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Tutorial 3: Demand and Supply (cont.)

 

The Market Mechanism

In Tutorial 2 we noted that buyers and sellers were motivated to voluntarily trade goods and services by a personal interest in seeking the greatest surplus, or net benefit, from such an exchange. Markets facilitate these exchanges and in so doing generate the highest possible social surplus.

Now we turn our attention to how a market generates the price and quantity of a good traded.

We have already generated a graphical model of a demand curve and a supply curve. Because a market is an institution that brings buyers and sellers together, we can overlay the demand and supply curves to get a graphical depiction of a market:

 

Graph of inverse demand and supply equations.

 

Excess Supply (aka Market Surplus) Top of page.

[Not to be confused with buyer's or seller's surplus...]

Once the buyers and sellers are together, suppose an initial market price of $130 per unit is announced. At that price, the demand curve (D1) shows that buyers are willing and able to purchase approximately 140 units/t. The supply curve (S1) shows that approximately 260 units/t are offered for sale. This leaves sellers holding 260 - 140 = 120 units unsold during this time period. These unsold units indicate that there is an excess supply, or surplus, of goods at that market price.

How will sellers respond to the existence of these unsold goods? During the next time period they will reduce production and, because unit costs will be lower, will drop the price. As long as a surplus exists, there is pressure on sellers to push prices downward. As price drops buyers increase the quantity demanded in part because additional buyers with lower reservation prices will now be interested in an exchange. Market price continues to drop until it reaches $100 per unit, where, because the quantity demanded and the quantity supplied are equal at 200 units per period, the surplus is gone.

 

Excess Demand (aka Market Shortage) Top of page.

Now suppose an initial market price of $50 per unit is announced. At that price, the demand curve (D1) shows that buyers are willing and able to purchase approximately 300 units/t. The supply curve (S1) shows that approximately 100 units/t are offered for sale. This leaves buyers with an unrealized demand of 300 - 100 = 200 units unpurchaseable during this time period. Because buyers cannot buy as many goods as they want, there is an excess demand, or shortage, of goods at that market price.

How will sellers respond to the existence of excess demand for their goods? During the next time period they will increase production and, because unit costs will be higher, will raise the price. As long as a shortage exists, there is pressure on sellers to push prices upward. As price rises, buyers decrease the quantity demanded in part because some buyers have a reservation price that becomes exceeded by a rising market price. Market price continues to rise until it reaches $100 per unit, where, because the quantity demanded and the quantity supplied are equal at 200 units per period, the shortage is gone.

 

Equilibrium Top of page.

Notice that the pressure on sellers to lower or raise price came out of their goal to gain the most seller's surplus as possible -- no surplus benefit is enjoyed until a sale is made. Buyers too are interested in gaining the most buyer's surplus as possible. They will buy more or less as prices fall or rise because no surplus is enjoyed until a purchas is made. Although no one is directing these exchanges, a price is eventually reached where the quantity offered for sale is equal to the quantity purchased.

The price at which there is neither shortage nor surplus is called an equilibrium price, and is shown in the graph by the symbol P*. The quantity bought/sold at this price is called an equilibrium quantity, and is shown in the graph by the symbol Q*.

We can use the mathemagical form of the demand and supply equations to calcuate the equilibrium price and quantity. Recall from Tutorial 3a, that if we hold the P-PINE variables constant and only allow Price to vary, we can write the equation for demand as:

QD(Price | PPINE) = b0 - b1*Price,

where b0 = b2*Pref - b3*Pc + b4*Ps + b5*In - b6*Ii + b7*N + b8*E(Price) + b9*E(Inc).

Let b0 = 400 and b1 = 2. The resulting demand equation is

QD(P) = 400 - 2*P.

In Tutorial 3b we saw that if we hold the SP-PENT variables constant and only allow Price to vary, we can write the equation for market supply as:

QS(Price | SP-PENT) = d0 + d1*Price,

where d0 = d2*Sub - d3*Tax - d4*Pi - d5*Ps - d6*E(Price) + d7*N + d8*T.

Let d0 = 0 and d1 = 2. The resulting supply equation is

QS(P) = 0 + 2*P.

In equilibrium, QD(P*) = QS(P*), i.e., neither a shortage nor a surplus exist at the equilibrium price, P*. To calculate that quantity, set QD(P) = QS(P) and solve for P:

QD(P) = QS(P)
400 - 2*P = 0 + 2*P
400 = 4*P
P* = $100/unit

Once equilibrium price is known, replace P in either the inverse demand or inverse supply equation with P*:

QD(P*) = 400 - 2*100
Q* = 200 units/t

or

QS(P*) = 0 + 2*100
Q* = 200 units/t

 

Now let's explore how the market mechanism establishes a new equilibrium price and quantity when any of the non-price variables change demand (P-PINE) or supply (SP-PENT)...