1. ALGEBRAIC REPRESENTATION OF SUPPLY, DEMAND, AND EQUILIBRIUM
Chapter 5 Appendix
ALGEBRAIC REPRESENTATION OF SUPPLY, DEMAND, AND EQUILIBRIUM

2. The Laws of Supply and Demand in Equations
An example of a supply equation is:
QS = P
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.

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 = QD P = 10 - P
Add P to both sides P = P
-5 + 3P = 10
Add 5 to both sides = +5
3P = 15
Divide both sides by P = 5
Insert P = $5 in either QD or QS equation
QS = (2 x 5) = 5 units

4. Supply and Demand Equilibrium
$10
QS = P 8 6
Price 5 4
QD = 10 - P 2 1 2 3 4 5 6 7 8 9 10
Quantity

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 = P + 3 = -2 + P
To determine the new equilibrium price, set the new quantity supplied equal to quantity demanded and solve for P.
10 – P = P
P = $4
To determine equilibrium quantity, substitute P in either the demand or supply equation.
QD = 10 – 4 = 6 units

6. Price Ceilings and Price Floors
When demand and supply are
QS = P 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 = (4) = 3
QD = 10 – 4 = 6
The result is a shortage of 6 – 3 = 3 units

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 = (P – 1)
QS = P
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

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