The law of demand says that, other things equal, a higher price for a good or service leads people to demand a smaller quantity of that good or service. On a graph, this means the demand curve is a downward sloping function of the price of the good or service being studied. For each quantity, the demand curve reveals the maximum price consumers are willing (and able) to pay. Similarly, at each level of the price, the demand curve reveals the maximum quantity that consumers are willing (and able) to purchase. In the case of a linear expression, a demand curve in its simplest form would be:

where P is the price, Q^d is the quantity, and a and b are positive constants.¹ That b × Q^d is subtracted from a constant tells us the law of demand holds here—as price rises, all else constant, a lower level of quantity is demanded and vice versa (the demand curve slopes downward). The b term describes how sensitive the price is to changes in the quantity demanded (i.e., the slope of the demand curve). If b takes on a larger value, then the demand curve becomes relatively steeper—the same change in quantity results in a larger change in the maximum price consumers are willing to pay. If b takes on a smaller value, the effect is opposite—the demand curve becomes relatively flatter and the same change in quantity results in a smaller change in the maximum price consumers are willing to pay.

Although Equation 3A-1 looks straightforward, there is a lot more going on beneath the surface. The constant a contains information on the factors that shift the demand curve: changes in the price(s) of related goods and services, changes in income, changes in tastes, changes in expectations, and changes in the number of consumers. For example, the annual demand for maple syrup, with the price in dollars per litre and the quantity in millions of litres, may be given by a linear demand curve such as:

with a expanded to include several factors multiplied by constants that are summarized in Table 3A-1. These factors are all multiplied by positive constants that, like b, describe how sensitive the demand curve is to changes in those factors. The constant a₀ picks up the impact of all other determinants of the demand for maple syrup that have been left out of the equation of the demand curve.

Note that the “other things equal” assumption means that everything in the demand curve equation, except P and Q^d, are being held constant. So, other things equal, when we move along the demand curve as P and Q^d change—the quantity demanded either increases or decreases. If one of these other factors does change, then the entire demand curve shifts either to the right (up) or left (down)—demand either increases or decreases. Figure 3A-1 examines a shift in the demand curve using algebra.

Let us simplify the expanded equation. Suppose the following values apply for factors that affect the demand curve for maple syrup: P_{corn syrup} = $10, P_{pancake mix} = $5, Y = $40, which represents the average income of a Canadian (in thousands of dollars), Tastes = 9, = $20 (per litre), and Pop = 34, which is the population of Canada (in millions of people). Suppose also the values for the constants are a₀ = $5, a₁ = 0.25, a₂ = 2, a₃ = 0.5, a₄ = $0.45, a₅ = 1.5, a₆ = $0.05, and b = 1.25.

Given these assumed values, the demand curve for maple syrup becomes: