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# Using an Equation

Although tables and graphs are very useful in representing the Market Equilibrium for a product, equations are sometimes used as well. Although many students try to avoid using equations, this is actually the easiest (and shortest) way to represent the Market Equilibrium for a product. For example, what if I wanted to know what the equilibrium price of red wine was?  That is, the price where both consumers and producers would both sell and buy equal quantities. Getting the precise number from the table may be difficult. It would require extrapolating from the points that are there. On the other hand, if I gave you an equation it would be very easy.

Suppose I told you the demand for red wine was represented by the following equation:

Q = 70,000 - 2,000*P

and that the supply for red wine was represented by the following equation:

Q = 5,000 + 2,000*P

If we wanted to find the equilibrium price, we wouldn't even have to worry about the equilibrium quantity because we know that the quantity would be equal for supply and demand.  Therefore we can simply set each equation equal to the other:

70,000-2,000*P = 5,000 + 2,000*P

By the rules of Algebra, the equation can be reduced:

65,000 = 4,000P
16.25= P

Thus the equilibrium price is of a case of red wine is \$16.25.

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