Suppose, we have the following demand and supply relationships:

**Demand: Q _{D} = 120 - 2P **

We found before that, for this market, equilibrium price and quantity are:

**P = 50** and

**Q = 20**

Now, suppose demand shifts back so that the new demand relationship is:

**Q _{D2} = 90 - 2P **

We can solve for the new equilibrium:

**90 - 2P = -30 + P **

**120 = 3P**

**P = 40**

**Q = 10**

Our simple demand and supply system confirms the result of our graphical analysis: When demand decreases (shifts back), equilibrium price and quantity both fall.

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