An algebraic approach to Market Equilibrium

Market Equilibrium - Algebraically

As teachers of Economics, we often limit ourselves to one approach of teaching Market Equilibrium. We frequently use the theoretical approach with the aid of a graph. I too was very guilty of this, until I discovered that it can also be taught or supplemented using an Algebraic approach.

Market equilibrium can be determined algebraically using a demand function and a supply function. The demand function shows the exact relationship between price and quantity demanded and the supply function shows the exact relationship between supply and quantity supplied. These two functions represent the exact intentions of buyers and sellers in the market and can be used to determine equilibrium quantity and equilibrium price without having to visually scope where it is on a graph.

EXAMPLE:

A demand function and supply function for carrots is given by:

Q_d  =  50   -   2p           (demand function)

Q_s  =  -6   +   12p         (supply function)

Where                         :  Q_d =  quantity demanded

                                    Q_s  =  quantity supplied

                                    p    =  price     

Since equilibrium is where quantity demanded is equal to quantity supplied (Q_d  =  Q_s ), then the equilibrium price can be determined by equating the demand and supply functions and then solving for price.

STEP I : Equate the demand and supply functions

            Q_d    =   Q_s

   50  -  2p    =  -6   +   12p

STEP II : Put all like terms together

    50  -  2p    =  -6   +   12p

    50  +  6   =   2p   +   12p

   56   =   14P

STEP III            :  Solve for p by dividing both sides by 14

       =   

   4      =     p

The equilibrium price is therefore $4.00

So what is equilibrium quantity?

We can use any of the functions to determine equilibrium quantity by simply substituting the price of $4.00 into the respective equations, then solve them to determine the equilibrium quantity.

Example One:                                                             Example Two:

Q_d  =  50  -  2p                                                                        Q_s   =   -6  +  12p

Q_d  =  50 -  2($4)                                                    Q_s    =   -6   +   12 ($4)                                                                        

Q_d   =   50   -   8                                                           Q_s    =   -6   +   48

Q_d   =  42                                                                     Q_s    =   42

Equilibrium quantity at the Market price of $4.00 is 42 carrots

The basics of Supply and Demand

The use of these instructional video reports will help students  understand concepts about demand , supply and market equilibrium. By using these videos, it is expected that teachers will make new connections between topics, and discover links between these topics and the world outside the classroom. The videos attached contain information on the following:


The Law of Demand
http://www.youtube.com/watchv=xrZqbL0bs8Q&feature=relmfu


The Law of Supply
http://www.youtube.com/watchv=RF8pY9WrFc4&feature=relmfu


Price Equilibrium
http://www.youtube.com/watchv=05_oTFlrYek&feature=related

TOPIC: The Supply Curve


The supply curve unlike the demand curve is upward sloping. The is a result of the law of supply, which states that when the price of the good is high so is the quantity supplied, and when the price of the good is low, the amount being placed on the market will also fall. Suppliers will therefore put more goods on the market at a higher price.

In the graph, it can be seen that as the producer can increase the price of cookies produced, more cookies are supplied on the market. At each price and corresponding quantity, when the points are joined, the supply curve for the good is formed.


Movement along the Supply Curve:

When the price of a good increases, it is an incentive for suppliers to put more goods on the market, because profits will be higher. Therefore, supply is greater at a higher price. There is a positive relationship between price and the quantity supplied, as when price increases, the quantity supplied increases and when price decrease the quantity supplied decreases.

The price of the good in this graph has increased from $3,000 to $4,000 and has caused a movement up the supply curve. The quantity supplied of that good also increases, from 5 to 6. Since quantity supplied has increased, there is an extension in supply. When there is a movement down the curve, the price falls from $3,00 to $2,000, and there is a contraction in demand.


Shifts of the supply curve:

A supply curve shifts ONLY as a result of changes in a non-price determinant, meaning any factor that is not price.

The information at the bottom of the graph explains the factors that cause the supply curve to shift to the left, indicating a decrease in supply of the good) and a shift to the right, indicating an increase in supply).

TOPIC: The Demand Curve
The determinants of demand and supply are the factors that affect the demand and the supply of a good. The determinants of demand are different from the determinants of supply. The only determinant however, that is common to demand and supply is price.
On the demand and supply curves, there can be either movements on the curve or a shift of the curve. Shifts are a result of changes in a non-price determinant. However, movements along any one of these curves are a result of changes ONLY in price.
Movement along the demand curve:
As the law of demand states, when the price of the good is high demand is low and vice versa. This can be depicted on the demand curve by a movement. This means that there exist an inverse or negative relationship between price and the quantity demanded - when the price of the good increases quantity demanded falls and when the price of the good decreases quantity demanded increases.

In the graph above, when the price of the good increases from $10.00 to $15.00, there is a movement up the demand curve from b to a. This causes the quantity demanded of the good to fall from 10 to 6. This we call a contraction in demand. There is an extension in demand however the price of the good has fallen from $15.00 to $10.00. As a result there is a movement down the demand curve from a to b. Quantity demanded has therefore increased from 6 to 10.

Market Equilibrium

UNDERSTANDING MARKET EQUILIBRIUM

A simplified version of market equilibrium for teachers.

In Economics, the term equilibrium means a state of balance or equality. Market equilibrium is therefore a condition where quantity demanded is equal to quantity supplied, that is, the point at which the quantity that suppliers are willing to produce exactly equals the quantity that consumers are willing to purchase. The price at which demand and supply meet is called the equilibrium price or the market clearing price and the quantity is referred to as the equilibrium quantity.

In the graph above, the demand and supply curves intersect to determine the equilibrium price and quantity. The equilibrium price is $6.00 per pound and the quantity demanded of coffee is 25 million tonnes.

With an upward sloping supply curve and a downward sloping demand curve, there can only be one point of intersection. This means that there can only be one equilibrium price in the market for coffee. Any other price will create a state of disequilibrium in the market. This will force the invisible hands to come into play in order to restore equilibrium.

At any price above the equilibrium price of $6.00, quantity supplied will be greater than quantity demanded, creating a surplus or glut on the market.

A surplus will cause the market price to fall. Why? Take for example the coffee producers who have excess inventory. What will they do? They will most likely put them up for sale at lower prices. At a lower price, the consumers will demand more of the product and the producers supply less coffee (law of demand and supply) until an equilibrium is reached. A surplus places a downward pressure on price.

At any price below the equilibrium price of $6.00, quantity demanded will be greater than quantity supplied, creating a shortage on the market.

A shortage will cause the market price to rise. Why? When there is a shortage, coffee producers face an increased demand for the limited supply of their product. Since they have a profit motive, they will respond by increasing the price per pound of coffee, causing consumers to reduce their demand for coffee until an equilibrium is reached. Remember, at a higher price, consumers' quantity demanded for coffee will fall and suppliers' quantity supplied of coffee will increase (law of demand and supply). Therefore, a shortage places an upward pressure on price in order to bring back equilibrium.