if the price is rising, investors many times equate this with strong demand and are more willing to invest in that sector of the economy. On the other hand, if price is falling and investors feel it is because of weak demand, they will be less willing to invest in that sector. For example, the price of DVD's was increasing dramatically in the early 2000s and investors shifted a large amount of resources into that sector of the economy. As another example, the popularity of cell phones and their high price in the 2010s caused a large influx of investment into that sector. If prices are fixed they cannot provide investors with this sort of information.

9 See http://ksfm.cbslocal.com/2012/04/23/how-much-are-your-body-parts-worth-on-the-black-market/ If we allowed the market to allocate the resource only the wealthy would be able to afford the procedure. Is there a better way of doing this? How should a life and death procedure be allocated? This is a normative question that cannot be easily answered.

p

X, Y

S

Dp*

S D

shortage

Price Ceiling

11

Fixed prices can cause allocation problems to arise. First, consider a price ceiling. The price is fixed at p* in the figure and no higher price can be charged. At p* demand is greater than supply, D > S, and we will observe a shortage of the good. Price is not being used to allocate the good in this case. Some other method has to be found to allocate the good like rationing or standing in a line or queue. Examples include rent controls that keep the price of an apartment below equilibrium, and the price of health care where the government chooses how much to reimburse doctors treating patients in the Medicare program.

Application: Some have suggested that salaries be capped in professional sports. This would act as a price ceiling. At issue is the growing gap between rich teams and poor teams in some sports like baseball. Teams in a lucrative television market will be able to sign contracts that provide them with more revenue from the networks showing the games than teams in weaker television markets. This will give the wealthier teams an advantage when buying players. Many leagues institute television revenue sharing across teams to reduce this advantage and make the game more competitive.

Application: The price of health care is fixed below the market price for anyone in a health insurance program or Medicare in the US. This would imply there are shortages in health care and that care is being rationed. Rationing is another mechanism that is commonly used when prices are fixed. First come first served is an example of such a mechanism. So waiting in line is an alternative to allowing prices to increase.

Next consider the case of a price floor. No lower price can be charged. At p* below, supply is greater than demand and there is a surplus. Examples include dairy price supports and the minimum wage.

Example: The minimum wage. Suppose p = wage rate of unskilled workers, X = demand

for unskilled workers, Y = supply of unskilled workers, and p* is a price floor set above the equilibrium price. Does an increase in the minimum wage, increase unemployment among unskilled workers? The traditional theory says yes. However, Alan Krueger and David Card of Princeton challenged this view. They did a survey of firms and discovered that more firms would be willing to hire workers at a higher minimum wage than a lower one. Krueger and Card hypothesized that the higher wage was providing a signal to the job market. High skill workers require a higher wage than low skill workers to compensate them for their higher skill level. If a higher wage attracts a higher skilled worker, then we might expect unemployment to fall as firms are more willing to hire skilled workers than unskilled workers.

Application: Seattle instituted a city-wide minimum wage of $15 per hour in 2015, which will be put into effect gradually. Large employers (companies with more than 500 employees) have to raise their wage to $11 in 2015 and gradually to $15 by 2017. Smaller employers (fewer than 500 workers) have more time before they have to raise it the full amount. It will be interesting to see how this will affect employment in Seattle. However, there is no strong

p

X, Y

S

D

p*

D S

surplus

Price Floor

12

evidence that increasing the minimum wage causes an increase in unemployment. In fact, many studies find no effect at all!10

Example: Rent controls. Imagine there are two groups of poor people, those who can get a rent controlled apartment and those who cannot. The rent for those in controlled apartments is too low because of the price ceiling. The owners have no incentive to maintain the building and it begins to deteriorate as a result. Some buildings will be condemned forcing poor people who had been in a rent controlled apartment to seek another apartment that is not rent controlled. This migration of people within the city will raise rents for those who do not have a rent controlled apartment and they will actually be worse off than before rent controls were imposed. There is also an important distinction between the short run response and the long run response. In the short run price controls alter incentives in determining the supply of a product actually brought to the market. In the long run, controls can reduce the profitability of an investment. For example, in terms of investing in the quality of an apartment building, landlords who have rent controlled apartments may reduce the amount of maintenance. This can cause the amenities of the building to deteriorate over time.

Application: President Nixon's wage and price freeze. Inflation was becoming a problem so President Nixon imposed a price and wage freeze August 15, 1971 for 90 days. This was unprecedented in peacetime and the upcoming election in 1972 may have contributed to imposing the freeze, which polls indicated was desired by the public. The controls were imposed on large corporations and labor unions and so did not completely eliminate inflation. The freeze lasted close to 1000 days. Inflation was running at about 5% in 1971. By August 1972 it was down to 2.9%. When the controls were finally lifted the shortages caused by the controls caused inflation to spiral upwards to 7.4% by August 1973 and over 10% a year later.

3.10 Elasticity The concept of the elasticity measures the shape and position of the demand or supply curve. This is of critical importance for a number of reasons. First, a firm producing and selling a good needs to know how a change in its price will affect its sales. Suppose a competing firm has

Reduce your price: How much do sales increase?

recently lowered its price. The firm might contemplate lowering its price and it will need to know how a price cut will affect its own sales. The flatter the demand curve, the larger the 10 For a recent summary see: http://www.theguardian.com/commentisfree/2014/jun/11/the-evidence-is-clear-increasing-the-minimum-wage-doesnt-cause-unemployment

p

X∆X is large

p

X

Sales increase a lot :You're the hero!

DD

Sales increase only by asmall amount : You're the goat!

∆X is small

13

increase in sales for a given price cut, and the steeper the demand curve, the smaller the increase in sales for the same price cut. If you tell your boss to lower price because sales will increase a lot, as in the diagram on the left, you would be the hero of the company if you’re right. Of course, if you’re wrong because demand is actually really steep, as in the diagram on the right, then you might lose your job!

A second reason involves public policy. When a law is passed imposing a tax, it must state in the law exactly who will collect the tax. This is known as the legal incidence of the tax. A tax can be imposed on the supply side of the market, the demand side, or both. For example, sales taxes are usually imposed on firms; the firm collects the tax. On the other hand, social security payroll taxes are usually imposed on both the employer and the employee. However, the final economic incidence of a tax will depend on the shape of the supply and demand curves. In many cases, some agents will be able to shift their share of the burden of the tax onto the other side of the market. This is important because many politicians make assertions about the burden of a tax that are wrong, but politically popular. For example, many politicians claim that raising taxes on corporations will raise a lot of revenue but not harm consumers. However, when the corporate tax is imposed, many companies raise their price passing on some of the tax to consumers, or lower their wages passing some of the tax onto their own workers, thus shifting the tax burden to others.

Application: Social security programs worldwide are typically funded by a tax imposed 50% on workers and 50% on employers. Yet, policy analysts believe that employers are able to shift their part of the tax to workers in the form of lower wages so workers bear perhaps 90% of the tax.

Application: During the health care debate of 1993-‘94 a number of health care proposals were put forward. Some of the proposals were a bit hazy on financing. Some, however, would rely on the payroll tax with its 50 – 50 split. Under the Clinton proposal there would be a split of 80 – 20 imposed on employers and employees, respectively.11 However, if the evidence on the social security payroll tax is correct, this split is artificial; we would expect the tax to almost be fully borne by workers. Yet, Democrats at the time made a big deal out of the fact that employers would pay 80% of the tax.

To get at some of these issues we can define the price elasticity of demand as the percent change in quantity demanded for a given percent change in price. It is defined mathematically in the following way,

𝑬𝑫𝒑 = −∆𝑿𝑿∆𝒑𝒑

where ∆𝑋/𝑋 is the percent change in quantity and ∆𝑝/𝑝 is the percent change in price. There are statistical techniques that can be used to estimate this sort of elasticity using data on price and quantity (and other variables that affect demand). We can solve this first formula for the percent change in X,

∆𝑿𝑿 = −

∆𝒑𝒑 𝑬𝑫𝒑.

11 For a discussion of the Clinton plan and the various Republican alternatives in the ’93 – ’94 debate. see http://www.nytimes.com/1993/09/23/us/clinton-s-health-plan-the-republican-alternatives.html In fact, some of the Republican alternatives in 1993 have features like the individual mandate, for example, that are contained in The Affordable Care Act, also known as Obamacare. Seehttp://www.politifact.com/punditfact/statements/2013/nov/15/ ellen-qualls/aca-gop-health-care-plan-1993/

14

This is convenient if we know the elasticity EDp and the percent change in price. We can plug into the second formula to figure out how much quantity demanded will change given a particular change in price.

Example: Suppose the elasticity of demand for cruise ship vacations is EDp = 1.56, and

suppose price falls by 10%, so Δp/p = -10% < 0. How much will quantity demanded increase? Substitute into the second formula and simplify:

∆!!=  − −0.10 1.56 = 0.156 or 15.6%

So quantity demanded for cruise ship vacations increases by 15.6% for a ten percent drop in price. During a recession the demand for cruise ship vacations falls. A company offering such services can cut their price in order to restore demand for their product.

Example: Suppose the elasticity of demand for coffee is EDp = 0.22. and suppose price

increases by 17% = 0.17 because global warming is killing coffee trees. How much will the quantity of coffee consumed fall? Substitute into the second formula and simplify:

∆!!=  − 0.17 0.22 = −0.0374 or 3.74%

Coffee consumption falls by only 3.74% given a 17% increase in the price of coffee. Note: if the price elasticity of demand is less than one, the percentage change in

quantity will be smaller than the percentage change in price and the demand curve will be steep. If the price elasticity is greater than one, the percent change in quantity will be larger than the percent change in price and the demand curve will be flat.

Example, suppose EDp = 3.70. What happens if there is a 10% decrease in price, i.e.,

suppose Δp/p = - 0.10? Substitute into the second formula, Δx/x = - (- 0.10)(3.7) = 0.37 or 37% So a 10% decrease in price increases quantity demanded by 37%, which is much larger than

10%. Example: EDp = 3.70. What happens if there is a 12% decrease in price, i.e., suppose Δp/p =

- 0.12? Substitute into the formula, Δx/x = - (- 0.12)(3.7) = 0.444 or 44.4% Quantity demanded increases by 44.4% when the price falls by 12%. The increase in quantity

is large because the elasticity is large in magnitude. This reflects a demand curve that has a very shallow slope.

In the usual graph of a demand curve, the slope of the demand curve is Δp/Δx = m and since

the demand curve slopes downward, m < 0. The minus sign in the elasticity formula changes the number from being negative to being positive. For example, if the slope is –2, and p/x = 3, then the elasticity is −(−1/2)3 = 3/2 > 0. So we could also write the formula as EDp = - (1/m)(p/x). As long as demand slopes downward, the price elasticity of demand will be positive.

The flatter the demand curve, the smaller m is and the larger the price elasticity of demand. The steeper the demand curve, the larger m is and the smaller the price elasticity of demand. So demand is more sensitive to price the greater the elasticity in magnitude and this is reflected by a shallow or flat slope of the demand curve.

15

To see the impact of the slope on the elasticity, fix p = p* and x = x* so that p*/x* is fixed. Then swivel the demand curve from A to B to C about the point (x*, p*). As the demand curve gets steeper, m is getting larger in magnitude so 1/m is getting smaller in magnitude. As 1/m gets smaller, so does the elasticity, EDp = - (1/m)(p*/x*). So the price elasticity of demand gets smaller as the demand curve gets steeper.

There are two extreme special cases of interest. When the demand curve is perfectly

horizontal, we say it is "perfectly elastic.” On other hand, if the demand curve is perfectly vertical, we say it is "perfectly inelastic." In the first case, the slope of the demand curve gets smaller and smaller as we approach the perfectly elastic case. As m gets smaller, 1/m gets very large and goes to infinity for a perfectly elastic demand curve, i.e., EDp = ∞. On the other hand, as the demand curve gets steeper m goes up so 1/m goes down. In the extreme case, 1/m goes to zero as demand becomes perfectly vertical. If the demand curve is perfectly inelastic it has zero elasticity, i.e., EDp = 0.

Why do the two cases differ so dramatically? The greater the number of substitutes for a

good, the flatter the demand curve will be; the fewer the number of substitutes, the steeper the curve will be. Why? Suppose there is a close substitute available for the good in question and suppose the firm tries to raise its price for the good. What will happen? As the firm raises its price, it will lose almost all of its customers who will simply switch to the substitute good instead. 2% milk is highly substitutable for 1% milk. Brown eggs are highly substitutable for white eggs. On the other hand, if demand is perfectly inelastic, people are willing to pay any price to obtain the good because there are no close substitutes. Examples include a Mariners fan rooting for the Mariners rather than some other team, a book to a librarian, dental care for a hockey player, alcohol to an alcoholic, and cigarettes to a heavy smoker.

p

X

ABC

p*

X*

Elasticity falls as the Demand curvegets steeper and increases as it gets flatter.

p

X

p

X

DD

Perfectly Elastic Perfectly Inelastic

EDp EDp = 0= ∞

16

3.11 Elasticity and the firm's revenue Firms sometimes have to respond to market pressures and increase or lower their price in order to remain competitive. This will affect their revenue and hence their profits. So they are keenly interested in how much they will gain or lose in sales revenue when they alter their price. A firm's revenue is given by R = P x Y, where P is price and Y is quantity of sales, and Y = X in equilibrium, i.e., supply equals demand, so R = P x X. If demand slopes downward, a price cut will increase sales, so P falls and X rises. However, the net effect on R = P x X depends on which variable, P or X, changes the most. Revenue will fall if the price drop is larger than the quantity increase; revenue will increase if the increase in sales is larger than the price drop. We can get at this through use of the elasticity concept.

Since R = P x X, a change in revenue can only come from one of two places, a change in price or a change in sales. Thus, ΔR = XΔP + PΔX. Thus, the response of revenue to a change in price is given by

∆𝑹∆𝒑= 𝑿(𝟏 − 𝑬𝑫𝒑) .

This formula tells us if a price change will increase or decrease the firm's revenue.12 Example: Suppose demand is very elastic, e.g., EDP = 2. Then, ΔR/ΔP = X(1 – 2) = - X <

0. In this case, a price cut, ΔP < 0, will increase revenue ΔR > 0 because a reduction in price will be offset by a much larger increase in sales. This happens because the demand curve is very elastic, or flat.

Example: Suppose EDP = 1/2 instead. This is the case of a very inelastic demand curve. Substitute into the formula, ΔR/ΔP = X(1 – 1/2) = X/2 > 0. A price cut, ΔP < 0, leads to a loss in revenue (ΔR < 0) because demand is highly inelastic, price falls more than sales increase causing revenue to fall. So the above formula can help the firm decide whether to cut its price or not, a very useful thing!

Consider the following example. Initially, suppose the firm depicted on the left is charging a

price of $5 and it sells 50 units at that price so revenue is $250 at point a. Suppose the firm considers raising its price to $7, a move from a to b on its demand curve. Unfortunately, sales will fall off to only 20 units at the higher price. And revenue will fall to $140 (7x20) from $250, a net loss of $110. The gain due to the higher price is $2x20 = $40 but the loss in revenue due to lower sales is $5x30 = $150. The loss outweighs the gain causing revenue to fall.

A price inelastic demand curve is depicted on the right. Initially, revenue is $200 = 5x40. After the price increase, revenue rises to $266 = 7x38. The loss in sales due to the price increase is only $10 = 5x2, while the gain is $76 = 2x38. Thus, a large price increase causes only a small loss in sales and a net gain. A firm facing an elastic demand curve should try not to raise its price or its revenue will fall. On the other hand, a firm facing an inelastic demand curve can raise its price and gain revenue.

12 We can derive the formula in the following way, ΔR/ΔP = X + P(ΔX/ΔP) = X(1 + (P/X)(ΔX/ΔP)) = X(1 - EDP).

17

Application: The pricing of vinyl classical records in the 1930s is a classic example. The

Columbia Broadcasting Company bought the American Record Company in the 1930's and changed the name to Columbia Records. Edward Wallerstein wanted an estimate of the price elasticity of demand and temporarily lowered the price to make the estimate. A classical record cost $1.50 and a pop record was 35¢. Wallerstein reduced the price of a classical record to $1.00. After the estimate was made, Wallerstein was convinced demand was highly elastic so he permanently reduced prices and the response was enormous; the increase in sales was even larger than Wallerstein's estimate so revenue increased even more than expected. A 33.3% price reduction increased sales by 100%. What was the elasticity?

3.12 Other Elasticity Concepts There are other elasticity concepts that are of some use. We can also define the price elasticity of supply,

𝑬𝑺𝒑     =∆𝒀𝒀∆𝒑𝒑

If the law of supply holds the supply curve will be upward sloping and the elasticity will be

positive. In that case, the price elasticity gives us the supply response to a change in price. Everything that is true of the demand elasticity is also true of the supply elasticity. The steeper the supply curve, the larger its slope and the smaller its elasticity. The flatter the supply curve, the smaller its slope and the larger its elasticity.

Solve to get ∆𝒀𝒀 = 𝑬𝑺𝒑  

∆𝒑𝒑

If ESp = .24 (the supply curve is steep and inelastic) and price increases by 10%, then output supplied increases by 2.4%. If ESp = 1.4 (the supply curve is flat and very elastic), and price increases 10%, then output supplied increases by 14%.

We can define an elasticity with respect to any variable that supply or demand

depends on. Suppose we are interested in the relationship between income and quantity demanded. We can define the income elasticity of demand as

P

Q

b

a

loss

75

gain

D

P

Q

ba

loss

75

gain

D20 50 3840

Elastic Demand Inelastic Demand

18

𝑬𝑫𝑰 =∆𝑿𝑿∆𝑰𝑰

This is related to the Engel curve. If X is a normal good, the Engel curve is upward sloping.

If ΔI > 0, then ΔX > 0, too. In this case, the income elasticity will be positive. For example, the income elasticity of gasoline has been estimated to be about EDI = 0.82. Thus, a 10% increase in income will lead to an 8.2% increase in the quantity of gasoline demanded. To see this, solve the formula for the percent change in X,

∆𝑿𝑿 = 𝑬𝑫𝑰

∆𝑰𝑰

and substitute into the formula, (ΔX/X) = (0.10) x 0.82 = 0.082 = 8.2%. An inferior good, e.g., macaroni and cheese, will have an Engel curve that is negatively

sloped so X and I move in opposite directions, i.e., corr(X, I) < 0, and the income elasticity will be negative. Suppose EDI = - 0.23 for macaroni and cheese and there is a 7% increase in income. What will happen to the demand for macaroni and cheese? Substitute into the formula, (ΔX/X) = (- 0.23) x (0.07) = - 0.0161. A 7% increase in income will reduce the quantity demanded for macaroni and cheese by about 1.6%. What happens if income falls by 3.4%? Then (ΔX/X) = - 0.23 x (− 0.034) = 0.00782 = 0.78%, an increase of less than 1%. If income falls, the quantity demanded of macaroni and cheese increases because it is an inferior good.

Other prices also affect demand. For two goods, say, X1 and X2, that are substitutes, X1 increases when P2 increases. The quantity demanded for X2 falls when its price increases. If X1 and X2 are substitutes, then X1 will shift out when P2 increases, i.e., corr(X1, P2) > 0. We can define a cross price elasticity in the following way,

𝑬𝟏𝟐 =

∆𝑿𝟏𝑿𝟏∆𝒑𝟐𝒑𝟐

In the notation "E12," the "1" in the "12" subscript stands for X1 while the "2" in the "12" subscript stands for P2. In the case of substitutes, E12 > 0. In the case of complements, E12 < 0. For example, if the p2 increases 10% and E12 = 2, then x1 increases 20%. Because they are substitutes On the other hand, if the price p2 falls by 12% and E12 = - 0.32, then x1 increases 3.84% because they are complements.

3.13 Public Policy Issue: Who bears the burden of a tax? When the government imposes a tax it must do so in a specific law and it must state in the law who is to collect the tax. This is known as the legal incidence of the tax. The economic incidence of a tax is how much of the tax is borne by consumers and firms after the market has adjusted to the tax. It is the properties of the supply and demand curves that will determine the economic incidence of a tax, not the law, and the economic incidence will generally differ from the legal incidence.

The starting point of our analysis is point A, where S = D. The initial price is p0 and the initial quantity is Q0. There are three steps in the analysis. Suppose the tax is imposed on consumers by law. First shift the demand curve down by the amount of the tax to obtain the "after tax" demand curve D*. Second, find the new quantity transacted after the tax, Q1, where S = D*. Third, find the two new prices that determine the economic incidence of the

19

tax, the after tax consumer price pc and the after tax producer price pp. The difference between the two, pc - pp, is always equal to the tax rate. The consumer price, pc, can be found at point C on the before-tax demand curve at the new quantity Q1. This is the price consumers are willing to pay to receive Q1. The producer price pp can be found at point B where S = D*. This is the point where firms are willing to supply Q1 at price pp. From the diagram, it appears that both sides of the market share in the burden of the tax because the consumer price goes up by a portion of the tax and the producer price falls by a portion of the tax. The economic incidence reveals that both consumers and firms share in the burden of the tax even though the entire tax was initially imposed on consumers. Firms bear part of the tax because the price the firm gets to keep fell from po to pp.

Next, suppose the government legally imposes the entire tax on firms in the same market. First, start at A in the diagram on the right and shift the supply curve up by the amount of the tax to obtain the new "after tax" supply curve S*. Second, find the new quantity Q1 where S* = D, point D in the diagram. Finally, find the two after-tax prices, pc and pp. The consumer price can be found from the demand curve at the new quantity Q1, point D. The producer price can be found from the old supply curve S at the new quantity Q1, point E. It appears that firms are able to shift some of the tax to consumers because pc increased by a portion of the tax while pp fell but by only a small portion of the tax.

Example: p0 = $1.00, tax rate = 10¢ per unit. Then pc = $1.05 and pp = $0.95. Both sides

share in the tax equally, consumers pay 5¢ more out of a tax of 10¢ and firms get to keep 5¢ less out of a tax of 10¢. It doesn't matter on whom the law imposes the tax; both sides share in it equally in this example.

There are two general conclusions. First, the economic incidence of the tax depends on the properties of supply and demand, not what it says in the law. Second, it doesn't matter who initially pays the tax. The initial burden will generally be shifted so that in general both sides of the market will share in the burden of the tax. The consumer price will rise a bit and the price the firm gets to keep will fall.

In some extreme cases one side of the market might even be able to shift all of the tax to the other side. For example, suppose demand is perfectly inelastic. A tax on firms causes the supply curve to shift up by the amount of the tax. The consumer price rises by the full amount of the tax. Firms shift 100% of the tax to consumers!

General rule: the more price elastic demand is, the more the burden of a tax will be shifted to firms because there are substitutes for the firm's good. The less price elastic demand is, the

p

X,Y

p

0

0

D

S

Impose a Tax on Consumers Impose a Tax on Producers

D*

tax

Q Q1

p

p

c

p

p

X,Y

p

0

0

D

S

Q Q1

p

p

c

p

tax

S*

tax

taxA AD

B

C

E

20

fewer good substitutes there are for the taxed good and the greater the burden borne by consumers will be. The greater the price elasticity of supply, the lower the burden firms will bear. The more price inelastic supply is, the greater the burden firms will bear.

Application: In late 1990 a luxury tax was passed. The purpose was to raise revenue to

reduce the federal deficit. The Bush Administration estimated that the tax would raise about $1.5 billion over 5 years or about $300m each year. However, the tax only raised $31m in 1991. Why? Sales of yachts, a primary target of the tax, fell by 90%. The demand for luxury goods was more elastic than the Bush Administration had reckoned. In fact, the tax cost the Treasury Department more than $31m to administer and actually increased the deficit!

3.14 The Market in Foreign Exchange Note that in any market in the US, the price is denominated in "$ per unit" of the good. In Japan, the price is denominated in "Yen per unit," and so on for other countries. The quantity variable is simply the units of the good, e.g., ounces, gallons, barrels, etc. We can apply the analysis of supply and demand to the market for foreign exchange. There are people who are willing to buy and sell various currencies and the exchange rates are the prices of the various currencies determined in the marketplace. In the market for US dollars, for example, the "price of a dollar" is denominated in some other currency like British pounds per dollar or Yen per dollar, and the quantity is "dollars." For example, suppose we compare the dollar to the British pound, £. Then the "price" of a dollar is how many pounds one is willing to give up to receive one dollar, £/$.

From the diagram below, 0.75 British pounds will exchange for $1. The number of pounds one is willing to give up for $1 is known as the exchange rate between pounds and dollars. If there is an increase in the demand for dollars, D will shift out and the price or the exchange rate will rise. Dollars will become more valuable because it takes more pounds to buy a dollar and the dollar is said to appreciate in value. Of course, the pound is the currency the dollar is appreciating against so we could also say the pound is depreciating against the dollar.

p

X,Y0

0

DS

Q Q

pc

p

tax

A

S*

p = p

1=

$D

S£/$

0.75

21

Let e(£/$) represent the exchange rate "pounds per dollar." In the example above this is e(£/$) = 0.75. This says 0.75£ = 1$. There is also a "pound sterling" market. When comparing the pound with the US dollar in the pound sterling market, the price of a pound is the number of dollars you must give up to get one pound, or e($/£), i.e., dollars per pound. This will be the multiplicative inverse of the exchange rate in pounds per dollar, i.e., e($/£) = 1/e(£/$). So if e(£/$) = 0.75, then e($/£) = 1/0.75 = 4/3 = 1.33334, or 1.33334$ = 1£.

There is an intimate connection between the supply of one currency and the demand for

another currency. In order to obtain one currency you must give up another to get it. When the demand for one currency increases, currency traders must be supplying another currency. Suppose the demand for dollars increases as depicted and suppose traders are supplying pounds. Then, as the demand for dollars shifts out, so, too, does the supply of pounds. This causes the dollar to appreciate and become more valuable relative to the pound and the pound to depreciate or become less valuable relative to the dollar. If the dollar appreciates to e(£/$) = 0.90 so 0.90£ = 1$, as in the diagram, then the pound must depreciate from e($/£) = 1.334 to e($/£) = 1.111.

If markets are efficient, certain equivalences must hold across currencies. Let € = Euros, and suppose e(€/£) = 3.5 so 3.5 € = 1£, i.e., it takes 3.5 Euros to obtain one pound. Then, if e(£/$) = 0.67, we can figure out how many Euros it takes to get one dollar. Since 1£ = 3.5 €, it follows that (0.67) x 1£ = (0.67) x (3.5) € = 2.345 €, and since 0.67£ = 1$, it also follows that 1$ = 2.345€, i.e., e(€/$) = 2.345. Thus, e(€/£)e(£/$) = e(€, $). Furthermore, e($/€) = 1/(e(€/$) = 0.4264. As another example, let ¥ = Japanese yen, L = Italian lira. Suppose, e(L/¥) = 2 so 2L = 1¥ and e(¥/$) = 125 so 125¥ = 1$. Then e(L/$) = 250 and e($/L) = 0.004. This follows because e(L/$) = e(L/¥) e(¥/$) and e($/L) = 1/ e(L/$).

3.15 Consumer's Surplus Consider the demand curve. It tells us what people are willing to pay for each unit of the good. Consider the demand for apples. There is a consumer who is willing to pay $10 for the first apple but doesn't have to because she can pay the going market price, which is lower. The rectangle a is an additional surplus or gain she receives by paying the low market price for the first apple rather than what she was willing to pay, $10. She is willing to pay $9 for the second apple but doesn't have to; she pays the market price and so the rectangle b is another surplus gain. The total consumer's surplus is the triangle emphasized in the Figure on the right. When the market price falls, consumers are better off and the surplus triangle increases in size. When the market price rises, the surplus triangle gets smaller and consumers are worse off. So we can use the consumer's surplus as a measure of the consumer's well being when the market price changes.

$D

S£/$

0.75

D

S$/£

1.3340.90

D'

S'

1.111

£dollar market British pound market

22

Consider a simple example depicted below. The Consumer's Surplus for the price of $8 when

500 units are purchased is given by the triangle 16-8-A. The formula for calculating the area of a triangle is Area = (1/2)(base)(height). The base of the Consumer's Surplus triangle is 500 and the height is 8. Thus, the Consumer's Surplus is $2000.

When the price changes the Consumer's Surplus changes as well. Suppose the price increases

from $8 to $12. The new Consumer's Surplus after the price increase is area C. The new Consumer's Surplus is (1/2)(250)(4) = 500. Therefore, the loss in Consumer's Surplus when the price increases from $8 to $12 is 2000 - 500 = $1500. (Note area D = (250)(4) = 1000 and area E = (1/2)(250)(4) =500 for a total loss in CS of 1000 + 500 = 1500.)

3.16 Summary and conclusion We studied the most basic concepts of the marketplace in this chapter, supply and demand, and developed a simple but powerful model of a single market. The market price is generally determined by supply and demand. There is a natural mechanism that equilibrates the market and markets tend to be amazingly stable as a result.

When governments attempt to fix prices, a misallocation of resources will generally occur. The classic examples are rent controls, agricultural price supports, and the minimum wage. When apartment rents are too low, there is no incentive for developers to build new apartments or for owners to maintain existing buildings. When prices paid to farmers are kept too high by a price floor, too many resources are devoted to agriculture and the price to consumers is too low possibly contributing to the obesity problem. Should salaries of athletes be capped?

We applied the model of a single market to the imposition of a tax and foreign exchange. In general, the laws of supply and demand will allocate the burden of a tax between buyers and sellers, not the law. A tax imposed on one side of the market can be shifted entirely to the other side of the market. We also studied the market for foreign exchange. Currencies can be bought and sold just like any other commodity and this activity determines exchange rates.

applesD

$1098

S

1 2

market price

surplus

ab

consumer's surplustriangle

apples

P

Q

S

D

500

8

16

consumer'ssurplustriangle A

P

Q

S

D

500

8

16

A

S'B

12

250

C

D E

23

Important Concepts Determinants of demand Change in quantity demanded versus a change in demand Shifts in demand Income (normal good, inferior good) Other prices (substitute, complement) Determinants of supply Price control Elasticity price elasticity of demand income elasticity of demand cross price elasticity of demand (substitutes, complements) price elasticity of supply Tax incidence legal incidence economic incidence Foreign exchange Consumer's surplus Review Questions 1. What is the difference between a change in demand and a change in quantity demanded? 2. How does the demand curve shift when income changes? Discuss both the normal goods

case and the inferior goods case. 3. How does the demand curve respond when the price of another good changes? Discuss

the substitutes case and the complements case. 4. What variables might affect supply? How will the supply curve respond to a change in

any of these variables? 5. Predict how the equilibrium price and quantity will respond to a change in income.

Predict how the equilibrium price and quantity will respond to a change in the price of a substitute commodity. Predict how the equilibrium price and quantity will respond to a change in the price of a good that is a complement.

6. How does a price ceiling affect the market? How does a price floor affect the market? 7. Carefully define the various elasticities. What does a positive cross price elasticity of

demand mean? What does a negative income elasticity of demand mean? 8. Who bears the economic burden of a tax? What is the difference between the legal

incidence of a tax and the economic incidence? 9. How is an exchange rate defined? What happens to the exchange rate when a currency

appreciates? When it depreciates? Practice Questions 1. Suppose X = D(P, I, A), where A = advertising. Also assume corr(X, P) < 0, corr(X, I) >

0 and corr(X, A) > 0. How can the firm offset the drop in sales of its good if a recession occurs and income falls?

a. The firm can raise price. b. The firm can maintain its advertising. c. The firm can increase its advertising. d. The firm can lower its advertising.

24

2. Suppose there is a price ceiling imposed on tuition for college. What would happen to

the shortage if the demand for college degrees increased? a. Nothing, since a price ceiling in this case would not affect the market. b. The shortage would decrease over time as demand shifted out. c. The shortage would increase over time as demand shifted out. d. With a price ceiling there is a surplus and the surplus will increase as demand

shifts out. 3. Suppose corr(grade in 305, sunshine) < 0. Graph the relationship below.

4. If the elasticity of the supply of grain (Y) with respect to the temperature (T) is 0.71 and

the temperature increases by 8%, what is the effect on supply? a. 5.68% d. 0.0568% b. 0.568% e. 568% c. 56.8%

5. If the demand for beer near a college campus is perfectly inelastic, who will bear the

burden of an increase in the tax on beer? a. Beer companies. b. Students. c. Both beer companies and students will share in the burden. d. Burger King will bear the burden after the riot. 6. Suppose demand for Gatorade is given by X = D(p, q, I, E), where p is price, q is the

price of a related good like coke, I is income, and E is the amount of exercise undertaken. Assume corr(X, E) > 0, i.e., X and E are positively correlated, and corr(X, I) > 0. Supply is given by Y = S(p, w) where p is price and w is unit labor cost. What would happen to p if a new report were released extolling the health aspects of exercise?

a. Price would increase because demand would shift out. b. Price would increase because demand would shift in. c. Price would decrease because supply would shift out. d. Price would decrease because supply would shift in. 7. From the last question, the graph of X versus E would be a. upward sloping. b. downward sloping. c. flat.

grade

sunshine

25

Answers 1. c. 2. c. 3. The graph should be downward sloping; your grade will probably fall if the sun is shining and the weather is pleasant since you will be less motivated to study. 4. a. 5. b. 6. a. 7. a.