# Demand Curve Determination

To illustrate, consider the relation depicted in Equation 4.3 and Table 4.1. Assuming that import car prices, income, population, interest rates, and advertising expenditures are all held constant at their Table 4.1 values, the relation between the quantity demanded of new domestic cars and price is expressed as2

Q = -500P + 210(\$50,000) + 200(\$45,000) + 20,000(300)

Alternatively, when price is expressed as a function of output, the industry demand curve (Equation 4.4) can be written:

2 At first blush, an 8 percent interest rate assumption might seem quite high by today's standards when 2.9 percent financing or \$2,500 rebates are sometimes offered to boost new car sales during slow periods. However, so-called "teaser" rates of 2.9 percent are subsidized by the manufacturer; that is why promotions feature 2.9 percent financing or (rather than and) \$2,500 rebates. In such instances, the alternative \$2,500 rebate is a good estimate of the amount of interest rate subsidy offered by the manufacturer.

Equations 4.4 and 4.5 both represent the demand curve for automobiles given specified values for all other variables in the demand function. Equation 4.5 is shown graphically in Figure 4.1 because it is common to show price as a function of quantity in demand analysis. As is typical, a reduction in price increases the quantity demanded; an increase in price decreases the quantity demanded. The -500 slope coefficient for the price variable in Equation 4.4 means that a \$1 increase in the average price of new domestic automobiles would reduce the quantity demanded by 500 cars. Similarly, a \$1 decrease in the average price of new domestic automobiles would increase quantity demanded by 500 cars. When price is expressed as a function of quantity, as in Equation 4.5, a one-unit increase in Q would lead to a \$0.002 reduction in the average price of new domestic cars. A 1-million car decrease in Q would lead to a \$2,000 increase in average prices. 