Demand Curve · aiwiki.page

A demand curve is a graphical representation of the relationship between the price of a good or service and the quantity buyers are willing and able to purchase during a specified period, holding other determinants of demand constant. In microeconomics, it is a central component of the supply-and-demand model. Price conventionally appears on the vertical axis and quantity demanded on the horizontal axis. Most demand curves slope downward: a lower price corresponds to a greater quantity demanded, other things equal. (openstax.org)

Definition and representation

Demand is not simply desire for a product: it incorporates willingness and ability to pay. A demand schedule lists quantities demanded at different prices; a demand curve plots that relationship. A particular point represents quantity demanded, whereas demand refers to the entire relationship. The quantity must be associated with a defined product, population, and period—for example, liters of gasoline demanded per week in a particular market. (openstax.org)

The relationship can be expressed as a function:

Q_d=D(P;\mathbf{z}),

where $P$ is the good’s own price and $\mathbf{z}$ represents other determinants, such as income, preferences, and prices of related goods. A curve holds $\mathbf{z}$ fixed. Where the relationship is invertible, inverse demand expresses price as a function of quantity:

P=P(Q_d).

This formulation matches the conventional placement of price on the vertical axis. Demand schedules and their graphical translation were explicitly discussed by Alfred Marshall in Principles of Economics. (openstax.org)

Movements along the curve and shifts

A change in the good’s own price, with other determinants unchanged, produces a movement along a demand curve. A change in another determinant produces a shift: buyers demand a different quantity at a given price. Thus, a fall in price ordinarily increases quantity demanded, not demand. (openstax.org)

Important causes of shifts include:

Income. Higher income increases demand for a normal good but decreases demand for an inferior good.
Prices of related goods. A rise in the price of a substitute generally increases demand for the good; a rise in the price of a complement generally decreases it. Substitute and complementary goods are defined by these relationships.
Preferences. Changes in tastes can alter demand at unchanged prices.
Buyer population. Changes in the number or composition of buyers affect market demand.
Expectations. Anticipated future prices or income can affect current purchases.

A rightward shift conventionally denotes increased demand; a leftward shift denotes decreased demand. A shift need not be parallel: the response can differ across prices. (openstax.org)

Consumer choice and the downward slope

Modern consumer theory derives demand from choices among affordable consumption bundles, represented using utility and indifference curves. Ordinary, or Marshallian, demand holds money income and other prices constant while the good’s own price changes. Hicksian, or compensated, demand instead holds utility constant by adjusting the expenditure available to the consumer. (ocw.mit.edu)

A price change has two analytically distinct effects:

The substitution effect reflects a change in relative prices while utility is held constant.
The income effect reflects the change in purchasing power caused by the price change.

For a normal good, both effects reduce purchases when its price rises. For an inferior good, the income effect works in the opposite direction. (ocw.mit.edu)

For differentiable, single-valued demands, the own-price Slutsky equation states:

\frac{\partial x_i(\mathbf{p},m)}{\partial p_i} = \frac{\partial h_i(\mathbf{p},u)}{\partial p_i} - x_i(\mathbf{p},m) \frac{\partial x_i(\mathbf{p},m)}{\partial m},

where $x_i$ is ordinary demand, $h_i$ is compensated demand, $\mathbf{p}$ is the price vector, and $m$ is income; compensated demand is evaluated at the utility attained under the original prices and income. Under standard consumer-choice assumptions, the compensated own-price effect is nonpositive. (ocw.mit.edu)

An ordinary demand curve can nevertheless slope upward over a range when an inferior good’s opposing income effect outweighs its substitution effect. Such a good is a Giffen good. Inferiority alone does not imply this behavior: an inferior good may still have downward-sloping demand. (ocw.mit.edu)

Individual, market, and firm demand

An individual demand curve describes one buyer’s purchases. Market demand combines quantities demanded by all buyers at each common price:

Q_d(P)=\sum_{k=1}^{N}q_k(P).

This is horizontal aggregation, not addition of the prices buyers are willing to pay. Marshall described the construction of market demand by adding individual demands at a given price. (econlib.org)

Market demand also differs from the demand confronting a particular seller. Under perfect competition, an individual firm takes the market price as given and faces a horizontal demand curve in the idealized model, even when market demand slopes downward. A monopolist, as the sole seller, faces market demand itself and generally must lower its price to sell more. The relevant curve therefore depends on whether the analysis concerns a buyer, a firm, or the whole market. (openstax.org)

Slope, elasticity, and functional forms

Price elasticity measures proportional responsiveness rather than the curve’s geometric slope. Where demand is differentiable and $P,Q_d>0$ , signed point elasticity is

\varepsilon_d=\frac{dQ_d}{dP}\frac{P}{Q_d}.

For downward-sloping demand, it is negative, although its absolute value is commonly reported. Demand is elastic when $|\varepsilon_d|>1$ , inelastic when $|\varepsilon_d|<1$ , and unit elastic when $|\varepsilon_d|=1$ . Elasticity is dimensionless; slope depends on measurement units. A straight line can therefore have constant slope but changing elasticity. (openstax.org)

For two observations, midpoint or arc elasticity is

\varepsilon_{\mathrm{arc}} = \frac{(Q_2-Q_1)/[(Q_1+Q_2)/2]} {(P_2-P_1)/[(P_1+P_2)/2]}.

Using midpoint denominators gives the same result whether the change is evaluated from the first observation to the second or in reverse. (openstax.org)

A useful illustrative linear specification is

Q_d=\max\{0,a-bP\},\qquad a,b>0.

On its positive-quantity segment, inverse demand is $P=a/b-Q_d/b$ , and elasticity is

\varepsilon_d=-\frac{bP}{a-bP}.

These expressions show directly why constant slope does not imply constant elasticity. Another illustrative specification,

Q_d=AP^{-\eta},\qquad A,\eta>0,

has constant signed elasticity $-\eta$ , as follows by differentiation.

Demand responsiveness also depends on the adjustment period. For many goods, consumers have more opportunities to substitute or change equipment over longer periods, making long-run demand more elastic than short-run demand. This is a common pattern rather than a universal rule. (openstax.org)

Equilibrium, revenue, and welfare

A demand curve alone does not determine the price or quantity actually traded. In the basic competitive model, market equilibrium occurs where quantity demanded equals quantity supplied. Changes in supply can produce movements along an unchanged demand curve; demand shifts change the equilibrium with a given supply curve. (openstax.org)

Demand also constrains revenue. For a seller charging one price, total revenue is $R(Q)=P(Q)Q$ , so marginal revenue is

MR=P(Q)+QP'(Q).

Consequently, marginal revenue lies below price where inverse demand slopes downward: selling an additional unit requires reducing the price on other units as well. A monopolist’s output decision compares marginal revenue with marginal cost, subject to the conditions for profit maximization. (openstax.org)

Demand’s elasticity determines how a price change affects revenue: along downward-sloping demand, a price increase raises revenue on an inelastic segment and lowers it on an elastic segment. (openstax.org)

In standard graphical analysis, consumer surplus is the area below inverse demand and above the price paid, up to the quantity purchased:

CS=\int_0^{Q^*}P(q)\,dq-P^*Q^*.

This measures the difference between buyers’ willingness to pay and their expenditure and is used in welfare economics to analyze gains from exchange. (openstax.org)

Empirical interpretation and limitations

A scatterplot of observed prices and sales does not automatically reveal a demand curve. Observations may reflect simultaneous shifts in supply and demand rather than price changes with demand determinants held fixed. Estimating the demand response therefore requires distinguishing price variation from changes in other demand conditions. This is a central identification problem in econometrics. (arxiv.org)

Instrumental variables can help identify demand when they generate relevant price variation without directly changing demand or being correlated with unobserved demand determinants. Whether those conditions are credible depends on the application; the statistical method alone does not establish them. (arxiv.org)

Finally, market demand must not be confused with aggregate demand. The latter is a macroeconomic relationship between an economy-wide price level and planned expenditure on domestic output, conventionally graphed against real GDP. It is not simply the horizontal sum of product demand curves: its variables and the mechanisms underlying its slope differ from those of demand in an individual market. (openstax.org)

References

Demand, Supply, and Equilibrium in Markets for Goods and Servicesopenstax.org
Shifts in Demand and Supply for Goods and Servicesopenstax.org
Principles of Economicseconlib.org
Unit 2: Consumer Theoryocw.mit.edu
Consumer Theory — Lecture Slidesocw.mit.edu
How a Profit-Maximizing Monopoly Chooses Output and Priceopenstax.org
Price Elasticity of Demand and Price Elasticity of Supplyopenstax.org
Elasticity and Pricingopenstax.org
Elasticity and Pricingopenstax.org
Chapter 3 Key Concepts and Summaryopenstax.org
Philip G. Wright, Directed Acyclic Graphs, and Instrumental Variablesarxiv.org