1.3: The Demand Schedule

The demand schedule is the relationship between own-quantity demanded and corresponding own-price levels. Several variables could affect the demand for a product, including the prices or quantities of related goods. The adjective “own-quantity” is used to mean the quantity of the product being analyzed. For example, the own-quantity of beef could be represented as \(Q_{BEEF}\) and the own-price of beef as \(P_{BEEF}\). The price of pork, \(P_{PORK}\), could conceivably affect demand for beef, but this is not the own-price of beef. The point to be made is that the demand schedule is the relationship between the product’s own-quantity and its own-price holding all other variables that could affect demand constant at some fixed value. The normal convention in this course will be to use subscripts to denote the product in question. For example, \(Q_{1}\) refers to the demand for good 1, \(P_{2}\) refers to the price of good 2, etc.

The demand schedule can be expressed mathematically as \(Q_{1} = f P_{1}\) or \(P_{1} = f^{-1} (Q_{1})\). The term “direct demand” is used when \(Q_{1}\) is on the left-hand side of the equation and the term “inverse demand” when \(P_{1}\) is on the left-hand side. When showing a demand relationship as an equation, the normal practice is to express the relationship in terms of direct demand. However, it will generally be graphed in inverse form with the price of the product on the vertical axis and the quantity on the horizontal axis. This convention is consistent with most microeconomics text books and can be useful when you want to simultaneously show production (supply side) relationships on the same plot. Many textbooks, however, do not distinguish between direct and inverse demand. The distinction is being made here because you learned back in middle-school algebra that if \(y = f(x)\), then \(y\) goes on the vertical axis and \(x\) goes on the horizontal. The term “inverse demand,” permits adherence to both algebraic and economic conventions.

Demonstration \(\PageIndex{1}\): An inverse market demand schedule

The Law of Demand

The law of demand states that quantity and price are negatively related. In other words, if the price of the product increases, then the quantity demanded will decrease and vice versa. The law of demand reflects two phenomena. First, consumer preferences generally exhibit diminishing marginal utility. Diminishing marginal utility is a technical way of saying that consumers receive lower amounts of additional satisfaction from each additional unit of a product they consume. Because of diminishing marginal utility, the price will need to fall to induce consumers to buy more units of products that they already consume. This contributes to the negative relationship between quantity demanded and price. Second, in most cases, different consumers place different valuations on the same product. For example, suppose that Jane and John Doe would both enjoy tickets to a St. Louis Cardinals baseball game. Jane loves baseball and is a huge Cardinals fan. John mildly enjoys baseball and prefers the Minnesota Twins. It would stand to reason that Jane would probably place a higher value on the tickets than John would. The point here is that it is often the case that some consumers are very enthusiastic about a product and are willing to participate in the market even when the price is high. Other, less enthusiastic, consumers stay out of the market at high prices but are willing to participate once the price comes down a bit. For this reason, the number of consumers willing to participate in the market increases as the price falls and decreases as the price rises. This also contributes to the negative relationship between quantity demanded and price.

Because of diminishing marginal utility and differences in valuation across consumers, an increase (decrease) in price has two potential effects, each of which contributes to the negative relationship between quantity and price.

1. Each consumer buys less (more) of the product due to diminishing marginal utility.
2. The total number of consumers decreases (increases) as consumers with valuations close to the prevailing price exit (enter) the marketplace.

Demand Shifters

The demand schedule characterizes the relationship between quantity demanded and that product’s own-price. For instance, the demand schedule for beef would show the relationship between quantity of beef demanded and the price of beef holding everything else constant. What happens if something else changes? There are other prices that could affect the demand for beef. For many consumers, pork or poultry serve as reasonable substitutes for beef. Consequently, if pork or poultry prices decline (rise) relative to beef prices, one would expect reduced (increased) quantities of beef to be demanded. This suggests that other factors, aside from a product’s own-price, need to be considered. These other factors are called demand-shift variables. If the value of a shift variable changes, you will need to plot a new demand schedule that reflects the updated relationship between quantity demanded and the product’s own-price. The following are some common demand shift variables.

Prices of related goods (substitutes or complements)

Related goods in demand are classified as substitutes in consumption or complements in consumption. A substitute in consumption is a good that the consumer can use instead of the good in question to meet his or her underlying want or need. For example, if you are analyzing the demand schedule for beef, then chicken, pork, or fish are all reasonable substitute products. After all, one could order a chicken, pork, or seafood entree from the menu in lieu of beef; or the supermarket shopper may decide to cook chicken breasts, pork chops, or fish fillets for dinner instead of beef. Formally, product 2 is considered to be a substitute for product 1 if an increase (decrease) in the price of product 2 causes an increase (decrease) in the demand schedule for product 1. In other words, there is a positive relationship between the price of product 2 and the quantity of product 1 that consumers demand.

A complement in consumption is a good that the consumer uses along with the good in question. For example, if you are analyzing the demand for sport utility vehicles (SUVs), then gasoline is reasonable complementary product. After all, an SUV is a large automobile and uses a lot of gas. In recent years, gasoline prices appear to have had an effect on the demand schedule for SUVs. During periods of high gasoline prices, sales of SUVs suffer. Formally, product 2 is considered to be a complement for product 1 if an increase (decrease) in the price of product 2 causes a decrease (increase) in the demand schedule for product 1. In other words, there is a negative relationship between the price of product 2 and the quantity of product 1 that consumers demand.

Consumer income

Consumer incomes can also shift the demand schedule, but the direction and magnitude of the shift depend on the characteristics of the good in question. Some goods are classified as normal goods. Consumption of a normal good increases as income increases. Formally, good 1 is said to be a normal good if an increase (decrease) in income causes an increase (decrease) in the demand schedule for good 1. In other words, there is a positive relationship between consumption of good 1 and the amount of income available to consumers. Other goods are classified as inferior goods. Consumption of an inferior good decreases as income increases. Formally, good 1 is said to be an inferior good if an increase (decrease) in income causes an decrease (increase) in the demand schedule for good 1. In other words, there is a negative relationship between consumption of good 1 and the amount of income available to consumers. It is important to emphasize that the adjective “inferior” only refers to the income relationship and does not imply that the consumer dislikes the good in question.

Tastes and preferences

Demand is subject to trends, fashions, health concerns, and a variety of other considerations. For example, in 2012, media coverage of lean finely textured beef (LFTB), characterized as “pink slime”, had an impact on demand for ground beef. This would classify as information that led to an unfavorable change in preferences (meaning the product in question is less favored by consumers than before). Conversely, a growing number of studies linking blueberries to improved health has impacted demand for blueberries in a positive way. This would classify as a favorable change in preferences.

• Link to a 2012 magazine article on the LFTB controversy by economists J. Ross Pruitt and David P. Anderson (visit choicesmagazine.org).
• Link to the 2012 ABC News Segment on LFTB mentioned in the magazine article (visit youtube.com).
• Link to LSU AgCenter publication Blueberries and Your Health (visit lsuagcenter.com).

Population

Market demand reflects the sum of all consumers in the marketplace. All else equal, as the number of consumers increases (decreases), the demand schedule will increase (decrease).

Demonstration \(\PageIndex{2}\): Demand shift variables change the demand schedule

Demand Schedules from a Linear Demand Relationship

A general demand relationship would need to include all the demand shifters that could affect demand in addition to own-price. With this in mind, consider the following demand equation for good A:

\(Q_{A} = 20Pop + 0.01M + 2P_{B}- 4P_{A}\)

In this equation, \(Q_{A}\) is the quantity of good A in thousands of units, \(Pop\) is population in millions of persons, \(M\) is disposable income in dollars, \(P_{B}\) is the price of good B in dollars, and \(P_{A}\) is the price of good A in dollars. Given this equation, you are able to answer some general questions about the demand for good A.

• Is good A a normal good or an inferior good? How can you tell? Good A is a normal good. You can tell because the coefficient associated with the income variable (0.01) is a positive number. If this were a negative number, you would have an inferior good.
• Is good B a substitute or a complement to good A? How can you tell? Good B is a substitute for good A. You can tell because the coefficient associated with the price of good B is a positive number. If this were a negative number, you would instead conclude that good B is a complement to good A.
• Does the demand for good A conform to the law of demand? How can you tell? Yes. The coefficient associated with the price of good A is a negative number showing an inverse relationship between the quantity of good A and the price of good A.
• What variables shift the demand schedule? In this case, there are three variables: population \(Pop\), income \(M\), and the price of the substitute good \(P_{B}\). Remember that the demand schedule is the relationship between own-price and own-quantity. In the equation above, \(P_{A}\) represents the own-price and \(Q_{A}\) represents the own-quantity. Thus, every right-hand-side variable other than \(P_{A}\) is a demand shifter.

The demand schedule shows the relationship between own-price and own-quantity demanded holding all else constant. In this case, “all else” consists of the three demand shifters. Thus, to get an equation for the demand schedule you need to fix these shift variables at some value. Let us use a value of 3 million for \(Pop\), $30,000 for \(M\), and $20 for \(P_{2}\). Using these values, you get the direct demand schedule:

\(Q_{A} = 20(3) + 0.01(30000) + 2(20) -4P_{A}\)

or

\(Q_{A} = 400-4P_{A}\)

Remember that this is the direct demand schedule because \(Q_{A} = f(P_{A})\). It is simple enough to get the inverse demand schedule. Simply solve to get \(P_{A}\) on the left side of the equation. The inverse demand schedule is

\(P_{A} = 100 - \dfrac{1}{4} Q_{A}\)