Consumer Behavior

The Budget Constraint

The budget constraint represents the combinations of goods a consumer can purchase given their income and the prices of goods. It is a fundamental concept in microeconomics for understanding consumer choices.

• Budget Set: All combinations of goods the consumer can afford. Mathematically: $I \geq P_1 x_1 + P_2 x_2$.

• Budget Constraint: Combinations that exactly exhaust the budget: $I = P_1 x_1 + P_2 x_2$.

• Slope of Budget Constraint: Indicates the opportunity cost of one more unit of the horizontal-axis good, measured in units of the vertical-axis good given up. Slope: $-\frac{P_1}{P_2}$.

• Intercepts: $\frac{I}{P_1}$ and $\frac{I}{P_2}$ show the maximum quantity of each good if all income is spent on one good.

• Pivots: Caused by a change in the price of one good; only that good's intercept moves.

• Shifts: Caused by a change in income or proportional change in both prices; the constraint shifts parallel.

• Example: If $I = 360$, $P_a = 6$, $P_b = 4$, intercepts are 60 A and 90 B; slope $-\frac{4}{6} = -\frac{2}{3}$.

Solving the Consumer's Problem

Consumers aim to maximize their utility given their preferences, prices, and income. The solution involves equating the marginal benefit per dollar across goods and exhausting the budget.

• Objective: Maximize utility: $\max U = u(x_1, x_2)$ subject to $I = P_1 x_1 + P_2 x_2$.

• Solution: $\frac{MB_1}{P_1} = \frac{MB_2}{P_2}$ and $I = P_1 x_1 + P_2 x_2$.

• Graphical Solution: Tangency of the budget constraint and the highest attainable indifference curve.

• Example: $I = 24$, milk $4$, cookies $2$. Buy units with highest $MB/P$ until money runs out.

Elasticity

Elasticity measures the responsiveness of one variable to changes in another, typically in percentage terms.

• General Definition: $\varepsilon = \frac{\%\Delta y}{\%\Delta x}$

• Midpoint Formula: $\%\Delta x = \frac{x_{new} - x_{old}}{(x_{new} + x_{old})/2}$

• Price Elasticity of Demand: $\varepsilon = \frac{\%\Delta Q_d}{\%\Delta P}$

• Cross-Price Elasticity: $\varepsilon_{ij} = \frac{\%\Delta Q_i}{\%\Delta P_j}$

• Income Elasticity: $\varepsilon_I = \frac{\%\Delta Q_d}{\%\Delta Income}$

• Elasticity Types:

  • Elastic ($|\varepsilon| > 1$): Buyers are very responsive.

  • Inelastic ($0 < |\varepsilon| < 1$): Buyers are less responsive.

  • Unit Elastic ($|\varepsilon| = 1$): Proportional response.

  • Perfectly Elastic ($|\varepsilon| = \infty$): Horizontal demand.

  • Perfectly Inelastic ($|\varepsilon| = 0$): Vertical demand.

• Example: Price rises from $5$ to $6$, quantity falls from $2,000$ to $1,400$: $\varepsilon = -1.94$ (elastic).

Consumer Surplus

Consumer surplus is the benefit buyers receive from purchasing goods at a price lower than their willingness to pay.

• Definition: Willingness to pay minus price paid.

• Graphical Representation: Area below demand curve and above price.

• Formula: $CS = \frac{1}{2} \times Q \times (\text{demand's price intercept} - P)$

• Example: Bananas: intercept $110$, $P = 50$, $Q = 80$; $CS = \frac{1}{2} \times 80 \times 60 = 2,400$.

Indifference Curves and Utility

Indifference curves represent combinations of goods that yield the same utility to the consumer. Utility is a measure of satisfaction.

• Utility: Satisfaction from consuming goods, measured in utils.

• Indifference Curve: All combinations of two goods with equal utility. Slope is $-\frac{MB_1}{MB_2}$ (the marginal rate of substitution).

• Properties: Indifference curves cannot cross if preferences are well-behaved.

• Consumer's Problem: Solved at tangency: $\frac{MB_1}{MB_2} = \frac{P_1}{P_2}$ or $\frac{MB_1}{P_1} = \frac{MB_2}{P_2}$.

Producer Behavior

Production and Marginal Product

Production is the process of converting inputs into outputs. The production function describes the relationship between inputs and outputs.

• Production Function: Technology determines output from inputs.

• Marginal Product (MP): Extra output from one more unit of input: $MP = \frac{\Delta Q}{\Delta L}$

• Increasing Returns: MP rises as more workers are added (specialization).

• Diminishing Returns: MP falls as more workers share fixed resources.

• Example Table:

• Relationship: MP ↑ → MC ↓; MP ↓ → MC ↑.

Costs

Costs are categorized as fixed, variable, and marginal. Understanding cost behavior is essential for firm decision-making.

• Total Cost (TC): $TC = FC + VC$

• Fixed Cost (FC): Does not change with output.

• Variable Cost (VC): Changes with output.

• Marginal Cost (MC): $MC = \frac{\Delta TC}{\Delta Q}$

• Average Total Cost (ATC): $ATC = \frac{TC}{Q}$

• Average Fixed Cost (AFC): $AFC = \frac{FC}{Q}$

• Average Variable Cost (AVC): $AVC = \frac{VC}{Q}$

• Relationship: $ATC = AFC + AVC$

• Short Run vs. Long Run: Short run has at least one fixed input; long run all inputs are variable.

• MC and ATC/AVC: MC crosses ATC and AVC at their minimums.

• Finding Fixed Cost: $FC = (ATC - AVC) \times Q$

Long-Run Costs and Economies of Scale

The long-run average total cost (LRATC) curve is derived from the lowest short-run ATC for each output level. Economies of scale describe how costs change as output increases.

The Firm's Problem

Firms aim to maximize profit by choosing the optimal output level. In perfect competition, firms are price takers.

• Objective: Maximize profit.

• Profit Maximization: Produce where $MR = MC$. In perfect competition, $MR = P$.

• Total Revenue (TR): $TR = P \times Q$

• Marginal Revenue (MR): $MR = \frac{\Delta TR}{\Delta Q}$

• Economic Profit: $\text{Economic profit} = TR - TC = (P - ATC) \times Q$

• Example: $P = 12$, $Q = 50$, $ATC = 15$: Profit = $(12 - 15) \times 50 = -150$ (loss).

• Demand Curve: Horizontal at market price; $P = MR = AR$.

• Long-Run Equilibrium: Zero economic profit; $P = MC = \min ATC$.

Market Adjustment and Entry/Exit

Firms enter or exit the market in response to profits or losses, driving the market toward equilibrium.

• Positive Profits: Entry increases supply, price falls, profits shrink.

• Losses: Exit decreases supply, price rises, losses shrink.

• Long-Run Equilibrium: $P = \min ATC$, profit = 0.

The Firm's Supply Curve

The supply curve shows the quantity a firm will produce at each price.

• Short-Run Supply: MC curve above minimum AVC.

• Long-Run Supply: MC curve above minimum ATC.

• Shutdown Point: Minimum AVC; if $P < \min AVC$, firm shuts down.

• Profit Table:

• Exit: Firms leave in the long run if $P < \min ATC$.

Elasticity of Supply

Price elasticity of supply measures how responsive quantity supplied is to price changes.

• Definition: $\varepsilon_s = \frac{\%\Delta Q_s}{\%\Delta P}$

• Interpretation: $\varepsilon_s > 1$ is elastic; $\varepsilon_s < 1$ is inelastic.

• Example: $P$ rises from $10$ to $12$, $Q_s$ from $100$ to $130$: $\varepsilon_s = 1.43$ (elastic).

Producer Surplus

Producer surplus is the benefit sellers receive from selling at a price above their minimum acceptable price.

• Definition: Price received minus minimum acceptable price (MC).

• Graphical Representation: Area above supply curve and below price.

• Formula: $PS = \frac{1}{2} \times Q \times (P - \text{Supply's price intercept})$

• Example: Supply starts at $2$, $P = 10$, $Q = 400$: $PS = \frac{1}{2} \times 400 \times 8 = 1,600$.

Efficiency of Perfectly Competitive Markets

The Invisible Hand and Market Efficiency

Perfectly competitive markets efficiently allocate resources through self-interest and market prices, as described by Adam Smith's 'Invisible Hand'.

• Within Industry: Firms produce where $P = MC$; output at lowest total cost.

• Across Industries: Entry and exit move resources to highest-valued uses.

• Among Buyers: Goods go to buyers who value them most.

• Market Price Functions:

  1. Signal information

  2. Provide incentives

  3. Allocate goods

Social Surplus and Pareto Efficiency

Social surplus is the total benefit to society from market transactions. Pareto efficiency means no one can be made better off without making someone else worse off.

• Reservation Value: Maximum WTP for buyers, minimum acceptable price for sellers.

• Social Surplus: $\text{Social Surplus} = \text{Consumer Surplus} + \text{Producer Surplus}$

• Example: Demand intercept $20$, supply intercept $4$, equilibrium $P = 12$, $Q = 100$: $CS = 400$, $PS = 400$, $SS = 800$.

Deadweight Loss (DWL)

Deadweight loss is the reduction in social surplus when the market quantity is not at the efficient level.

• Definition: DWL is the area between demand and supply curves between actual and efficient quantities.

• Formula: $DWL = \frac{1}{2} \times (Q_{efficient} - Q_{actual}) \times (P_{demand} - P_{supply\ at\ Q_{actual}})$

• Example: Equilibrium $Q = 100$, quota $Q = 60$, buyers would pay $14$, seller MC = $6$: $DWL = \frac{1}{2} \times 40 \times 8 = 160$.

Equity and the Equity-Efficiency Trade-off

Equity concerns fairness in the distribution of economic surplus. Policies to increase equity often reduce efficiency, creating a trade-off.

• Definition: Equity is fairness in distribution; efficiency is maximizing total surplus.

• Trade-off: Policies for equity (taxes, transfers, price controls) usually create DWL.

• Competitive Markets: Efficient but not necessarily equitable.

When Markets Are Not Efficient

Perfectly competitive markets are efficient under certain assumptions. Efficiency fails when these assumptions are violated.

• Externalities: Costs or benefits affect third parties (e.g., pollution).

• Market Power: Monopoly restricts output.

• Information Problems: Incomplete or asymmetric information.

• Public Goods/Common Resources: Non-excludable or rival goods.

• Government Interventions: Price controls, quotas, taxes.