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Demand and Supply

Supply Curve

Determinants of Supply

The supply curve illustrates how the quantity supplied responds to changes in various factors. Below is a breakdown of the determinants:

Determinants Effect on Curve
Price Move along curve (no shift)
Input price Shift curve
Technology Shift curve
Expectations Shift curve
Number of sellers Shift curve

Note

When price decreases while income remains constant, consumers' purchasing power increases.

Elasticity Concepts

Price Elasticity of Demand (PED)

Formula:

\[ PED = \frac{\Delta \text{Quantity Demanded\%}}{\Delta \text{Price\%}} $$ $$ PED \in [0, +\infty) \]
Types of Price Elasticity of Demand

  • Perfectly Elastic Demand \(PED = \infty\): The demand curve is a horizontal line.

  • Relatively Elastic Demand
    \(PED > 1\): Percentage change in quantity demanded exceeds percentage change in price (\(\Delta QD\% > \Delta P\%\)).

  • Unit Elastic Demand
    \(PED = 1\): Percentage change in quantity demanded equals percentage change in price (\(\Delta QD\% = \Delta P\%\)).

  • Relatively Inelastic Demand
    \(0 < PED < 1\): Percentage change in quantity demanded is less than percentage change in price (\(\Delta QD\% < \Delta P\%\)).

  • Perfectly Inelastic Demand
    \(PED = 0\): The demand curve is a vertical line.

Total Revenue and Elasticity
\[ TR = P \cdot Q \]
  • \(Price \propto TR \implies \text{Inelastic}\)
  • \(Price \propto \frac{1}{TR} \implies \text{Elastic}\)
  • \(Price = C \implies \text{Unit Elastic}\)

2.2 Price Elasticity of Supply (PES)

Formula:

\[ PES = \frac{\Delta \text{Quantity Supplied\%}}{\Delta \text{Price\%}} $$ $$ PES \in [0, +\infty) \]
Simple Formula
  • \(\Delta \text{Quantity Supplied\%} = \frac{Q_2 - Q_1}{Q_1}\)
  • \(\Delta \text{Price\%} = \frac{P_2 - P_1}{P_1}\)
Mid-Point Formula
  • \(\Delta \text{Quantity Supplied\%} = \frac{Q_2 - Q_1}{\frac{Q_2 + Q_1}{2}}\)
  • \(\Delta \text{Price\%} = \frac{P_2 - P_1}{\frac{P_2 + P_1}{2}}\)
Types of Price Elasticity of Supply

  • Perfectly Elastic Supply
    \(PES = \infty\): The supply curve is a horizontal line.

  • Relatively Elastic Supply
    \(PES > 1\): Percentage change in quantity supplied exceeds percentage change in price (\(\Delta QS\% > \Delta P\%\)).

  • Unit Elastic Supply
    \(PES = 1\): Percentage change in quantity supplied equals percentage change in price (\(\Delta QS\% = \Delta P\%\)).

  • Relatively Inelastic Supply
    \(0 < PES < 1\): Percentage change in quantity supplied is less than percentage change in price (\(\Delta QS\% < \Delta P\%\)).

  • Perfectly Inelastic Supply
    \(PES = 0\): The supply curve is a vertical line.

2.3 Income Elasticity of Demand (YED)

Formula**: $$ YED = \frac{\Delta \text{Quantity\%}}{\Delta \text{Income\%}} $$

  • \(YED > 0 \implies \text{Normal Good}\)
  • \(YED < 0 \implies \text{Inferior Good}\)

2.4 Cross-Price Elasticity of Demand (XED)

Formula:

\[ XED = \frac{\Delta \text{Quantity\% of X}}{\Delta \text{Price\% of Y}} \]
  • \(XED > 0 \implies \text{Substitutes}\)
  • \(XED < 0 \implies \text{Complements}\)

Market Equilibrium

Equilibrium Price

The equilibrium price is the point where the Demand Curve and Supply Curve intersect.

Changes in Supply and Demand

No Change in Supply Increase in Supply Decrease in Supply
No Change in Demand \(P=\), \(Q=\) \(P \downarrow\), \(Q \uparrow\) \(P \uparrow\), \(Q \downarrow\)
Increase in Demand \(P \uparrow\), \(Q \uparrow\) \(P ?\), \(Q \uparrow\) \(P \uparrow\), \(Q ?\)
Decrease in Demand \(P \downarrow\), \(Q \downarrow\) \(P \downarrow\), \(Q ?\) \(P ?\), \(Q \downarrow\)

Consumer and Producer Surplus

Consumer Surplus

  • Willingness to Pay (WTP): The maximum price a consumer is willing to pay for a good or service.
  • Marginal Buyer: The consumer who leaves the market first if the price rises further.
\[ \text{Consumer Surplus} = \text{Willingness to Pay} - \text{Actual Price} \]

Producer Surplus

  • Marginal Seller: The producer who leaves the market first if the price decreases further.
\[ \text{Producer Surplus} = \text{Actual Price} - \text{Cost} \]

Total Surplus

\[ \text{Total Surplus} = \text{Consumer Surplus} + \text{Producer Surplus} \]

surplus

Government Intervention in Markets

Price Ceiling

  • Effective only when actual price > price ceiling.
  • Causes a shortage:
    $$ \text{Shortage} = QD - QS $$
  • Protects consumers.

Price Floor

  • Effective only when actual price < price floor.
  • Causes a surplus:
    $$ \text{Surplus} = QS - QD $$
  • Protects producers.

Taxes

  • Tax burden depends on elasticity:
    $$ \text{Inelastic} \implies \text{Higher tax burden} $$
  • Size of tax:
    $$ \text{Size of Tax} = \text{Price of Demand} - \text{Price of Supply} $$
  • Tax revenue:
    $$ \text{Tax Revenue} = T \cdot Q $$
Impact of Taxes on Surplus
Without Tax With Tax Change
Consumer Surplus \(A + B + C\) \(A\) \(-(B + C)\)
Producer Surplus \(D + E + F\) \(F\) \(-(D + E)\)
Tax Revenue None \(B + D\) \(+(B + D)\)
Total Surplus \(A + B + C + D + E + F\) \(A + B + D + F\) \(-(C + E)\)

tax-graph

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