Transcript McGraw-Hill/Irwin

Chapter 5
Appendix
ALGEBRAIC REPRESENTATION
OF SUPPLY, DEMAND, AND
EQUILIBRIUM
McGraw-Hill/Irwin
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
5A-2
The Laws of Supply and
Demand in Equations
An example of a supply equation is:
QS = -5 + 2P
where QS is units supplied and P is price of each unit in
dollars per unit.
An example of a demand equation is:
QD = 10 - P
where QD is units demanded and P is price of each unit
in dollars per unit.
McGraw-Hill/Irwin
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
5A-3
Determination of Equilibrium
To find the equilibrium price and quantity, set the
quantity demanded equal to the quantity supplied and
solve for P:
QS = Q D
- 5 + 2P = 10 - P
Add P to both sides
+ P=
+P
-5 + 3P = 10
Add 5 to both sides
+5
= +5
3P = 15
Divide both sides by 3
P=5
Insert P = $5 in either QD or QS equation
QS = - 5 + (2 x 5) = 5 units
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Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
5A-4
Supply and Demand Equilibrium
$10
QS = - 5 + 2P
Price
8
6
5
4
QD = 10 - P
2
0
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7 8 9 10
Quantity
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
5A-5
Shifts of a Demand and
Supply Schedule
A shift in the supply curve is represented by a change in the
constant term in the supply equation. If suppliers are willing to
supply 3 more units at each price, add 3 to the right-hand side of the
supply equation:
QS = - 5 + 2P + 3 = -2 + P
To determine the new equilibrium price, set the new quantity supplied
equal to quantity demanded and solve for P.
10 – P = - 2 + 2P
P = $4
To determine equilibrium quantity, substitute P in either the demand
or supply equation.
QD = 10 – 4 = 6 units
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Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
5A-6
Price Ceilings and Price Floors
When demand and supply are
QS = - 5 + 2P
QD = 10 – P
P = $5 and Q = 5 units in equilibrium
To find out the effect of a price ceiling that is below equilibrium
price, substitute the price ceiling in the demand and supply
equations. If a price ceiling of $4 is imposed
QS = - 5 + 2(4) = 3
QD = 10 – 4 = 6
The result is a shortage of 6 – 3 = 3 units
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Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
5A-7
Taxes and Subsidies
A tax on suppliers reduces the price suppliers receive. So to show
the effect of a tax, subtract the tax from the price in the supply
equation. If a tax of $1 per unit is placed on suppliers, the supply
equation becomes
QS = - 5 + 2(P – 1)
QS = - 7 + 2P
To find the new equilibrium price, set quantity demanded equal to
the new, after-tax, supply equation and solve for P
-7 + 2P = 10 – P
P = $5.67
Substituting this price into the demand and supply equations
QS = QD = 4.33 units
McGraw-Hill/Irwin
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.
5A-8
Quotas
If a quota of 4.33 is placed on the market, the supply equation
becomes
QS = 4.33
The price that consumers are willing to pay for this quantity is
determined by the demand equation
4.33 = 10 – P
P = $5.67
Since consumers are willing to pay $5.67, this is what suppliers will
receive. Suppliers would have been willing to accept $4.67 for this
quantity, found by substituting the amount of the quota into the
original supply equation. The result is similar to the tax, except that
suppliers are better off because they receive $5.67 instead of $4.67
McGraw-Hill/Irwin
Copyright  2006 by The McGraw-Hill Companies, Inc. All rights reserved.