Theory of Demand and Supply: formula sheet

Key formulas

Demand function

Dx = f(Px, Py, Y, T, E, N)

Px = own price, Py = price of related goods, Y = income, T = tastes, E = expectations, N = number of buyers. Other factors are held constant.

Market demand

Market demand at a price = Σ individual demands at that price

Add quantities at the same price, not prices.

Linear demand function

Q = a − bP

a is the quantity demanded at zero price; b shows the fall in quantity for a ₹1 rise in price.

Movement vs shift

Own price changes → movement along the curve; any other determinant changes → shift of the curve

A rise in demand shifts the curve right; a fall shifts it left.

Law of demand

Price ↑ → Quantity demanded ↓; Price ↓ → Quantity demanded ↑ (other things equal)

Inverse relationship. The demand curve slopes downward from left to right.

Assumptions (ceteris paribus)

Income, tastes, prices of related goods, expectations and number of buyers are constant

If any of these changes, the curve shifts instead of the law being tested.

Reasons for downward slope

Diminishing marginal utility + income effect + substitution effect + new buyers/extra uses

Learn these four as a set.

Main exceptions

Giffen goods, Veblen goods, expected price changes, emergency necessities, ignorance, speculation

In these cases the curve may slope upward.

Movement along the curve

Own price changes, other factors constant → change in quantity demanded

Price falls → extension. Price rises → contraction. Same curve.

Shift of the curve

Any other determinant changes, price constant → change in demand

Rightward shift = increase. Leftward shift = decrease. New curve.

Factors that shift demand

Income, tastes, prices of related goods, expectations, population

Remember these as the 'other than own price' factors.

Related goods effect

Substitute price ↑ → demand ↑; Complement price ↑ → demand ↓

Applies to demand for the other good, not the good whose price rose.

Income effect on shifts

Normal good: income ↑ → demand ↑; Inferior good: income ↑ → demand ↓

Inferior goods behave the opposite way.

Price elasticity of demand (percentage method)

Ed = (% change in quantity demanded) ÷ (% change in price) = (ΔQ ÷ Q) ÷ (ΔP ÷ P)

Q and P are the original values. The value is negative for normal goods, but exam answers usually use the absolute value.

Arc (mid-point) elasticity

Ed = (ΔQ ÷ ΔP) × ((P1 + P2) ÷ (Q1 + Q2))

Use when the question asks for elasticity between two points and says average or mid-point.

Point elasticity

Ed = (dQ ÷ dP) × (P ÷ Q)

For a linear demand curve, dQ ÷ dP is the slope coefficient of Q on P.

Total outlay (expenditure) method

Price up, outlay down: Ed > 1. Price up, outlay up: Ed < 1. Outlay unchanged: Ed = 1

Outlay = P × Q. Reverse the logic for a price fall: price down and outlay up means Ed > 1.

Income elasticity of demand

Ey = (% change in quantity demanded) ÷ (% change in income)

Positive: normal good. Negative: inferior good. Above 1: luxury. Between 0 and 1: necessity.

Cross elasticity of demand

Exy = (% change in quantity of X) ÷ (% change in price of Y)

Positive: substitutes. Negative: complements. Zero: unrelated.

Market supply

Market supply at a price = Σ individual supplies at that price

Add quantities across firms at the same price. Do not add prices.

Movement along the curve

Own price ↑ → quantity supplied ↑ (extension); own price ↓ → quantity supplied ↓ (contraction)

Other determinants are assumed constant (ceteris paribus).

Shift of the curve

Favourable change in a non-price determinant → rightward shift (increase in supply); unfavourable change → leftward shift (decrease in supply)

A rightward shift means more is supplied at every price.

Effect of input cost

Input cost ↑ → supply ↓ (shift left); input cost ↓ → supply ↑ (shift right)

Higher cost lowers profit at each price.

Effect of tax and subsidy

Tax ↑ → supply ↓; subsidy ↑ → supply ↑

A tax raises the cost of production, a subsidy lowers it.

Law of supply

Price ↑ ⇒ Quantity supplied ↑ (other things equal)

Direct relationship. The supply curve slopes upward.

Elasticity of supply (percentage method)

Es = (% change in quantity supplied) ÷ (% change in price)

Es is normally positive, since price and quantity supplied move together.

Elasticity of supply (using values)

Es = (ΔQ ÷ Q) ÷ (ΔP ÷ P) = (ΔQ ÷ ΔP) × (P ÷ Q)

Here P and Q are the original price and quantity. ΔQ and ΔP are the changes.

Types of elasticity of supply

Es > 1 elastic; Es < 1 inelastic; Es = 1 unitary; Es = 0 perfectly inelastic; Es = ∞ perfectly elastic

A vertical supply curve means Es = 0. A horizontal one means Es = ∞. A linear supply curve through the origin has Es = 1 at every point. A linear curve that meets the price axis (positive intercept) has Es > 1. One that meets the quantity axis has Es < 1.

Equilibrium condition

Qd = Qs

Solve this equation for P to get the equilibrium price. Then substitute P into either equation for the equilibrium quantity.

Excess demand

Excess demand = Qd − Qs (when Qd > Qs)

Occurs at a price below equilibrium. Pressure on price is upward.

Excess supply

Excess supply = Qs − Qd (when Qs > Qd)

Occurs at a price above equilibrium. Pressure on price is downward.

Effect of a demand shift (supply unchanged)

Demand ↑ → P ↑, Q ↑; Demand ↓ → P ↓, Q ↓

Price and quantity move in the same direction.

Effect of a supply shift (demand unchanged)

Supply ↑ → P ↓, Q ↑; Supply ↓ → P ↑, Q ↓

Price and quantity move in opposite directions.

Quick revision

• Demand is the quantity buyers are willing and able to buy at each price in a given period.
• Law of demand: other things constant, a lower price raises quantity demanded, and a higher price lowers it.
• A change in the good's own price causes a movement along the curve; a change in any other determinant shifts the curve.
• An increase in demand shifts the curve right; a decrease shifts it left.
• Ed = % change in quantity demanded ÷ % change in price, usually read as a positive number.
• Ed > 1 is elastic, Ed < 1 is inelastic, Ed = 1 is unitary elastic.
• Supply rises with price: a higher price gives a higher quantity supplied, other things constant.
• A change in input costs, technology or taxes shifts the supply curve; own price moves along it.
• Equilibrium is where quantity demanded equals quantity supplied, giving the market price.
• If price is above equilibrium there is excess supply, and price tends to fall; if below, there is excess demand, and price tends to rise.
• If demand rises with supply unchanged, equilibrium price and quantity both rise.
• If supply rises with demand unchanged, equilibrium price falls and quantity rises.

Common mistakes

• Treating a price fall as an increase in demand. Fix: A price change only changes quantity demanded (a movement). Demand changes only when a non-price factor changes.
• Confusing substitutes with complements. Fix: Substitutes can replace each other, so demand moves with the other good's price. Complements are used together, so demand moves against it.
• Treating a shift of the demand curve as a violation of the law. Fix: The law is only about price changes with other factors constant. Other changes shift the curve.
• Saying Giffen goods are luxury goods. Fix: Giffen is inferior and staple. Veblen is a luxury bought for status.
• Calling a price-driven rise in purchases an 'increase in demand'. Fix: If the good's own price caused it, the term is extension of demand, not increase.
• Shifting the curve when the good's own price changes. Fix: Own price change means a move along the same curve. Only other factors shift it.
• Dividing by the new value instead of the original value when finding percentage change. Fix: Always take the original (first) value as the base, unless the question says mid-point.
• Confusing elasticity with the slope of the demand curve. Fix: Remember elasticity uses percentages and the ratio P ÷ Q, so it changes along a straight-line curve, while slope does not.
• Calling a price-driven change an 'increase in supply'. Fix: Use 'extension of supply' when only own price rises and 'increase in supply' only when the curve shifts.
• Treating a tax as something that raises supply. Fix: A tax raises cost, so supply falls. A subsidy lowers cost, so supply rises.

Exam tips

• Most questions test the difference between a movement along the curve and a shift. Decide this first.
• Learn the list of determinants with one example each, as options often use real goods like tea, coffee, petrol and cars.
• For inferior goods, expect an income question that reverses the usual direction.
• Market demand questions use small numbers. Add quantities at the same price and check you used the right price row.
• There is no negative marking, so attempt every question and eliminate wrong options first.
• Questions often ask you to pick the exception from four options. Learn Giffen and Veblen definitions word for word.
• Expect a 'which is NOT' question on reasons for the downward slope.
• Watch for scenarios where income or taste changes. The answer is a shift, not the law.