E XERCISES FOR C HAPTER 2
3.9 Useful techniques – demand and supply equations
To concentrate on the essentials, imagine that there are just two buyers of chocolate cookies in the economy. A has a stronger preference for cookies than B, so his demand is greater. To simplify, let the two demands have the same intercept on the vertical axis. The curves DA and DB indicate how many cookies A and B, respectively, will buy at each price. The market demand indicates how much they buy together at any price. Accordingly, at P1, A and B purchase the quantities QA1 and QB1 respectively. Thus Q1= QA1+ QB1. At a price P2, they purchase QA2 and QB2. Thus Q2= QA2+ QB2. Themarket demandis therefore the horizontal sum of the individual demands at these prices. In the figure this is defined by Dmarket.
Market demand: the horizontal sum of individual demands.
3.9 Useful techniques – demand and supply equations
The supply and demand functions, or equations, underlying Table3.1and Figure3.2can be written in their mathematical form:
Demand: P= 10 − Q Supply: P= 1 + (1/2)Q
A straight line is represented completely by the intercept and slope. In particular, if the variable P is on the vertical axis and Q on the horizontal axis, the straight-line equation relating P and Q is defined by P= a + bQ. Where the line is negatively sloped, as in the demand equation, the parameter b must take a negative value. By observing either the data in Table3.1 or Figure3.2it is clear that the vertical intercept, a, takes a value of $10. The vertical intercept corresponds to a zero-value for the Q variable. Next we can see from Figure 3.2 that the slope (given by the rise over the run) is 10/10 and hence has a value of −1. Accordingly the demand equation takes the form P= 10 − Q.
On the supply side the price-axis intercept, from either the figure or the table, is clearly 1. The slope is one half, because a two-unit change in quantity is associated with a one-unit change in price.
This is a positive relationship obviously so the supply curve can be written as P= 1 + (1/2)Q.
Where the supply and demand curves intersect is the market equilibrium; that is, the price-quantity combination is the same for both supply and demand where the supply curve takes on the same values as the demand curve. This unique price-quantity combination is obtained by equating the two curves: If Demand=Supply, then
10− Q = 1 + (1/2)Q.
Gathering the terms involving Q to one side and the numerical terms to the other side of the equation results in 9= 1.5Q. This implies that the equilibrium quantity must be 6 units. And this quantity must trade at a price of $4. That is, when the price is $4 both the quantity demanded and the quantity supplied take a value of 6 units.
Modelling market interventions using equations
To illustrate the impact of market interventions examined in Section3.7on our numerical market model for natural gas, suppose that the government imposes a minimum price of $6 – above the equilibrium price obviously. We can easily determine the quantity supplied and demanded at such a price. Given the supply equation
P= 1 + (1/2)Q,
it follows that at P= 6 the quantity supplied is 10. This follows by solving the relationship 6 = 1+ (1/2)Q for the value of Q. Accordingly, suppliers would like to supply 10 units at this price.
Correspondingly on the demand side, given the demand curve P= 10 − Q,
with a price given by P= $6, it must be the case that Q = 4. So buyers would like to buy 4 units at that price: There is excess supply. But we know that the short side of the market will win out, and so the actual amount traded at this restricted price will be 4 units.
C ONCLUSION
We have covered a lot of ground in this chapter. It is intended to open up the vista of economics to the new student in the discipline. Economics is powerful and challenging, and the ideas we have developed here will serve as conceptual foundations for our exploration of the subject. Our next chapter deals with measurement and responsiveness.
Key Terms 65
K EY T ERMS
Demand is the quantity of a good or service that buyers wish to purchase at each possible price, with all other influences on demand remaining unchanged.
Supply is the quantity of a good or service that sellers are willing to sell at each possible price, with all other influences on supply remaining unchanged.
Quantity demanded defines the amount purchased at a particular price.
Quantity supplied refers to the amount supplied at a particular price.
Equilibrium price: equilibrates the market. It is the price at which quantity demanded equals the quantity supplied.
Excess supply exists when the quantity supplied exceeds the quantity demanded at the going price.
Excess demand exists when the quantity demanded exceeds quantity supplied at the going price.
Short side of the market determines outcomes at prices other than the equilibrium.
Demand curve is a graphical expression of the relationship between price and quantity de-manded, with other influences remaining unchanged.
Supply curve is a graphical expression of the relationship between price and quantity supplied, with other influences remaining unchanged.
Substitute goods: when a price reduction (rise) for a related product reduces (increases) the demand for a primary product, it is a substitute for the primary product.
Complementary goods: when a price reduction (rise) for a related product increases (reduces) the demand for a primary product, it is a complement for the primary product.
Inferior good is one whose demand falls in response to higher incomes.
Normal good is one whose demand increases in response to higher incomes.
Comparative static analysis compares an initial equilibrium with a new equilibrium, where the difference is due to a change in one of the other things that lie behind the demand curve or the supply curve.
Price controls are government rules or laws that inhibit the formation of market-determined prices.
Quotas are physical restrictions on output.
Market demand: the horizontal sum of individual demands.