CHAPTER 4: APPLICATIONS OF SUPPLY AND DEMAND “You cannot teach a parrot to be an economist simply by teaching it to say “supply” and “demand.””
Anonymous SUMMARY A. Elasticity of Demand and Supply 1. Price elasticity of demand measures the quantitative response of demand to a change in price. Price elasticity of demand de mand (E ( E D) is defined as the percentage change in quantity demanded divided by the percentage change in price. That is, Price elasticity of demand = E D =
2.
3. 4.
5.
6.
percentage change in quantity demanded percentage change in price
In this calculation, the sign is taken to be positive, and P and Q are averages of old and new values. We divide price elasticities into three categories: (a) (a) Demand is elastic when the percentage change in quantity demanded exceeds the percentage change in price; that is, E D > 1. (b) Demand is inelastic when the percentage change in quantity demanded is less than the percentage change in price; here, E D < 1. (c) (c) When the percentage change in quantity demanded exactly equals the percentage change in price, we have the borderline case of unit-elastic demand, where E D = 1. Price elasticity is a pure number, involving percentages; it should not be confused with slope. The demand elasticity tells us about the impact of a price change on total revenue. A price reduction increases total revenue if demand is elastic; a price reduction decreases total revenue if demand is inelastic; in the unit-elastic case, a price change has no effect on total revenue. Price elasticity of demand tends to be low for necessities nec essities like food and shelter and high for luxuries like snowmobiles and vacation air travel. Other factors affecting price elasticity are the extent to which a good has ready substitutes and the length of time that consumers have to adjust to price changes. Price elasticity of supply measures the percentage change of output supplied by producers when the market price changes by a given percentage.
B. Applications to Major Economic Issues 7. One of the most fruitful arenas for application of supply-and-demand analysis is agriculture. Improvements in agricultural technology mean that supply increases greatly, while demand for food rises less than proportionately with income. Hence free-market prices for foodstuffs tend to fall. No wonder governments have adopted a variety of programs, like crop restrictions, to prop up farm incomes.
8. A commodity tax shifts the supply-and- demand equilibrium. The tax’s incidence (or impact on incomes) will fall more heavily on consumers than on producers to the degree that the demand is inelastic relative to supply. 9. Governments occasionally interfere with the workings of competitive markets by setting maximum ceilings or minimum floors on prices. In such situations, quantity supplied need no longer equal quantity demanded; ceilings lead to excess demand, while floors lead to excess supply. Sometimes, the interference may raise the incomes of a particular group, as in the case of farmers or low-skilled workers. Often, distortions and inefficiencies result.
CONCEPTS FOR REVIEW Elasticity Concepts Price elasticity of demand, supply, elastic, inelastic, unit-elastic demand, E D = % change in Q/% change in P, determinants of elasticity, total revenue = P × Q, relationship of elasticity and revenue change Applications of Supply and Demand Incidence of a tax, distortions from price controls, rationing by price vs. rationing by the queue FURTHER READING AND INTERNET WEBSITES Further Reading If you have a particular concept you want to review, such as elasticity, you can often look in an encyclopaedia of economics, such as John Black, Oxford Dictionary of Economics, Economics , or David W. Pearce, ed., The MIT Dictionary of Modern Economics . The most comprehensive encyclopaedia, covering many advanced topics in four volumes, is John Eatwell, Murray Milgate, and Peter Newman, The New Palgrave: A Dictionary of Economics . The minimum wage has generated a fierce debate among economists. A recent recen t book by two labour economists presents evidence that the minimum wage has little effect on employment: David Card and Alan Krueger, Myth and Measurement: The New Economics of the Minimum Wage. Wage . Websites There are currently no reliable online dictionaries for terms in economics. There are few good websites for understanding fundamental economic concepts like supply and demand or elasticities. There is a concise online encyclopaedia of economics at www.econlib.org/library/CEE.html , which is generally reliable but covers only a small number of topics. Sometimes, the free site of the Encyclopaedia Britannica at www.britannica.com will provide background or historical material. Current issues such as the minimum wage are often discussed in policy papers at the we bsite of the Economic Policy Institute, a think tank focusing on economic issues of workers, at www.epi.org
QUESTIONS FOR DISCUSSION 1. “A good harvest will generally lower the income of farmers.” Illustrate this proposition using a supply-and-demand diagram. A good harvest will shift the supply curve to the right (from SS to S’S’) – as more farm produce is produced at each price:
P
D
S
S'
E e c i r P
E'
S
S'
D
Quantity
Q
An increase in supply lowers the equilibrium price (the new equilibrium E’ is further down the price axis than E – the bold red arrows show the changes in price and quantity). Total revenues are equal to price times quantity ( P × Q). P is lower, and Q is higher – so it is ambiguous as to whether total revenues rise or fall. To determine this, the relationship between the change in quantity to the change in price, as the equilibrium moves along the demand curve from E to E’, needs to be known. The price elasticity of demand measures how much the quantity demanded of a good changes when its price changes. The precise definition of price elasticity is the percentage change in quantity demanded divided by the percentage change in price: E D =
percentage change in quantity demanded percentage change in price
If the percentage change in quantity is greater than the percentage change in price, demand is price elastic (E ( E D > 1). If the percentage change in quantity is lower than the percentage change in price, demand is price inelastic ( E D < 1). If the percentage change in quantity is equal to the percentage change in price, demand is unit-elastic ( E D = 1). The demand curve for farm produce will be price inelastic. inelastic. That is, even if bread becomes very cheap, people are unlikely to buy too much more of it – there’s only so much our taste buds and stomach can stomach! We also won’t store large quantities of bread we don’t consume immediately, as it goes stale if it is not frozen. Conversely, if bread became dear, we would still buy similar amounts as it is a necessity – we’d be more likely to cut back on luxuries to make way for the expensive bread.
As demand is inelastic, a fall in price will lead to a proportionally smaller rise in quantity demanded (by definition, E D < 1, so % change in Q < % change in P). Since Q has increased proportionally less than P has decreased, P × Q will be decreased – i.e. farm revenues are lower, hence farmers’ incomes are lower . This can also be seen from the diagram. Revenue is given by the area of the rectangle drawn from the origin to the equilibrium point. The area of the rectangle drawn to E’ (in light blue light blue)) is less than that of the rectangle drawn to E (in (in light pink). pink ). This diagram shows that, “A good harvest will generally lower the income of farmers.” 2. For each pair of commodities, state which you think is the more price-elastic and give your reasons: perfume and salt; penicillin and ice cream; automobiles and automobile tyres; ice cream and chocolate ice cream. Perfume will be more price-elastic than salt. Perfume is much more of a luxury. A low price would induce people to buy more perfume, but if price were increased too high people would substitute other goods for it.
Although not a necessity, nearly every household will have some salt as a food flavouring. A low price will not no t induce you to stockpile salt, and the price would have to rise very drastically for people to refrain from buying it.
Penicillin will be more price-elastic than ice cream. Ice cream will be less price-elastic because the time for you to consume it is much shorter than for penicillin. Ice cream melts very quickly (I’m assuming we’re buying a cone – not something you store in the refrigerator; and even if you did store it, there’s limited space) – so you buy it with a view of eating it immediately. Even if the price drops drastically, there is only so much ice cream you are willing to eat immediately. If penicillin were to drop in price, you would expect hospitals and pharmacies to buy more, as they can store it for a long time.
Automobiles will be more price-elastic than automobile tyres. While both are necessities, and are complements to each other, the following reasons lead me to think tyres will be more price-inelastic p rice-inelastic than the car. A car is more of a luxury good than a tyre – and certainly more expensive. You will take longer to decide which car to buy, and will be more sensitive to price as it is a larger expense. Conversely, tyres are relatively cheap and you are most likely to buy one immediately after an accident; in a hurry, without being too sensitive to price.
Chocolate ice cream will be more price-elastic than ice cream. If you are specifically looking for chocolate ice cream, and it rises in price, you are less likely to want to switch to cheaper vanilla or strawberry ice cream. If any ice cream will do, and chocolate ice cream rises in price, you will happily switch to cheaper flavours.
3. “The price drops by 1 percent, causing the quanti ty demanded to rise by 2 percent. Demand is therefore elastic, with E D > 1.” If you change 2 to ½ in the first sentence, what two other changes will be required in the quotation? “The price drops by 1 percent, causing the quantity demanded to rise by ½ percent. Demand is therefore inelastic, inelastic, with E D < 1.”
4. Consider a competitive market for apartments. What would be the effect on the equilibrium output and price after the following changes (other things held equal)? In each case, explain your answer using supply and demand. a. A rise in the income of consumers. Average incomes are a determinant of demand, so a rise in the income of consumers will increase the demand for apartments. An increase in demand, with supply constant for the time being, will lead to an increase in the price and quantity of apartments:
P
D
D'
S
E' e c i r P
E
D
S Quantity
D'
Q
b. A $10-per-month tax on apartment rentals. A $10-per-month tax means that for each ‘quantity’ of apartments, t he price of the apartment (i.e. the rent) will be $10 higher; shifting the supply curve up by $10 everywhere. This is effectively a decrease in supply. The supply curve shifts from SS to S’S’, leading to a higher price and lower quantity:
P
S' D
S $10 $1 0 E'
e c i r P
S'
E
D
S
Q
Quantity
c. A government edict saying apartments cannot rent for more than $200 per month. The government edict has placed a maximum ceiling of $200 per month on the price:
P
D'
D
S E
e c i r P
E'
$200 $2 00 cei lin ling g price
S
D'
Quantity
D
Q
If the edict were not in place, assume the market would clear at E, with supply and demand being in balance. The maximum ceiling (the grey line) prevents the price from rising to this point. At the ceiling price, demand does not match supply. There is greater demand for apartments than supply ( DD DD is further to the right than SS SS). ). The red line illustrates this. There is a shortage of apartments. A non-price mechanism is needed to ration the deficient supply to the demand – most likely allocation through the political system, as apartments are given out on some criteria of need. The demand is reduced to D’D’ and an equilibrium is found at E’. This has reduced the price and quantity of apartments.
d. A new construction technique allowing apartments to be built at half the cost. Due to the improved technology of apartment building, the cost of production has been halved. Twice as many apartments can be provided at the same price. The supply curve will shift to the right, from SS SS to to S’S’ S’S’ – – the quantity supplied will be doubled for each price. At the new equilibrium, E’, price will be lower and the quantity will be higher:
P
D
S'
S
E
e c i r P
E'
D
S, S'
Q
Quantity
e. A 20 percent increase in the wages of construction workers. A 20 percent increase in the wages of construction workers is an increase in input prices, and hence an increase in costs of production. The quantity of apartments at each price will be lowered, and the supply curve will shift to the left, from SS SS to to S’S’. The price of apartments will rise and their quantity will fall:
P
D
S'
S
E' e c i r P
E S' D
S Quantity
Q
5. Consider a proposal to raise the minimum wage by 10 percent. After reviewing the arguments in the chapter, estimate the impact upon employment and upon the incomes of affected workers. Using the numbers you have derived, write a short essay explaining how you would decide if you had to make a recommendation on the minimum wage. A minimum wage sets a minimum floor on wages. A supply-and-demand diagram can illustrate its effects on low paid workers:
Wages
S
D E
Wmin
U
LF
e c i r P
Wmarket M S
D Quantity
Employment
(N.B. I’ve used ‘Wages’ instead of price, and ‘Employment’ instead of quantity. But they
amount to the same thing, as your wage is the price paid for your labour, and employment is the quantity of workers paid.) Before the raise in the minimum wage, the market-clearing equilibrium would have been at M and the market wage paid to the low paid would have been W market. But as the minimum wage is raised to W min, the number of workers demanded moves up the demand curve, DD DD,, to E. This results in a new equilibrium where fewer workers are employed, but those that are enjoy a higher wage. Note also that the number of workers attracted to the market at the higher minimum wage (perhaps before they had lived on unemployed benefits, or been in education, or had been retired) moves up the supply curve, SS SS,, to LF LF.. We see that the quantity of workers supplied exceeds the quantity demanded (SS ( SS is is further to the right than DD DD)) – seen in the red line joining E and LF LF.. This represents a surplus of workers – unemployment, of an amount U. (N.B. There is a difference in the drop in employment and the rise in unemployment. Some people who were we re previously employed will be priced out of the jobs market – this is the drop in employment. But others, who were not previously working but would have entered the jobs market enticed by the higher wage, also find themselves priced out.)
So in summary, a rise r ise in the minimum wage will put some people out of work (employment falls), it would prevent some people from getting ge tting a job (unemployment rises), but those who do work at low wages have a higher wage. This answer has so far been qualitative. By considering price elasticities, a more quantitative answer can be given. The minimum wage has risen by 10 percent, so the percentage change in price (the denominator in the elasticity) is 10 percent. Studies suggest the price elasticity for low wage workers is 0.1 to 0.3.
E D =
percentage change in quantity demanded
If E D = 0.1 =
percentage change in price percentage change in quantity demanded 10
,
∴ Percentage change in quantity demanded = 10 × 0.1 = 1% A 10% increase in price, and a 1% drop in quantity gives: giv es: Total incomes = P’Q’ = 1.1P × 0.99Q = 1.089PQ So total incomes have increased by 9% (rounded from 8.9% = 1.089 − 1). If E D = 0.3, the same equation gives percentage change in quantity demanded = 3% A 10% increase in price, and a 3% drop in quantity gives: Total incomes = P’Q’ = 1.1P × 0.97Q = 1.067PQ So total incomes have increased 7% (rounded from 6.7% = 1.067 − 1). So, a 10 percent rise in the minimum wage, given price elasticities of demand between 0.1 – 0.3, 0.3, will reduce employment by 1 – 3 3 percent, but increase total incomes between 7 9 percent. – 9 Given this, would I support a raise in the minimum wage? The trade-off is, is a 7 – 9 percent increase in the incomes of low-wage workers worth a 1 – 3 percent drop in employment among low wage workers? To complicate matters, what would be the increase in unemployment? unemployment? The price elasticity of supply of low wage workers would need to be found for that, and how increased wages interacts with the benefits system and many other complications of that nature. Personally I would be disinclined to do so. A raise in the minimum benefits a large subset of low wage workers (who keep their jobs at higher wages) at the expense of those who lose their jobs or are priced out of getting a job. Those most affected are most likely to be the most marginal workers – teenagers who will be scarred for life by not being able to get a job early on, or those who have poorer prospects anyway, such as the disabled, or ethnic minorities.
Also, the increased wages are a cost to the employers of low wage workers. These are the people who have done most to help low wage workers by employing them, but now see their profits reduced or cannot expand any more mo re or are put out of business. My main problem then, is that to help one group of people who are deserving of our help, we have to hurt others who are equally or more deserving of our help. I think it would be better to give income support to low wage workers, either through inin work tax credits or benefits, or from a basic income scheme where all are given a cash transfer unconditionally. Any of these schemes would have to be paid for, which means higher taxes and inefficiencies placed elsewhere, which would hurt some. But, this pain could be taken by those who could better bear it, for instance through a tax on higher earners. This way, the help to the poor is achieved through some burden placed on the rich. But the minimum wage helps some of the poor through some burden placed on other poor people and those who help them. Income transfers seem a more moral course of action to me. But reasonable people can differ in their normative judgements. 6. A conservative critic of government programs has written, “Governments know how to do one thing well. They know how to create shortages and su rpluses.” Explain this quotation using examples like the minimum wage or interest-rate ceilings. Show graphically that if the demand for unskilled workers is price-elastic, a minimum wage will decrease the total earnings (wage times quantity demanded of labour) of unskilled workers. Maximum ceilings create shortages whereas minimum floors create surpluses. An example of a maximum ceiling would be an interest-rate ceiling. Interest rates are the price for borrowing money. Drawing a supply-and-demand diagram, with ‘interest rate’ in place of price, p rice, and ‘money’ in place of quantity of money:
) r a e y r e p t n e c r e p ( e c e i t r a P r t s e r e t n I
D
S
E
i market imax
E'
Interest rate rate ceiling ceili ng
D
S Quantity
Money
The market rate of interest, i market, bringing the supply and demand for money into balance, would be determined by the intersection of the supply and demand curves at E in the absence of the interest rate ceiling. If an interest rate ceiling was introduced (as has happened historically, when usury laws set a limit), then the interest rate would not reach imarket, but would fall to i max. At this interest rate, we see that the demand for money is greater than the supply of money ( DD DD is is further to the right than SS SS). ). There is a shortage of money for borrowing. A non-price mechanism for rationing the demand for borrowing money to bring it in line with supply at E’ will be needed. The bold red arrows show that the interest rate is lower, and the amount of money borrowed b orrowed is lower. An example of a minimum floor would be a minimum wage, which is explained in question 5:
Wages
S
D E
Wmin
U
LF
e c i r P
Wmarket M S
D
Employment
Quantity
If instead the demand for unskilled workers is price -elastic:
Wages
S
D U
E
Wmin e c i r P
LF
M
Wmarket D S Quantity
Employment
The total earnings are given by the rectangles drawn from the origin to M and E. The rectangle drawn to E (in light blue) blue) has a smaller area than that of the rectangle drawn to M (in light pink). pink). This shows that total earnings at the minimum wage in this priceelastic case are lower than that at the market wage . 7. Consider what would happen if a tariff of $2000 were imposed on imported automobiles. Show the impact of this tariff on the supply and the demand, and on the equilibrium price and quantity, of American automobiles. Explain why American auto companies and autoworkers often support restraints on automobiles. [In the question, we need to consider the demand for automobiles by American consumers, but with supply separately from American producers and world producers. In all supply-and-demand questions dealt with so far, we have only had to deal with one set of suppliers. A full treatment of this question would rely on knowledge of international trade, not yet dealt with so far in the text book. This is a first-attempt at the question, dealing with the intuition, but not that rigorous.] A $2000 tariff on imported automobiles shifts the supply curve for imported automobiles everywhere upwards by $2000. This is a reduction in supply, as the supply curve shifts from SS to S’S’:
D
P
S'
$2000 S
E' e c i r P
S' E D
S Quantity
Q
The new market equilibrium is found at a higher price and lower quantity. With fewer imported automobiles entering the American market, and those at a higher price, then assuming demand for automobiles unchanged, a greater quantity of American automobiles will be sold at higher price. This is why American auto companies and autoworkers often support import restraints. 8. Elasticity problems: a. The world demand for crude oil is estimated to have a short-run price elasticity of 0.05. If the initial price of oil were $30 per barrel, what would be the effect on oil price and quantity of an embargo that curbed world oil supply by 5 percent? (For this problem, assume that the oil-supply curve is completely inelastic.)
Assuming oil supply is completely inelastic, then the supply curves will be vertical. The oil embargo will reduce oil supply by 5 percent, shifting the supply curve to the left, from SS to S’S’:
P
S'
D
S
E' e c i r P
E
S'
S
Quantity
D
Q
The price of oil will rise, and the quantity demanded will fall. The percentage change in quantity demanded is 5 percent, as this is the reduction in supply. Given the elasticity of demand, the percentage change in price can be calculated. If E D, the elasticity of demand, is 0.05, then: E D =
percentage change in quantity demanded
0.05 = 0.05 =
percentage change in price 5 percentage change in price
So, the percentage change in price =
= 100
.
The price of oil will be $30 × 2 = $60 per barrel. In summary, price will rise 100 percent from $30 to $60 per barrel, and the quantity will fall by 5 percent. b. To show that elasticities are independent of units, refer to Table 3-1. Calculate the elasticities between each demand pair. Change the price units from dollars to pennies; change the quantity units from millions of boxes to tons, using the conversion factor of 10,000 boxes to 1 ton. Then recalculate the elasticities in the first two rows. Explain why you get the same answer. Using Table 3-1,
(1)
(2)
(3)
(4)
(5)
(6)
(7)
P
ΔP
Q
ΔQ
P 1 + P 2
Q 1 + Q 2
E D
2
2
1
4. 5
9. 9. 5
0.47
2
3. 5
11 11
0.64
3
2. 5
13.5
0.56
5
1. 5
17.5
0.43
5
9 1
4
10 1
3
12 1
2
15 1
1
20
If we change quantities: multiply ing P’s by 100 (100 pennies in a dollar), and Q’s by 100 (1 million boxes = 100 × 10,000 boxes = 100 tons): (1)
(2)
(3)
(4)
(5)
(6)
(7)
P
ΔP
Q
ΔQ
P 1 + P 2
Q 1 + Q 2
E D
2
2
100
450
950
0.47
200
350
1100
0. 0.64
300
250
1350
0. 0.56
500
150
1750
0. 0.43
500
900 100
400
1000 100
300
1200 100
200
1500 100
100
2000
The elasticities are the same. This shows that elasticities are independent of unit. This is because the elasticity uses percentage changes on both numerator and denominator. Percentage changes are independent of the units of the quantities, and the ratio of two percentages are dimensionless. c. Demand studies find that the price elasticity of demand for cocaine is 0.5. Suppose that half the cocaine users in New York City support their habit by predatory criminal activities. Using supply-and-demand analysis, show the impact on crime in New York City of an interdiction program that decreases the supply of crack into the New York market by 50 percent. (Assume that supply is completely inelastic for this exercise.) What would be the effect of reducing supply constraints on criminal activity and on drug use if the government reduced its interdiction efforts and this lowered the price of cocaine by 50 percent? Discuss the impact on price and addiction of a program that successfully rehabilitated half of the cocaine users. The supply of cocaine is completely price inelastic, so the supply curve will be vertical. The interdiction program reduces supply by 50 percent – so the supply curve shifts to the left, from SS SS to to S’S’:
P
S'
D
S
E' e c i r P
E S'
S Quantity
D
Q
The price of cocaine will rise and the quantity demanded will fall. If the percentage change in quantity is 50 percent, percen t, and the price elasticity is 0.5: E D =
percentage change in quantity demanded
0.5 = 0.5 =
percentage change in price 50 percentage change in price
So, percentage change in price =
.
= 100
The interdiction program has doubled the price of cocaine in New York City, as well as halved its quantity. It is not obvious what the adjustment will be to this new equilibrium. Will every individual reduce their consumption by half, spending double the amount of money on cocaine? Will some cease buying cocaine altogether, while some buy more? Assuming, as is likely, that a large number of those who resort to criminal activity to fund their habit still buy cocaine, unless they reduce their cocaine consumption by b y more than half, they will be spending more money on cocaine than previously. They will likely undertake more criminal activity to do this. In fact, the high price and scarcity will act as a powerful inducement of organised criminal activity – with gangs and the like getting involved in the drug trade. If the government then reduced the supply constraints so that the price halved, then the quantity demanded will double. If half of the cocaine users u sers were rehabilitated, then the demand would be reduced:
P
D'
S
D
E e c i r P
E' S
D
D'
Q As supply is completely inelastic, the reduction in demand will reduce the price, but not the quantity demanded. Those who were not rehabilitated would buy the cocaine that the rehabilitated half used to buy, but at a reduced price. d. Can you explain why farmers during a depression might approve of a government program requiring that pigs be killed and buried under the ground? Farmers killing pigs will reduce the supply of pig-based products, like bacon, ham, and pork onto the market. This will shift the supply curve left from SS SS to to S’S’:
P
D
S'
S
E' e c i r P
E S'
D
S Quantity
Q
The price of pig-produce will rise as the quantity falls. If the price elasticity of demand is inelastic (E (E D < 1), then the percentage change in price will be more than the percentage change in quantity, and total incomes for pig farmers (equal to price times quantity demanded) will rise. This is likely to be the case as farm produce is a necessity rather than a luxury, and while people can substitute beef or chicken for a while, few would forgo pig-products for a great length of time.
This can be seen on the supply-and-demand diagram, where the area of the rectangle going from the origin to the equilibrium point increases i ncreases as the equilibrium price rises. e. Look at the impact of the minimum wage shown in Figure 4-12. Draw in the rectangles of total income with and without the minimum wage. Which is larger? Relate the impact of the minimum wage to the price elasticity of demand for unskilled workers. Figure 4-12, with rectangles of total incomes with and without the minimum wage drawn in, is given below:
Wages
S
D E
Wmin
U
LF
e c i r P
Wmarket M S
D Quantity
Employment
Total incomes are larger when the minimum wage is in place. This can be seen because the area of the rectangle drawn from the origin to E (in ( in light blue) blue) is larger than that of the rectangle drawn from the origin to M (in light pink). pink ). This is because the demand for unskilled workers is inelastic. A percentage change in wages (price) yields a proportionally smaller percentage change in employment (quantity). Total incomes, which are the product of wages and employment, will be increased. 9. No one likes to pay rent. Yet scarcities of land and urban housing often cause rents to soar in cities. In response to rising rents and hostility towards landlords, governments sometimes impose rent controls . These generally limit the increases on rent to a small year-to-year increase and can leave controlled rents far below free-market rents. a. Redraw Figure 4-13 to illustrate the impact of rent controls for apartments.
P
D'
D
S E
e c i r P
E'
Rent ceiling
S
D'
D
Quantity
Q
Rent controls will reduce rents, but it will create a shortage of apartments, as shown by the distance between the demand curve DD and the supply curve SS – see the red line. line. b.
What will be the effect of rent controls on the vacancy rate of apartments?
At the rent ceiling, supply is greater than demand. There is a shortage of apartments – it is very difficult to find vacancies. c. What nonrent options might arise as a substitute for the higher rents? The shortage of apartments means they will need to be rationed by a nonrent mechanism. A likely mechanism is political allocation to those who meet criteria of need. d. Explain the words of a European critic of rent controls: “Except for bombing, nothing is as efficient at destroying a city as rent controls.” ( Hint: What would happen to maintenance?) Rising prices act as a signal to increase supply. With rent control, prices cannot rise to do this. Therefore there will be a lack of investment in apartments. If an apartment needed maintenance, the owner could not charge higher rent to pay the maintenance costs, so the maintenance would likely not be done. 10. Review the example of the New Jersey cigarette tax. Using graph paper or a computer, draw supply and demand curves that will yield the prices and quantities before and after the tax. For this example, assume ass ume that the supply curve is perfectly elastic. [ Extra elas ticity takes the form = −, where credit: A demand curve with constant price elasticity is the quantity demanded, P is is price, A is a scaling constant, and e is the (absolute Y is value) of the price elasticity. elas ticity. Solve for the values of A and e which will give the correct demand curve for the prices and quantities in the New Jersey example.] New Jersey doubled its cigarette tax from 40 cents to 80 cents per pack in 1998. This tax increase pushed the average price of cigarettes from $2.40 to $2.80 per pack. Cigarette consumption decreased from 52 million to 47.5 million packs. packs .
Plotting the two equilibrium points, labelled E and E’, on a price-quantity diagram:
P
2.85
E'
2.80 2.75 2.70 2.65 2.60 2.55 2.50 2.45
E
2.40 2.35 47
48
49
50
51
52
53
Q
Assuming the supply curves are perfectly elastic (so they are horizontal), the supply curves, SS SS and and S’S’, can be added. Note that the supply curve has been shifted upwards by 40 cents, the amount of the cigarette tax.
P
2.85
S'
2.80
E'
S'
2.75 2.70 2.65 2.60
0.40
2.55 2.50 2.45
E
2.40
S
S
2.35 47
48
49
50
51
52
53
Q
Any demand curve that joins the two equilibrium points in red red will will yield the prices and quantities before and after the tax:
P
2.85
E'
S'
2.80
S'
D
2.75
2.70 2.65 2.60
0.40
2.55 2.50
2.45
E
2.40
D
S
2.35
47
48
49
50
51
S
52
53
Q
The Extra credit part part of the question states that the demand curve is of the form: − = .
52 × 10 106 = 2.40− 47.5 × 106 = 2.80−
Before tax, Y = = 52 million, P = 2.40, so: After tax, Y = = 47.5 million, P = 2.80, so:
. . . (1) . . . (2)
Taking (1) / (2): × .×
=
The A The A’s on the top and bottom of the fraction cancel
. .
2.40 1.09 = 2.80
∴
1.09 × 2.80
= 2.40
Taking natural logarithms (ln or log e) of both sides:
ln(1 ln(1.0 .09 9 × 2.80 2.80− ) = ln 2.40 2.40− ln 1.09 .09 + ln 2.80 .80− = ln 2.40 2.40− ln 1.09 .09 ln 2.8 2.80 = ln 2.40 .40 ln 1.09 1.09 = (ln 2.80 2.80 ln 2.40 2.40)
Rules for logarithms: ln ab ln ab = ln a ln a + ln b ln c ln cd = d ln c ln c
0.091 = 0.154 ∴ =
.
= 0.59
.
(N.B. Here, the natural logarithm, ln, is used; although a logarithm with any base, such as , would yield the same result )
Putting = 0.59 into (1):
5 2 × 1 06 = 2.40−.
∴ =
52 × 106 2.40−.
= 8. 8.7 × 10
So a demand curve with constant price elasticity, that yields the prices and quantities before and after the tax, will be of o f the form:
= 8.7 × 10 −. If this is plotted:
P
2.85
E'
S' D
2.80 2.75
S'
2.70 2.65 2.60
0.40
2.55 2.50 2.45
E
2.40
S
2.35
S
D
47
48
49
50
51
52
53
Y
N.B. Zooming out, to see what a demand curve of constant elasticity looks like: like : 6.00
P
D
5.00 4.00 3.00
S'
2.00
S
E'
S' E
S
1.00
D 0.00 0
50
100
150
200
250
300
350
400
Y
