Question 3 — Explain the Demand Function. What are the Various Types of Demand?

Introduction

The demand function is a formal and systematic representation of consumer behaviour showing how the quantity demanded of a commodity depends on the factors that influence demand. TR Jain and V.K. Ohri stress that demand is not an isolated concept; it reflects a network of relationships among price, income, tastes, prices of related goods, expectations and other socio-economic determinants. A robust understanding of the demand function is essential for demand forecasting, price analysis and policy formulation. This answer presents an exhaustive treatment—definition, mathematical and graphical representation, properties, methods of specification and estimation, followed by a comprehensive classification of types of demand with examples and implications.

Definition and Conceptual Clarification

Demand Function: A demand function expresses the quantity demanded (Q) as a function of all the determinants that affect it. In symbolic terms:

Q = f(P, Y, T, Ps, Pc, E, N, G, O)

Where: P = price of the commodity; Y = consumer’s income; T = tastes and preferences; Ps = price of substitutes; Pc = price of complements; E = expectations about future prices/income; N = number of buyers (population); G = government policy/taxes/subsidies; O = other factors (season, credit conditions, advertising).

Interpretation

1. The function indicates how Q changes when one determinant changes and others are held constant (partial equilibrium ceteris paribus analysis).
2. It allows decomposition of demand changes into price effects and non-price effects (income, tastes, related prices etc.).
3. It is the basis for empirical demand estimation (econometrics) and theoretical comparative-static analysis.

Mathematical Forms of Demand Function

Demand functions may take different functional forms depending on assumptions about consumer behaviour and empirical fit. Common forms include:

1. Linear demand: Q = a − bP, where a, b > 0. Simple, easy to estimate; slope constant; convenient for short-run analysis.
2. Linear with multiple determinants: Q = a + bP + cY + dPs + ePc + … (signs expected: b < 0, c > 0 for normal goods, d > 0 for substitutes, e < 0 for complements).
3. Log-linear (constant elasticity): ln Q = α + β ln P + γ ln Y + …. Coefficients represent elasticities directly (β is price elasticity).
4. Cobb–Douglas style: Q = A P^{β} Y^{γ} …, multiplicative form often used for goods whose demand depends multiplicatively on variables.
5. Quadratic or Non-linear forms: To capture curvature, saturation or turning points: Q = a − bP + cP^2 or other flexible functional forms.

Graphical Representation and Demand Schedule

Though the demand function is a formal relation, it is commonly represented by a schedule and a demand curve. A demand schedule lists price–quantity pairs; the demand curve (price on Y-axis, quantity on X-axis) shows the inverse relation between price and quantity demanded for ordinary goods. The slope or curvature depends on the functional form chosen.

Properties of Demand Function (Important)

1. Negativity of price effect: For normal goods, ∂Q/∂P < 0 (law of demand holds).
2. Homogeneity in income-price models: Demand may be homogeneous of degree zero in prices and income in certain theoretical frameworks (only relative prices and real income matter).
3. Additivity: Market demand is the horizontal summation of individual demand functions.
4. Continuity and differentiability: For comparative statics and elasticity analysis, differentiability is assumed.
5. Elasticity measures: Price elasticity, income elasticity and cross elasticity are derivatives of the demand function and summarise responsiveness.

Determinants of Demand (Detailed Discussion)

1. Price of the commodity (P): Primary determinant; influences both substitution and income effects.
2. Income (Y): Higher income shifts demand for normal goods outwards; for inferior goods it may shift demand inwards.
3. Tastes and preferences (T): Changes due to fashion, advertising or information can significantly alter demand.
4. Prices of related goods (Ps, Pc): Substitutes and complements affect demand directionally.
5. Population and market size (N): Larger population increases market demand (horizontal summation effect).
6. Expectations (E): Expected future price or income changes affect present demand (stocking or postponement behaviour).
7. Government policy (G): Taxes, subsidies, price controls and public provision alter effective price and demand.
8. Seasonality and climatic factors (O): Seasonal goods show predictable demand shifts.

Estimation and Measurement (Brief Overview)

Empirical demand estimation uses observed data to fit a functional form (OLS, IV, time-series, panel methods). Important issues:

1. Specification: Choose functional form—linear, log-linear, or flexible forms depending on data patterns.
2. Endogeneity: Price may be endogenous (simultaneity of supply and demand); instrumental variables or structural models are used.
3. Aggregation: Individual demand aggregation to market demand must consider heterogeneity across consumers.
4. Elasticity estimation: Elasticities are estimated from derivatives/coefficients (point elasticity or arc elasticity methods).

Types of Demand — Exhaustive Classification and Examination

A precise classification helps in examination answers. TR Jain and V.K. Ohri emphasise clarity, examples and implications. Below is an expanded and exam-ready taxonomy:

1. Individual Demand vs Market Demand
   1. Individual demand: Demand of a single consumer for a commodity at various prices.
   2. Market demand: Horizontal sum of individual demands across all consumers at each price.
   3. Implication: Market demand curve is derived by aggregation and exhibits typical responsiveness properties if individual demands do.
2. Price Demand

   Demand as a function of own-price (Q = f(P)). Fundamental for demand analysis, elasticity measurement and revenue implications.

3. Income Demand

   Q = f(Y). Goods classified by income reaction: normal (dQ/dY > 0), inferior (dQ/dY < 0), and luxury/superior (income elasticity > 1).

4. Cross Demand

   Qx = f(Py). Positive cross elasticity indicates substitutes (e.g., tea and coffee); negative indicates complements (e.g., cars and petrol).

5. Derived Demand

   Demand for a factor or intermediate good derived from demand for final goods (e.g., demand for steel derived from demand for cars). Policy or shock in final goods markets translates into factor demand changes.

6. Joint Demand

   Goods demanded together for a single use (e.g., left and right shoes, printer and cartridges). Joint demand implies complementarity and interdependence in pricing decisions.

7. Composite Demand

   Goods with multiple uses (e.g., oil used for domestic heating, industry, transport). Change in demand for one use affects total demand and allocation to other uses.

8. Competitive Demand

   Demand for goods that compete for the same want (substitutes). Example: butter vs margarine; pricing strategy must consider cross-elasticity.

9. Composite and Autonomous Demand

   Autonomous demand arises independently of other demands (e.g., basic food needs). Induced demand is generated by related consumption (e.g., air travel induced by business expansion).

10. Seasonal and Cyclical Demand

    Demand varying with seasons (festivals, harvest) or business cycles (durable goods demand falls in recession). Planning requires seasonal adjustment and inventory strategies.

11. Speculative Demand

    Demand driven by expectations of capital gains or future price increases (commodities, assets). Speculative demand can destabilise markets and cause deviations from ordinary demand relations.

12. Government and Institutional Demand

    Demand originating from public authorities (defence procurement, public infrastructure). Institutional demand often differs in price sensitivity and procurement mechanisms.

Illustrative Examples (to demonstrate understanding)

Example 1 (Price Demand): If a branded notebook’s price falls from ₹60 to ₹40 and sales rise from 500 to 800 units, the demand function can be locally approximated and elasticity computed to inform pricing decisions.

Example 2 (Derived Demand): A rise in demand for housing increases demand for cement and steel; the function for steel will include housing demand as an indirect determinant.

Common Exam Approaches & Answer Strategy

1. Begin with a crisp definition of demand function and write the general functional form.
2. Give the standard functional forms (linear, log-linear, Cobb–Douglas) and state the economic interpretation of parameters.
3. List determinants and discuss their signs and economic intuition.
4. Provide a comprehensive classification of types of demand with short examples for each.
5. Conclude with a short paragraph relating demand function to elasticity and policy implications.

Conclusion (Model Examination Ending)

The demand function is a fundamental analytical construct that organises the complex influences on consumer behaviour into a tractable form. Mastery of its forms, properties and types enables precise demand forecasting, elasticity analysis and policy prescription. The various types of demand—price, income, cross, derived, joint, composite and others—reflect different economic relationships and require tailored analytical tools. A student who presents the definition, mathematical forms, determinants, classification and short applied examples in a structured manner will fully satisfy examination expectations.