Supply & Demand | Exercise on rent control agency of New York City

The rent control agency of New York City has found that aggregate demand is QD = 160 - 8P. 

Quantity is measured in tens of thousands of apartments. 

Price, the average monthly rental rate, is measured in hundreds of dollars. 

The agency also noted that the increase in Q at lower P results from more three-person families coming into the city from Long Island and demanding apartments. 

The city’s board of realtors acknowledges that this is a good demand estimate and has shown that supply is QS = 70 + 7P.

a.       If both the agency and the board are right about demand and supply, what is the free-market price? What is the change in city population if the agency sets a maximum average monthly rent of $300 and all those who cannot find an apartment leave the city?

b.      Suppose the agency bows to the wishes of the board and sets a rental of $900 per month on all apartments to allow landlords a “fair” rate of return. If 50% of any long-run increases in apartment offerings come from new construction, how many apartments are constructed?

ANSWER

a.       If both the agency and the board are right about demand and supply, what is the free-market price? What is the change in city population if the agency sets a maximum average monthly rent of $300 and all those who cannot find an apartment leave the city?

Set supply equal to demand to find the free-market price for apartments:

160 - 8P = 70 + 7P, or P = 6,

which means the rental price is $600 since price is measured in hundreds of dollars. Substituting the equilibrium price into either the demand or supply equation to determine the equilibrium quantity:

QD = 160 - 8(6) = 112

and

QS = 70 + 7(6) = 112.

The quantity of apartments rented is 1,120,000 since Q is measured in tens of thousands of apartments. If the rent control agency sets the rental rate at $300, the quantity supplied would be 910,000 (QS = 70 + 7(3) = 91), a decrease of 210,000 apartments from the free-market equilibrium.

Assuming three people per family per apartment, this would imply a loss in city population of 630,000 people. Note: At the $300 rental rate, the demand for apartments is 1,360,000 units, and the resulting shortage is 450,000 units (1,360,000 - 910,000).

However, excess demand (the shortage) and lower quantity demanded are not the same concept. The shortage of 450,000 units is the difference between the number of apartments demanded at the new lower price (including the number demanded by new people who would have moved into the city), and the number supplied at the lower price. But these new people will not actually move into the city because the apartments are not available.

Therefore, the city population will fall by 630,000, which is due to the drop in the number of apartments available from 1,120,000 (the old equilibrium value) to 910,000.

b.      Suppose the agency bows to the wishes of the board and sets a rental of $900 per month on all apartments to allow landlords a “fair” rate of return. If 50% of any long-run increases in apartment offerings come from new construction, how many apartments are constructed?

At a rental rate of $900, the demand for apartments would be 160 - 8(9) = 88, or 880,000 units, which is 240,000 fewer apartments than the original free-market equilibrium number of 1,120,000. Therefore, no new apartments would be constructed.

Supply & Demand | Find Market-Clearing Price & Quantity

Suppose the demand curve for a product is given by Q = 300 - 2P + 4I, where I is average income measured in thousands of dollars. The supply curve is Q = 3P - 50.

a.      If I = 25, find the market-clearing price and quantity for the product.

b.      If I = 50, find the market-clearing price and quantity for the product.

c.       Draw a graph to illustrate your answers.

ANSWER

a. If I = 25, find the market-clearing price and quantity for the product.

Given I = 25, the demand curve becomes Q = 300 − 2P + 4(25), or Q = 400 − 2P.  Set demand equal to supply and solve for P and then Q:

400 - 2P = 3P - 50

P = 90

Q = 400 - 2(90) = 220

b. If I = 50, find the market-clearing price and quantity for the product.

Given I = 50, the demand curve becomes Q = 300 - 2P + 4(50), or Q = 500 - 2P. Setting demand equal to supply, solve for P and then Q:

500 - 2P = 3P - 50

P = 110

Q = 500 - 2(110) = 280

c. Draw a graph to illustrate your answers.

It is easier to draw the demand and supply curves if you first solve for the inverse demand and supply functions, i.e., solve the functions for P. Demand in part a is P = 200 - 0.5Q and supply is P = 16.67 + 0.333Q. These are shown on the graph as Da and S. Equilibrium price and quantity are found at the intersection of these demand and supply curves. When the income level increases in part b, the demand curve shifts up and to the right. Inverse demand is P = 250 - 0.5Q and is labeled Db. The intersection of the new demand curve and original supply curve is the new equilibrium point.

Supply & Demand | True or False

Are the following statements true or false? Explain your answers.

a. The elasticity of demand is the same as the slope of the demand curve.

b. The cross-price elasticity will always be positive.

c. The supply of apartments is more inelastic in the short run than the long run.

a.      The elasticity of demand is the same as the slope of the demand curve.

False. Elasticity of demand is the percentage change in quantity demanded divided by the percentage change in the price of the product. In contrast, the slope of the demand curve is the change in quantity demanded (in units) divided by the change in price (typically in dollars).

The difference is that elasticity uses percentage changes while the slope is based on changes in the number of units and number of dollars.

b.      The cross-price elasticity will always be positive.

False. The cross-price elasticity measures the percentage change in the quantity demanded of one good due to a 1% change in the price of another good. This elasticity will be positive for substitutes (an increase in the price of hot dogs is likely to cause an increase in the quantity demanded of hamburgers) and negative for complements (an increase in the price of hot dogs is likely to cause a decrease in the quantity demanded of hot dog buns).

c.       The supply of apartments is more inelastic in the short run than the long run.

True. In the short run it is difficult to change the supply of apartments in response to a change in price. Increasing the supply requires constructing new apartment buildings, which can take a year or more. Therefore, the elasticity of supply is more inelastic in the short run than in the long run.

Supply & Demand | Explain the difference between a shift in the supply curve and a movement along the supply curve.

Explain the difference between a shift in the supply curve and a movement along the supply curve.

ANSWER

A movement along the supply curve occurs when the price of the good changes. A shift of the supply curve is caused by a change in something other than the good’s price that results in a change in the quantity supplied at the current price. Some examples are a change in the price of an input, a change in technology that reduces the cost of production, and an increase in the number of firms supplying the product.

Supply & Demand | Use supply and demand curves to illustrate how each of the following events would affect the price of butter and the quantity of butter bought and sold

Use supply and demand curves to illustrate how each of the following events would affect the price of butter and the quantity of butter bought and sold:

a. An increase in the price of margarine.

b. An increase in the price of milk.

c.  A decrease in average income levels.

ANSWER

a. An increase in the price of margarine.

Butter and margarine are substitute goods for most people. Therefore, an increase in the price of margarine will cause people to increase their consumption of butter, thereby shifting the demand curve for butter out from D₁ to D₂ in Figure 2.2.a. This shift in demand causes the equilibrium price of butter to rise from P₁ to P₂ and the equilibrium quantity to increase from Q₁ to Q₂.

                       

Figure 2.2.a

b. An increase in the price of milk.

Milk is the main ingredient in butter. An increase in the price of milk increases the cost of producing butter, which reduces the supply of butter. The supply curve for butter shifts from
S₁ to S₂ in Figure 2.2.b, resulting in a higher equilibrium price, P₂ and a lower equilibrium quantity, Q₂, for butter.

                       

                               Figure 2.2.b

Note: Butter is in fact made from the fat that is skimmed from milk; thus butter and milk are joint products, and this complicates things. If you take account of this relationship, your answer might change, but it depends on why the price of milk increased. If the increase were caused by an increase in the demand for milk, the equilibrium quantity of milk supplied would increase. With more milk being produced, there would be more milk fat available to make butter, and the price of milk fat would fall. This would shift the supply curve for butter to the right, resulting in a drop in the price of butter and an increase in the quantity of butter supplied.

c.  A decrease in average income levels.

Assuming that butter is a normal good, a decrease in average income will cause the demand curve for butter to decrease (i.e., shift from D₁ to D₂). This will result in a decline in the equilibrium price from P₁ to P₂, and a decline in the equilibrium quantity from Q₁ to Q₂. See Figure 2.2.c.

                              Figure 2.2.c

CPI | Exercise

Exercise - CPI

1. The price of a taco was $0.29 in 1970 and $1.09 in 2000.  

The CPI was 38.8 in 1970 and 172.2 in 2000.  

The 2000 price of a taco in 1970 dollars is _________

2. When 1983 is the CPI base year, the CPI value is 82.4 for 1980 and 172.2 for 2000.  

Suppose we want to convert this CPI series to have a base year of 2000 (that is, CPI2000 = 100).  

What is the value of the revised CPI for 1980?

3. The CPI in 1970 was 38.8 and in 1998 the CPI was 163.0.  
If the real value of a 1970 gallon of milk in terms of 1998 dollars is $0.70, 

what was the nominal price of milk in 1970?

4. The nominal price of a 1990 laptop was $3,500 and the CPI that year was 130.7.  
The nominal price of a laptop in 2010 was $600 and the CPI that year was 218.1.  

What is the real price of a 2010 laptop in terms of 1990 dollars?  By what percent has the real price of laptops changed?

5. The price to attend a NBA basketball game in Chicago is $55 while the CPI in Chicago is 153.  
The CPI in Charlotte is 108 while the price to attend a NBA basketball game is $52.  

Which city offers a smaller real cost of attending a NBA basketball game?

ANSWER

1. The price of a taco was $0.29 in 1970 and $1.09 in 2000.  

The CPI was 38.8 in 1970 and 172.2 in 2000.  

The 2000 price of a taco in 1970 dollars is $0.29

2. When 1983 is the CPI base year, the CPI value is 82.4 for 1980 and 172.2 for 2000.  

Suppose we want to convert this CPI series to have a base year of 2000 (that is, CPI2000 = 100).  

What is the value of the revised CPI for 1980? 47.9

3. The CPI in 1970 was 38.8 and in 1998 the CPI was 163.0.  If the real value of a 1970 gallon of milk in terms of 1998 dollars is $0.70, what was the nominal price of milk in 1970?  38.8($0.70)/163 = $0.17 

4. The nominal price of a 1990 laptop was $3,500 and the CPI that year was 130.7.  The nominal price of a laptop in 2010 was $600 and the CPI that year was 218.1.  What is the real price of a 2010 laptop in terms of 1990 dollars?  By what percent has the real price of laptops changed?

a. 130.7($600)/218.1 = $360  

b. -(360 - 3500)/3500 x 100% = 89.71%

5. The price to attend a NBA basketball game in Chicago is $55 while the CPI in Chicago is 153.  The CPI in Charlotte is 108 while the price to attend a NBA basketball game is $52.  Which city offers a smaller real cost of attending a NBA basketball game?

Chicago real value [NBA(Charlotte)] = 153(52)/108 = $73.67. The real value of a game in Charlotte exceeds the real value of a game in Chicago.  Chicago offers a smaller real cost of attending a game. 

Preliminaries | Exercise No. 2 Consumer Price Index

Exercise No. 2

The following table shows the average retail price of butter and the Consumer Price Index from 1980 to 2010, scaled so that the CPI = 100 in 1980.

	1980	1990	2000	2010
CPI	100	158.56	208.98	218.06
Retail price of butter (salted, grade AA, per lb.)	$1.88	$1.99	$2.52	$2.88

a.       Calculate the real price of butter in 1980 dollars. Has the real price increased/decreased/ stayed the same from 1980 to 2000? From 1980 to 2010?

b.      What is the percentage change in the real price (1980 dollars) from 1980 to 2000? From 1980 to 2010?

c.       Convert the CPI into 1990 = 100 and determine the real price of butter in 1990 dollars.

d.      What is the percentage change in the real price (1990 dollars) from 1980 to 2000? Compare this with your answer in (b). What do you notice? Explain.

a.       Calculate the real price of butter in 1980 dollars. Has the real price increased/decreased/ stayed the same from 1980 to 2000? From 1980 to 2010?

Real price of butter in year t = CPI 1980 / CPI t x nominal price of butter in year t.

	1980	1990	2000	2010
Real price of butter (1980 $)	$1.88	$1.26	$1.21	$1.32

The real price of butter decreased from $1.88 in 1980 to $1.21 in 2000, and it increased from $1.88 in 1980 to $1.32 in 2010, although it did increase between 2000 and 2010.

b.      What is the percentage change in the real price (1980 dollars) from 1980 to 2000? From 1980 to 2010?

Real price decreased by $0.67 (1.88 - 1.21 = 0.67) between 1980 and 2000. The percentage change in real price from 1980 to 2000 was therefore (-0.67/1.88) x 100% = -35.6%. The decrease was $0.56 between 1980 and 2000 which, in percentage terms, is (-0.56/1.88) x 100% = -29.8%.

c.       Convert the CPI into 1990 = 100 and determine the real price of butter in 1990 dollars.

To convert the CPI into 1990 = 100, divide the CPI for each year by the CPI for 1990 and multiply that result by 100. Use the formula from part a and the new CPI numbers below to find the real price of milk in 1990 dollars.

	1980	1990	2000	2010
New CPI	63.07	100	131.80	137.53
Real price of butter (1990 $)	$2.98	$1.99	$1.91	$2.09

d.      What is the percentage change in the real price (1990 dollars) from 1980 to 2000? Compare this with your answer in (b). What do you notice? Explain.

Real price decreased by $1.07 (2.98 - 1.91 = 1.07). The percentage change in real price from 1980 to 2000 was therefore (1.07/2.98) x 100% = -35.9%. This answer is the same (except for rounding error) as in part b. It does not matter which year is chosen as the base year when calculating percentage changes in real prices.

Price Elasticity | Price Elasticity of Demand | Price Elasticity of Supply

Price Elasticity

Price Elasticity of Demand

The price elasticity of demand is used to learn how much of a change will occur to the demand quantity when the price changes.

http://www.college-cram.com/study/economics/supply-and-demand/price-elasticity-of-demand-standard/

Price Elasticity of Supply

The price elasticity of supply is used to learn how much of a change will occur to the supply quantity when the price changes.

http://www.college-cram.com/study/economics/supply-and-demand/price-elasticity-of-supply/

Resources provided from www.College-Cram.com

Price Floor | Government Intervention and Economics: Price Floor

Price Floor

Definition of Price Floor

A Price Floor is a government-imposed minimum price charged on a product or service. It differs from a price ceiling in that it artificially prevents the price from falling too low.

Graph A shows the equilibrium price of a good or service, determined by the intersection of the supply curve and the demand curve.

(Equilibrium price is the price at which the quantity demanded for a good or service is equal to the quantity supplied. Typically, market forces do not move to change either demand or supply at the equilibrium price.)

A price floor can either be above or below the equilibrium price, as shown by the dashed and solid lines in Graph B.

The dashed line of Graph B represents the government’s imposed minimum price (price floor) below the market-determined equilibrium price, and has no measurable affect on the product’s price. In this case, the market is already producing a price higher than the imposed minimum.

A different affect occurs when the government’s imposed minimum price is above the market’s equilibrium price, as shown by the solid line in Graph B. Suppliers can no longer charge the price the market demands but are forced to raise minimum price set by the government’s price floor.

A high price floor forces consumers to pay a higher price decreasing the demand and even eliminating some consumers from the market. Producers on the other hand now charge more for the product and increase supply. The decrease in demand and increase in supply due to the new imposed higher price creates a surplus of the product. The government in order to maintain the price floor over a period of time must eliminate the surplus.

Source:

http://www.college-cram.com/study/economics/government-intervention/price-floor/

http://myllurmicroeconomics.blogspot.com/2013/01/supply-demand-additional-resources.html

Price Ceiling | Government Intervention and Economics: Price Ceiling

Price Ceiling

Definition of Price Ceiling

A Price Ceiling is a government-imposed maximum price for a product.

Impact of Government Imposed Price Ceiling that is above the equilibrium price

When a price ceiling imposed by a government is higher than the market equilibrium price, the price ceiling has no impact on the economy. It does not restrict supply nor encourage demand. It says you cannot charge (or be charged) more than an amount that is higher than is already being charged.

Graph A shows the equilibrium price of $5 for a product determined by the intersection of the supply and demand curves.

Equilibrium price is the price at which the quantity demanded is equal to the quantity supplied. Typically, market forces do not move to change either demand or supply at the equilibrium price.

If a government mandated price ceiling of $100 were imposed, nobody would notice, since the ceiling is so far above the market price. If the price ceiling were $5.01 it wouldn’t have an immediate effect, but the first time market forces change to increase the equilibrium price, the ceiling would no longer be below below the market price, and it’s impact would begin to be felt. [See section below on impact when price ceiling is below equilibrium price.]

Impact of Government Imposed Price Ceiling that is below the equilibrium price

A price ceiling can either be above or below the equilibrium price, as shown by the dashed and solid lines in Graph B.

The dashed line of Graph B represents the government’s imposed maximum price (ceiling price) above the market-determined equilibrium price, and has no measurable affect on the product’s price. In this case, the market is unable to produce a price as high as the ceiling price.

A different effect occurs when the government’s imposed maximum price is below the market’s equilibrium price, as shown by the solid line in Graph B. Suppliers can no longer charge the price the market demands but are forced to meet the maximum price set by the government’s price ceiling.

A low ceiling price can drive suppliers out of the market (reducing the supplied resources), while the lower price drives increased consumer demand. When the demand increases beyond the ability to supply, shortages occur. This creates a rationing of the product by the market. Some consumers could experience longer lines for the product or no available products when they need or desire to purchase.

Sometimes governments combine low price ceilings with government rationing programs that mandate how the market will allocate the now inadequate supply of goods.

Price Ceiling compared to a Price Floor

A Price Ceiling is a government-imposed maximum price charged on a product. It differs from a price floor in that a price ceiling artificially keeps prices from rising too high, which in theory allows consumers to afford the product or service, but can result in shortages and rationing. A price floor keeps prices from falling too low, which can protect producers, but can generate excess supply and waste.

Source:

http://www.college-cram.com/study/economics/government-intervention/price-ceiling/

http://myllurmicroeconomics.blogspot.com/2013/01/supply-demand-additional-resources.html