Chapter 3: Problem 17

How can you locate the equilibrium point on a demand and supply graph?

Short Answer

Expert verified

To locate the equilibrium point on a demand and supply graph, set the demand equation, \(Q_d = a - bP\), equal to the supply equation, \(Q_s = c + dP\). Solve for the equilibrium price, \(P = \frac{a - c}{b + d}\), and then substitute the equilibrium price back into either the demand or supply equation to find the equilibrium quantity, \(Q\). Finally, plot the demand and supply curves on a graph, and the equilibrium point will be the intersection of the two curves, with coordinates (Q, P).

Step by step solution

Identify the demand and supply equations

First, we need to identify the demand and supply equations for the market. Usually, the demand equation is given in the form \(Q_d = a - bP\), where \(Q_d\) is the quantity demanded, \(P\) is the price, and \(a\) and \(b\) are constants. The supply equation is typically given in the form \(Q_s = c + dP\), where \(Q_s\) is the quantity supplied, \(P\) is the price, and \(c\) and \(d\) are constants.

Equate the demand and supply functions

In order to find the equilibrium point, the quantity demanded must equal the quantity supplied. Let's set the demand equation equal to the supply equation: \(Q_d = Q_s\) \(a - bP = c + dP\)

Solve for the equilibrium price

Now, we will solve the equation for the equilibrium price, \(P\): \((b + d)P = a - c\) \(P = \frac{a - c}{b + d}\)

Solve for the equilibrium quantity

With the equilibrium price found, we can now plug the value of \(P\) back into either the demand or supply equation to find the equilibrium quantity, \(Q\). For example, using the demand equation: \(Q_d = a - bP\) \(Q = a - b \times \frac{a - c}{b + d}\)

Locate the equilibrium point on the graph

Finally, plot the demand and supply curves on a graph with the price on the vertical axis and the quantity on the horizontal axis. The point where the two curves intersect represents the equilibrium point, and its coordinates are the equilibrium quantity, \(Q\), and the equilibrium price, \(P\), which we found in Steps 3 and 4. This point indicates the market-clearing level at which the quantity demanded equals the quantity supplied.