price indices
Principles of Microeconomics: Market Equilibrium MARKET EQUILIBRIUM Linear Equations We can analyze Demand and Supply and Market equilibrium with linear equations. These are equations of the form Y = a + bX where a is the Y-intercept, i.e., the value of Y when X is zero, and b is the slope (rise/run = ∆Y/∆X) of the function. We know that the function is linear, i.e., a line, because the slope is constant. The slope is negative the Y falls with an increase in X and is positive if Y increases with an increase in X. Example: Suppose that the following equations describe the market Demand for and Supply of a Economics book. Demand: PD = 120 – 0.2QD
Supply: PS = 30 + 0.1QS
(P is in $s and Q is in units)
We don’t need to label these equations Demand and Supply since the negative slope of the first one and the positive slope of the second one tell us that they are Demand and Supply respectively. Since equilibrium implies that PD = PS we simply equate the right-hand side of each equation to find equilibrium. Equilibrium => PD = PS => 120 – 0.2Q = 30 + 0.1Q 90 = 0.3Q Q = 300 =>
=> Q = 300
P = 120 – 0.2*30 = $60
or P = 30 + 0.2*30 = $60
(P must be the same for Demand and Supply at equilibrium Q) The following diagram depicts these equations and this equilibrium. Note that 120 is the vertical (Y) intercept for Demand and that 30 is the vertical intercept for Supply. The horizontal intercept for Demand is 120/0.2 = 600.
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Principles of Microeconomics: Market Equilibrium
140
Price ($s)
Demand for and Supply of an Economics Book
120
100
Supply 80
Po
60
40
Demand
20
0
Do
0 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6
Qo Quantity
GOVERNMENT IMPACT ON MARKETS 1.
Fixed Prices The government can fix prices to achieve policy objectives but there are economic
ramifications. a) Price Floors (Minimum Prices) A government may wish to protect producers against low prices by establishing a minimum price (price floor) for a commodity. The classic commodities for price floors have been agricultural products such as eggs, milk, or peanuts, but minimum wages and minimum exchange rates are also common historically. A price floor is effective only if it is above the equilibrium price since the market would move to the equilibrium price. Governments assume or hope that the minimum price is a temporary measure to help producers in a depressed market but the existence of a price floor above the equilibrium price at that point results in surplus (unsold) commodities. It is difficult to simply decree minimum prices since some producers will sell below minimum price on the black market thereby driving down the
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Principles of Microeconomics: Market Equilibrium price. Governments usually have to establish the price floor, therefore, by purchasing surplus commodities. Example #1. Suppose that the government enacts a minimum price on textbooks by promising to buy any surplus commodities at $70. The following diagram depicts this situation.
140
Price ($s)
Goverment Price Floor
120
100
Supply
80
PFloor Po
60
40
Demand
20
Surplus
0 0 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6
Qd
Qs
We can find the specific amount of the surplus and the cost to the government of the price floor by calculating the surplus as the difference between the quantity demanded and the quantity supplied in the market at $70 $70 = 120 – 0.2QD
=> Qd = (120 – 70)/0.2 = 250
$70 = 30 + 0.1QS
=> Qs = (70 – 30)/0.1 = 400
=> Surplus = Qd – Qs = 400 – 250 = 150 Cost to the Government in buying this surplus = 150*70 = $10,500 Total Revenue of Firms = 400 * 70 = $28,000 Total Expenditure of Consumers = 250*70 = $17,500 NOTE: Price floors supported by government purchases have two problems: -3-
Principles of Microeconomics: Market Equilibrium 1.Governments must purchase the unsold surplus. 2.Consumers must pay a higher price. Example #2. What is the effect of Minimum Wage Laws? Economists use Demand/Supply analysis of price floors to criticize minimum wage laws (but we will see later that this is a simplistic analysis). The diagram below depicts the Demand for and Supply of unskilled labour in Ontario with the market at an initial equilibrium at Wo (e.g., $8/hour), the price of labour and employment of Qo, the quantity of labour . Suppose that the government imposes a minimum wage of WMIN (e.g., $9/hour) to increase incomes of unskilled labour. What is the effect on unskilled workers of a minimum wage? Wage ($s) Supply
WMIN Wo Demand Qd Qo Qs Surplus
Labour
The diagram above depicts the initial equilibrium and the quantity demanded (Qd) and quantity supplied (Qs) at the minimum wage. Notice that the increase in minimum wage decreases the quantity demanded of labour by firms, resulting in a loss of unskilled jobs from Qo to Qd. The loss of jobs for unskilled labour is even worse than this, however, since the minimum wage attracts Qs – Qo workers into unskilled labour. Since these entrants probably have better skills than the original workers, the actual loss of unemployment among the original unskilled workers is Qs –
-4-
Principles of Microeconomics: Market Equilibrium Qd. The criticism of minimum wage laws is therefore that they create unemployment in the very group that they are supposed to benefit. b) Price Ceilings (Maximum Prices) Governments can also legislate price ceilings or maximum prices to keep commodities (such as food or gasoline) affordable or prevent speculation. Rent controls or control of exchange rates (such as China’s maintenance of a relatively low Yuan) are also examples of price ceilings. Price ceiling, however, created shortages of commodities. This can lead to a black market price because buyers are willing to pay more than the legal price for the commodity. Example #1. The government imposes a price ceiling of $50 on textbooks
140
Goverment Price Ceiling
Price ($s)
120
100
Supply
PBM 80 Po 60
PCeiling 40
Demand
20
Shortage
0 0 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6
Qd
Qs
50 = 120 – 0.2Qd=> Qd = 350 50 = 30 + 0.1Qs
=> Qs = 200
Shortage = Qd – Qs = 350 – 200 = 150 Maximum Black Market Price (i.e., maximum price paid for quantity supplied) => Given quantity supplied of 200, PBM = 120 – 0.2*200 = $80 -5-
Principles of Microeconomics: Market Equilibrium Example #2.
Rent Controls
The economic argument against rent controls is that they create a shortage of housing for the people they’re supposed to help and can lead to higher than equilibrium prices if a black market develops. Suppose that the government imposes rent controls on apartments in the vicinity of the university to provide cheap housing for students Rent ($s) Supply
Rent BM Rent 0 Rent MAX Demand Qs Qo Qd Shortage
Apartments
The diagram above shows the rent controls reduce the quantity supplied of apartments because some landlords decide that it is not worthwhile to rent at the lower rate. There is also an increase in the number of individuals seeking apartments due to the lower rents. The decrease in available apartments for students may equal Qd – Qs. Not only that, the competition for the available apartments may increase the price of apartments to PBM above the original equilibrium price. (We don’t show this here but rent controls may decrease investment in building new apartments thus increasing the shortage). 2.
Quotas We saw that government attempts to benefit producers through price floors incurred a cost for
the government to buy surplus commodities. Government prefer to establish quotas, i.e., limits on
-6-
Principles of Microeconomics: Market Equilibrium the output of producers, since they don’t entail a cost to the government. Canada established Marketing Boards to control the output of agricultural commodities such as milk and eggs. In our textbook example, the government could impose a quota of 200 books on producers. This would push the price up to $70 without entailing the cost of buying the surplus. It would still cause higher prices for consumers, however.
140
Price ($s)
Goverment Quota
120
100
Supply
80
PQuota Po 60 40
Demand
20
0 0 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6
Qs
3.
Qd
Taxation (We will discuss this in a future lecture)
Deriving a Linear Functions from two Price/Quantity Observations We can easily construct a demand function from two Price/Quantity observations given the assumption that demand is linear and that there is no change in the ceteris paribus conditions. We simply find the slope of the line as the ratio ∆P/∆Q and then solve for the intercept term through substitution. Example #1: Suppose that we know that 1 million cars (of a particular type) sold when the price was $20,000 and that 500,000 cars sold when the price was $25,000. => ∆P/∆Q = (25,000 – 20,000)/(500,000 – 1,000,000) = 5,000/-500,000 = - 0.01
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Principles of Microeconomics: Market Equilibrium => This gives us P = a – 0.01Q for the Demand equation. Substitute the specific P and Q combinations into this equation to get => 20,000 = a – 0.01(1,000,000)
and 25,000 = a – 0.01(500,000)
=> a = 30,000 for both equations (both equations must give the same a or ∆P/∆Q is wrong) => Demand: P = 30,000 – 0.01Q We can calculate the Supply function from two Price/Quantity observations. Example. Suppose that firms produce 1,400,000 cars at P = $25,000 and $400,000 cars at P = $20,000. What is the supply function if it is linear? => ∆P/∆Q = (25,000 – 20,000)/(1,400,000 – 400,000) = 5,000/1,000,000 = 0.005 => This gives us P = c + 0.005Q for the Supply equation. Substitute the specific P and Q combinations into this equation to get => 20,000 = c + 0.005(400,000)
and 25,000 = a + 0.005(1,400,000)
=> c = 18,000 for both equations (both equations must give the same c or ∆P/∆Q is wrong) => Supply: P = 18,000 + 0.005Q Now we can calculate the equilibrium price in this market. => PD = PS => 30,000 – 0.01Q = 18,000 + 0.005Q => Q = 800,000 and P = 22,000
-8-
Supply: PS = 30 + 0.1QS
(P is in $s and Q is in units)
We don’t need to label these equations Demand and Supply since the negative slope of the first one and the positive slope of the second one tell us that they are Demand and Supply respectively. Since equilibrium implies that PD = PS we simply equate the right-hand side of each equation to find equilibrium. Equilibrium => PD = PS => 120 – 0.2Q = 30 + 0.1Q 90 = 0.3Q Q = 300 =>
=> Q = 300
P = 120 – 0.2*30 = $60
or P = 30 + 0.2*30 = $60
(P must be the same for Demand and Supply at equilibrium Q) The following diagram depicts these equations and this equilibrium. Note that 120 is the vertical (Y) intercept for Demand and that 30 is the vertical intercept for Supply. The horizontal intercept for Demand is 120/0.2 = 600.
-1-
Principles of Microeconomics: Market Equilibrium
140
Price ($s)
Demand for and Supply of an Economics Book
120
100
Supply 80
Po
60
40
Demand
20
0
Do
0 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6
Qo Quantity
GOVERNMENT IMPACT ON MARKETS 1.
Fixed Prices The government can fix prices to achieve policy objectives but there are economic
ramifications. a) Price Floors (Minimum Prices) A government may wish to protect producers against low prices by establishing a minimum price (price floor) for a commodity. The classic commodities for price floors have been agricultural products such as eggs, milk, or peanuts, but minimum wages and minimum exchange rates are also common historically. A price floor is effective only if it is above the equilibrium price since the market would move to the equilibrium price. Governments assume or hope that the minimum price is a temporary measure to help producers in a depressed market but the existence of a price floor above the equilibrium price at that point results in surplus (unsold) commodities. It is difficult to simply decree minimum prices since some producers will sell below minimum price on the black market thereby driving down the
-2-
Principles of Microeconomics: Market Equilibrium price. Governments usually have to establish the price floor, therefore, by purchasing surplus commodities. Example #1. Suppose that the government enacts a minimum price on textbooks by promising to buy any surplus commodities at $70. The following diagram depicts this situation.
140
Price ($s)
Goverment Price Floor
120
100
Supply
80
PFloor Po
60
40
Demand
20
Surplus
0 0 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6
Qd
Qs
We can find the specific amount of the surplus and the cost to the government of the price floor by calculating the surplus as the difference between the quantity demanded and the quantity supplied in the market at $70 $70 = 120 – 0.2QD
=> Qd = (120 – 70)/0.2 = 250
$70 = 30 + 0.1QS
=> Qs = (70 – 30)/0.1 = 400
=> Surplus = Qd – Qs = 400 – 250 = 150 Cost to the Government in buying this surplus = 150*70 = $10,500 Total Revenue of Firms = 400 * 70 = $28,000 Total Expenditure of Consumers = 250*70 = $17,500 NOTE: Price floors supported by government purchases have two problems: -3-
Principles of Microeconomics: Market Equilibrium 1.Governments must purchase the unsold surplus. 2.Consumers must pay a higher price. Example #2. What is the effect of Minimum Wage Laws? Economists use Demand/Supply analysis of price floors to criticize minimum wage laws (but we will see later that this is a simplistic analysis). The diagram below depicts the Demand for and Supply of unskilled labour in Ontario with the market at an initial equilibrium at Wo (e.g., $8/hour), the price of labour and employment of Qo, the quantity of labour . Suppose that the government imposes a minimum wage of WMIN (e.g., $9/hour) to increase incomes of unskilled labour. What is the effect on unskilled workers of a minimum wage? Wage ($s) Supply
WMIN Wo Demand Qd Qo Qs Surplus
Labour
The diagram above depicts the initial equilibrium and the quantity demanded (Qd) and quantity supplied (Qs) at the minimum wage. Notice that the increase in minimum wage decreases the quantity demanded of labour by firms, resulting in a loss of unskilled jobs from Qo to Qd. The loss of jobs for unskilled labour is even worse than this, however, since the minimum wage attracts Qs – Qo workers into unskilled labour. Since these entrants probably have better skills than the original workers, the actual loss of unemployment among the original unskilled workers is Qs –
-4-
Principles of Microeconomics: Market Equilibrium Qd. The criticism of minimum wage laws is therefore that they create unemployment in the very group that they are supposed to benefit. b) Price Ceilings (Maximum Prices) Governments can also legislate price ceilings or maximum prices to keep commodities (such as food or gasoline) affordable or prevent speculation. Rent controls or control of exchange rates (such as China’s maintenance of a relatively low Yuan) are also examples of price ceilings. Price ceiling, however, created shortages of commodities. This can lead to a black market price because buyers are willing to pay more than the legal price for the commodity. Example #1. The government imposes a price ceiling of $50 on textbooks
140
Goverment Price Ceiling
Price ($s)
120
100
Supply
PBM 80 Po 60
PCeiling 40
Demand
20
Shortage
0 0 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6
Qd
Qs
50 = 120 – 0.2Qd=> Qd = 350 50 = 30 + 0.1Qs
=> Qs = 200
Shortage = Qd – Qs = 350 – 200 = 150 Maximum Black Market Price (i.e., maximum price paid for quantity supplied) => Given quantity supplied of 200, PBM = 120 – 0.2*200 = $80 -5-
Principles of Microeconomics: Market Equilibrium Example #2.
Rent Controls
The economic argument against rent controls is that they create a shortage of housing for the people they’re supposed to help and can lead to higher than equilibrium prices if a black market develops. Suppose that the government imposes rent controls on apartments in the vicinity of the university to provide cheap housing for students Rent ($s) Supply
Rent BM Rent 0 Rent MAX Demand Qs Qo Qd Shortage
Apartments
The diagram above shows the rent controls reduce the quantity supplied of apartments because some landlords decide that it is not worthwhile to rent at the lower rate. There is also an increase in the number of individuals seeking apartments due to the lower rents. The decrease in available apartments for students may equal Qd – Qs. Not only that, the competition for the available apartments may increase the price of apartments to PBM above the original equilibrium price. (We don’t show this here but rent controls may decrease investment in building new apartments thus increasing the shortage). 2.
Quotas We saw that government attempts to benefit producers through price floors incurred a cost for
the government to buy surplus commodities. Government prefer to establish quotas, i.e., limits on
-6-
Principles of Microeconomics: Market Equilibrium the output of producers, since they don’t entail a cost to the government. Canada established Marketing Boards to control the output of agricultural commodities such as milk and eggs. In our textbook example, the government could impose a quota of 200 books on producers. This would push the price up to $70 without entailing the cost of buying the surplus. It would still cause higher prices for consumers, however.
140
Price ($s)
Goverment Quota
120
100
Supply
80
PQuota Po 60 40
Demand
20
0 0 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 20 40 60 80 00 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6
Qs
3.
Qd
Taxation (We will discuss this in a future lecture)
Deriving a Linear Functions from two Price/Quantity Observations We can easily construct a demand function from two Price/Quantity observations given the assumption that demand is linear and that there is no change in the ceteris paribus conditions. We simply find the slope of the line as the ratio ∆P/∆Q and then solve for the intercept term through substitution. Example #1: Suppose that we know that 1 million cars (of a particular type) sold when the price was $20,000 and that 500,000 cars sold when the price was $25,000. => ∆P/∆Q = (25,000 – 20,000)/(500,000 – 1,000,000) = 5,000/-500,000 = - 0.01
-7-
Principles of Microeconomics: Market Equilibrium => This gives us P = a – 0.01Q for the Demand equation. Substitute the specific P and Q combinations into this equation to get => 20,000 = a – 0.01(1,000,000)
and 25,000 = a – 0.01(500,000)
=> a = 30,000 for both equations (both equations must give the same a or ∆P/∆Q is wrong) => Demand: P = 30,000 – 0.01Q We can calculate the Supply function from two Price/Quantity observations. Example. Suppose that firms produce 1,400,000 cars at P = $25,000 and $400,000 cars at P = $20,000. What is the supply function if it is linear? => ∆P/∆Q = (25,000 – 20,000)/(1,400,000 – 400,000) = 5,000/1,000,000 = 0.005 => This gives us P = c + 0.005Q for the Supply equation. Substitute the specific P and Q combinations into this equation to get => 20,000 = c + 0.005(400,000)
and 25,000 = a + 0.005(1,400,000)
=> c = 18,000 for both equations (both equations must give the same c or ∆P/∆Q is wrong) => Supply: P = 18,000 + 0.005Q Now we can calculate the equilibrium price in this market. => PD = PS => 30,000 – 0.01Q = 18,000 + 0.005Q => Q = 800,000 and P = 22,000
-8-
