Price

Price-Demand Relationship

Figure 2 1 shows a simple linear relationship between price and demand.

Figure 2-1

Price–Demand Relationship

Generally, there is an inverse relationship between price and demand: as the price increases, demand decreases; as the price decreases, demand increases. This relationship is often represented as a linear function on a graph. The linear price-demand relationship can be expressed as:

The linear price-demand relationship can be expressed as:

Equation 2‑1

a is the price-axis intercept, representing the maximum price at which demand falls to zero — meaning no one is willing to buy at that price..
b is the slope of the line, indicating how much the price decreases for each unit increase in demand.
Equivalently, b represents the amount by which demand increases for each unit decrease in price.
Both a and b are positive constants.
By solving for D, we can express demand as a function of price:

Other Relationships

Figure 2-2 and Table 2-1 show some examples of various price-demand relationships.

Figure 2-2

Examples of Price–Demand Relationships

In addition to linear relationships, there are other relationships such as Nonlinear, Exponential, Logarithmic, Inverse (Hyperbolic), Power Law, Piecewise/Step Pricing, as well as no clear relationships, including some unusual ones, such as when consumers want more if the price increases. Table 2-1 shows several commonly used mathematical forms that represent different types of price-demand relationships.

Table 2‑1

Price-Demand Relationship Examples

No Relationships

Moreover, there are scenarios where no relationship exists between price and demand at all. We will consider several examples to explain the concept of the independence of price and demand in engineering economics. Although price may fluctuate due to supply and demand, many breakeven analyses can be performed to support decision-making under the assumption that price and demand are independent during the analysis period.

The Unusual Convention

One exception in engineering economic analyses (or any economic analyses) to standard conventions is that, in contrast to typical practice in engineering, science, and other disciplines, price is plotted along the Y-axis, even though it is the independent variable. Demand is a consumer response based on the price set by the producer, making demand a dependent variable.

Therefore, many textbooks and economic analyses commonly use the functional form D = f(p) while still plotting price on the Y-axis. However, if someone looks at graphs plotted with price (p) on the Y-axis and demand (D) on the X-axis and translates that graph into a mathematical formula, it is translated as p = f(D). To understand the basic concepts of price, demand, revenue, cost, profit, and breakeven points, both forms (D = f(p) and p = f(D)) have been used in various textbooks and refereed sources.

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