Microeconomics Study Notes: Elasticity, Market Equilibrium, Opportunity Cost, Surplus, and Utility

Elasticity of Demand

Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of quantity demanded to changes in price. It is a key concept in microeconomics for understanding consumer behavior and market dynamics.

• Definition: Price elasticity of demand (PED) is the percentage change in quantity demanded divided by the percentage change in price.

• Formula: $\text{PED} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}$

• Calculation Example: If the quantity demanded of skipping ropes rises from 1250 to 1750 units when the price falls from $1.25 to $0.75 per unit:

  • Change in quantity demanded: $1750 - 1250 = 500$

  • Average quantity: $(1750 + 1250)/2 = 1500$

  • Change in price: $0.75 - 1.25 = -0.5$

  • Average price: $(0.75 + 1.25)/2 = 1$

  • PED: $\frac{500}{1500} \div \frac{-0.5}{1} = \frac{1}{3} \div -0.5 = -0.67$

  • Interpretation: The absolute value is 0.67, so demand is inelastic.

• Elastic vs. Inelastic Demand:

  • Elastic: $|PED| > 1$ (quantity demanded changes more than price)

  • Inelastic: $|PED| < 1$ (quantity demanded changes less than price)

Elasticity Calculation for Other Goods

• Example: For cereal, if price rises from $5 to $7 and quantity demanded falls from 800 to 400:

  • Change in price: $7 - 5 = 2$

  • Average price: $(7 + 5)/2 = 6$

  • Change in quantity: $400 - 800 = -400$

  • Average quantity: $(400 + 800)/2 = 600$

  • PED: $\frac{-400}{600} \div \frac{2}{6} = -0.67 \div 0.33 = -2$

  • Interpretation: The absolute value is 2, so demand is elastic.

Market Equilibrium

Equilibrium Price and Quantity

Market equilibrium occurs where the quantity demanded equals the quantity supplied. The intersection of the demand and supply curves determines the equilibrium price and quantity.

• Example: For knobs, demand curve $P = 75 - 6Q_d$, supply curve $P = 35 + 2Q_s$:

  • Set $Q_d = Q_s = Q^*$ and $P^* = 75 - 6Q^* = 35 + 2Q^*$

  • Solve: $75 - 6Q^* = 35 + 2Q^* \Rightarrow 8Q^* = 40 \Rightarrow Q^* = 5$

  • Equilibrium price: $P^* = 75 - 6 \times 5 = 45$

• Shifts in Equilibrium: If price is fixed above equilibrium, quantity supplied exceeds quantity demanded, leading to surplus.

Opportunity Cost and Comparative Advantage

Opportunity Cost

Opportunity cost is the value of the next best alternative forgone when making a choice. It is fundamental in determining comparative advantage and trade patterns.

• Definition: Opportunity cost of producing one good is the amount of another good that must be given up.

• Example Table:

	Shirts	Shoes
Mexico	100	40
Chile	60	60

• Opportunity Cost Calculations:

  • Mexico: 1 shirt costs $40/100 = 0.4$ shoes; 1 shoe costs $100/40 = 2.5$ shirts

  • Chile: 1 shirt costs $60/60 = 1$ shoe; 1 shoe costs $60/60 = 1$ shirt

• Comparative Advantage: Mexico has a lower opportunity cost for shirts, Chile for shoes. Mexico should specialize in shirts, Chile in shoes.

Gains from Trade

• Before and After Trade Table:

	Before trade	After trade	Gains from trade
Shirts	30 + 30 = 60	70	10
Shoes	30 + 30 = 60	60	0

• Interpretation: Specialization and trade increase total output and allow both countries to consume beyond their production possibilities.

Consumer and Producer Surplus

Surplus Calculations

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. Producer surplus is the difference between the price received and the minimum price at which producers are willing to sell.

• Consumer Surplus (CS): $CS = \frac{1}{2} \times (\text{max price} - \text{equilibrium price}) \times (\text{equilibrium quantity})$

• Producer Surplus (PS): $PS = \frac{1}{2} \times (\text{equilibrium price} - \text{min price}) \times (\text{equilibrium quantity})$

• Total Surplus: $\text{Total Surplus} = CS + PS$

• Deadweight Loss (DWL): Occurs when market output is restricted below the efficient level. $DWL = \frac{1}{2} \times (\text{efficient quantity} - \text{restricted quantity}) \times (\text{difference in price})$

Utility Maximization

Total and Marginal Utility

Utility is the satisfaction derived from consuming goods and services. Marginal utility is the additional satisfaction from consuming one more unit.

• Example Table:

Hours per day	Total utility from windsurfing	Total utility from snorkeling
1	120	40
2	220	76
3	300	106
4	360	128
5	396	140
6	412	150
7	422	158

• Marginal Utility (MU): $MU = \text{Change in total utility} / \text{Change in quantity}$

• Utility Maximization: Allocate spending so that $\frac{MU_1}{P_1} = \frac{MU_2}{P_2}$ for all goods.

• Example: Max spends $35 on windsurfing ($10/hr) and snorkeling ($5/hr). He maximizes utility when marginal utility per dollar is equalized across activities.

Income and Cross Elasticity

Income Elasticity of Demand

Income elasticity measures how quantity demanded changes as consumer income changes.

• Formula: $E_I = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in income}}$

• Example: If demand for designer jeans increases from 42,000 to 56,000 as income rises from $56,000 to $71,500:$E_I = \frac{(56,000 - 42,000) / 42,000}{(71,500 - 56,000) / 56,000} = \frac{14,000 / 42,000}{15,500 / 56,000} = 0.33 / 0.28 = 1.18$

• Interpretation: If $E_I > 1$, the good is a luxury; if $0 < E_I < 1$, it is a necessity.

Cross Elasticity of Demand

• Definition: Measures the responsiveness of demand for one good to changes in the price of another good.

• Formula: $E_{xy} = \frac{\% \text{ change in quantity demanded of good } x}{\% \text{ change in price of good } y}$

• Interpretation: If $E_{xy} > 0$, goods are substitutes; if $E_{xy} < 0$, goods are complements.

Shifts in Demand

Factors Affecting Demand

Demand for a good can shift due to changes in income, prices of related goods, consumer preferences, and other factors.

• Examples:

  • A medical report showing health benefits of chicken increases demand for chicken (rightward shift).

  • A rise in the price of beef leads consumers to substitute chicken for beef (rightward shift in chicken demand).

  • If chicken is a normal good, an increase in income increases demand for chicken (rightward shift).

Additional info: Some explanations and tables have been expanded for clarity and completeness.