Microeconomics Study Notes: Consumer and Producer Theory, Production, Costs, and Market Structures

4.2 The Income and Substitution Effects of a Price Change

Section 1: Decomposing the Total Effect of a Price Change

When the price of a good changes, the total effect on quantity demanded can be separated into the substitution effect and the income effect. This decomposition is crucial for understanding consumer behavior for normal and inferior goods.

• Substitution Effect: The change in consumption resulting from a change in the relative price of goods, holding utility constant.

• Income Effect: The change in consumption resulting from the change in purchasing power due to the price change.

• Graphical Decomposition: Use an imaginary (compensated) budget line, parallel to the new budget line but tangent to the original indifference curve, to separate the effects.

• Normal Good: Both effects move quantity in the same direction as the price change.

• Inferior Good: Substitution effect dominates, but income effect works in the opposite direction.

• Example: If the price of apples falls, the substitution effect increases apple consumption (apples are relatively cheaper), and the income effect also increases consumption if apples are normal goods.

Section 2: Giffen Goods

A Giffen good is an inferior good for which the income effect outweighs the substitution effect, causing quantity demanded to rise as price rises.

• Definition: A good with an upward-sloping demand curve due to a strong negative income effect.

• Graphical Decomposition: The substitution effect still reduces quantity as price rises, but the income effect is so negative that total quantity demanded increases.

• Example: Staple foods for very poor consumers (e.g., bread or rice in some historical contexts).

Section 3: Perfect Complements and Perfect Substitutes

These are special cases of consumer preferences that affect the decomposition of price changes.

• Perfect Complements: Goods consumed in fixed proportions (e.g., left and right shoes). Substitution effect is zero; only income effect operates.

• Perfect Substitutes: Goods that can replace each other perfectly (e.g., two brands of bottled water). Only the cheaper good is consumed; substitution effect is large.

• Price Elasticity: Salt (a necessity) is price inelastic; houses (luxury) are price elastic due to the nature of their demand curves.

4.3 Market Demand: Aggregating Individual Demand Curves

Horizontal Summation

Market demand is found by summing individual demand curves horizontally at each price level.

• Graphical Method: At each price, add the quantities demanded by all consumers.

• Algebraic Aggregation: For two linear demand curves, find the 'kink' point where one consumer drops out, then sum piecewise.

• n Identical Consumers: If each has $Q_i = a - bP$, then market demand is $Q = nQ_i = na - nbP$.

• Equilibrium: To find equilibrium, pick the relevant segment, solve for price and quantity, and check if the solution is within the range.

4.4 Applications of the Consumer Choice Model

Section 1: Gasoline Tax-and-Rebate Policy

Policies that tax gasoline and rebate the proceeds to consumers alter the budget constraint.

• Budget Line: The new budget line (B3) reflects the tax and rebate, not simply a parallel shift.

• Implication: Gasoline consumption decreases, but consumers are worse off due to the distortion.

Section 2: Changes Allowing Consumption of the Original Bundle

If a policy change allows the consumer to still afford their original optimal bundle, and preferences are strictly convex, the consumer is better off.

• Graphical Reasoning: The new budget line is tangent to a higher indifference curve.

5.1 Production Basics

Section 1: Production Function

The production function shows the maximum output obtainable from given inputs.

• Notation: $Q = F(K, L)$, where $K$ is capital and $L$ is labor.

• Table Schedule: A table showing output for various input combinations.

Section 2: Short Run vs Long Run

• Short Run: At least one input is fixed (e.g., capital).

• Long Run: All inputs are variable.

• Fixed Inputs: Inputs that cannot be changed in the short run.

• Variable Inputs: Inputs that can be changed in the short run.

5.2 Production in the Short Run

Section 1: Plotting Short-Run Production Functions

• Set $K$ constant in $Q = F(K, L)$ to get $Q = g(L)$.

• Example: If $Q = KL$ and $K = 4$, then $Q = 4L$.

• Use a schedule to plot the total product curve.

Section 2: Properties of Short-Run Production Functions

• Passes through the origin (zero input yields zero output).

• Initially, output grows at an increasing rate (specialization).

• Eventually, output grows at a decreasing rate (law of diminishing returns).

• Law of Diminishing Returns: Adding more of a variable input to fixed inputs will eventually yield smaller increases in output.

• Historical Note: Malthus's prediction of inevitable starvation did not account for technological progress.

Section 3: Total, Marginal, and Average Products

• Total Product (TP): Total output produced.

• Marginal Product of Labor (MPL): Additional output from one more unit of labor.

  • Discrete: $MPL = \Delta Q / \Delta L$

  • Continuous: $MPL = \frac{\partial Q}{\partial L}$

  • Example: If $Q = 2L$, then $MPL = 2$.

• Average Product of Labor (APL): Output per unit of labor.

  • Discrete: $APL = Q / L$

  • Continuous: $APL = Q / L$

  • Example: If $Q = 2L$, then $APL = 2$.

• Relationship: $MPL$ pulls $APL$ up if $MPL > APL$, and pulls it down if $MPL < APL$. They intersect at $APL$'s maximum.

5.3 Production in the Long Run

Section 1: Isoquants

An isoquant shows all combinations of inputs that yield the same output.

• Example: For $Q = 2KL$ and $Q = 16$, $K = 8/L$.

• Isoquant maps: Higher isoquants (northwest) represent higher output levels.

Section 2: Marginal Rate of Technical Substitution (MRTS)

• Definition: MRTS is the rate at which one input can be substituted for another, holding output constant.

• Formula: $MRTS = -\frac{dK}{dL}$ along an isoquant.

• For $Q = 2KL$ and $Q = 16$: $K = 8/L$, so $MRTS = 8/L^2$.

• General Formula: $MRTS = \frac{MPL}{MPK}$

• Example: For $Q = 2KL$, $MPL = 2K$, $MPK = 2L$, so $MRTS = K/L$.

• Isoquant Shapes: Perfect substitutes have straight-line isoquants; perfect complements have right-angle isoquants.

6.1 Costs in the Short Run

Section 1: Total, Variable, and Fixed Costs

• Fixed Cost (FC): Costs that do not vary with output (e.g., rent).

• Variable Cost (VC): Costs that vary with output (e.g., labor).

• Total Cost (TC): $TC = FC + VC$

• Example: If $w = 10$, $r = 0.25$, $K_0 = 120$, then $FC = 30$, $VC = 10L$, $TC = 30 + 10L$.

Section 2: Graphing Cost Functions

• FC is flat; TC and VC are parallel, separated vertically by FC.

• Given $TC = 30 + 10L$, $FC = 30$, $VC = 10L$.

Section 3: Average and Marginal Costs

• Average Fixed Cost (AFC): $AFC = FC / Q$

• Average Variable Cost (AVC): $AVC = VC / Q$

• Average Total Cost (ATC): $ATC = TC / Q = AFC + AVC$

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

Section 4: Graphing Short-Run Average and Marginal Cost Curves

• AFC decreases as output increases.

• AVC and ATC are typically U-shaped.

• MC intersects AVC and ATC at their minimum points.

• Example: For $TC = 8 + 2Q$, $AFC = 8/Q$, $AVC = 2$, $ATC = 8/Q + 2$, $MC = 2$.

6.2 Costs in the Long Run

Section 1: Isocost

• Isocost Line: All combinations of $K$ and $L$ that cost the same total amount.

• Equation: $C = wL + rK$

• Example: $C = 10L + 20K$, $C_0 = 50$

Section 2: Cost Minimization

• Find the input combination $(L_0, K_0)$ that produces $Q_0$ at minimum cost.

• Example: For $Q = KL$, $Q_0 = 18$, $w = 10$, $r = 20$:

• Set $K_0L_0 = 18$ and $K/L = 10/20$ (from tangency), solve for $L = 6$, $K = 3$.

• Minimum cost: $6 \times 10 + 3 \times 20 = 120$.

Section 3: Equal Marginal Products per Dollar

• Optimal input mix: $\frac{MPL}{w} = \frac{MPK}{r}$

• If not equal, reallocate spending to increase output without increasing cost.

Section 4: Effect of Changes in Input Prices

• Changing input prices rotates the isocost line, leading firms to substitute toward the cheaper input.

Section 5: Long-Run Expansion Path and Cost Curves

• As output increases, the cost-minimizing input combination traces the expansion path.

• Long-run total cost curve (LRTC) is derived from the expansion path.

• Long-run marginal cost (LRMC) and long-run average cost (LRAC) are defined similarly to short-run counterparts.

• All costs are variable in the long run; no fixed costs.

7.1 Short-Run Profit Maximization for Perfectly Competitive Firms

Section 1: Perfect Competition

• Four conditions: product homogeneity, free entry/exit, perfect information, price-taking behavior.

• Serves as a benchmark for other market structures.

Section 2: Short-Run Profit Maximization (General)

• Economic Profit: Revenue minus opportunity cost (explicit + implicit costs).

• Profit Maximization: Occurs where $MR = MC$.

Section 3: Short-Run Profit Maximization for a Perfectly Competitive Firm

• Firm is a price taker; faces a flat demand curve at market price $P$.

• Revenue: $R(q) = Pq$; Marginal Revenue: $MR = P$.

• Profit maximization: $P = MC(q^*)$.

• Example: If $P = 18$, find $q^*$ such that $MC(q^*) = 18$.

Section 4: The Shutting Down Condition

• Firm should shut down if $P < AVC_{min}$.

• Example: For $TC(q) = 5q^2 + 10q + 100$, $AVC(q) = 5q + 10$, so $AVC_{min} = 10$.

• If $P < 10$, shut down; otherwise, produce where $P = MC(q)$.

7.2 Short-Run Supply Curves for Competitive Firms and Markets

Section 1: Firm's Short-Run Supply Curve

• Supply curve is the portion of the MC curve above $AVC_{min}$.

• Example: For $TC(q) = 5q^2 + 10q + 100$, $MC(q) = 10q + 10$, $AVC(q) = 5q + 10$.

Section 2: Short-Run Competitive Industry Supply

• Market supply is the horizontal sum of individual firm supply curves.

• For $n$ identical firms: If $Q_i = c + dP$, then $Q = n c + n d P$.

7.3 Short-Run Competitive Equilibrium

Section 1: Short-Run Competitive Equilibrium

• Firms take market price as given and produce where $P = MC$.

• Firms may earn positive, negative, or zero economic profit.

Section 2: Efficiency

• Competitive equilibrium is allocatively efficient: resources are used where they are most valued.

7.4 Adjustments in the Long Run

Section 1: Long-Run Competitive Equilibrium

• Positive economic profit leads to entry, shifting supply right and lowering price until profit is zero.

• Negative profit leads to exit, shifting supply left and raising price until profit is zero.

• Long-run equilibrium price equals minimum LRAC.

Section 2: Long-Run Supply Curve

• Cannot simply sum individual supply curves; entry/exit changes number of firms.

• Long-run supply curve relates minimum LRAC to quantity supplied.

8.1 Welfare Analysis

Section 1: Consumer Surplus

• Definition: The area between the demand curve and the market price, up to the quantity purchased.

• Calculation (linear demand): $CS = \frac{1}{2} (Q^*) (P_{max} - P^*)$

Section 2: Producer Surplus

• Definition: The area between the market price and the supply curve, up to the quantity sold.

• Formula: $PS = \Pi - (-FC) = R - VC$

• In the short run, $PS$ and profit differ by fixed cost; in the long run, they are equal.

8.2 Government Policy and Welfare

Section 1: Competition Maximizes Welfare

• Competitive equilibrium maximizes total (social) welfare (First Fundamental Theorem of Welfare Economics).

Section 2: Welfare Effects of Government Intervention

• Interventions (e.g., price ceilings) cause deadweight loss, reducing welfare.

• May improve equity, leading to an efficiency-equity tradeoff.

Section 3: Example – Market for Human Kidneys

• Price ceiling at zero (by law) creates deadweight loss, though some recipients benefit.

9.1 Monopoly I

Section 1: Monopolist’s Marginal Revenue Curve

• Monopolist faces the market demand curve and chooses price/quantity to maximize profit.

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

• Linear Demand: For $P = t - kQ$, $MR(Q) = t - 2kQ$

• Example: For $P = 80 - 15Q$, $MR(Q) = 80 - 25Q$

Section 2: Marginal Revenue and Elasticity

• $MR(Q) = P(Q) \left(1 + \frac{1}{\epsilon}\right)$, where $\epsilon$ is price elasticity of demand.

• MR is positive only when demand is elastic ($\epsilon > 1$).

• Profit-maximizing output is always on the elastic portion of the demand curve.

Section 3: Profit Maximization for a Monopolist

• Set $MR(Q) = MC(Q)$ to find profit-maximizing quantity.

• Price is found by plugging $Q^*$ into the demand equation.

• Compute total revenue, total cost, and profit at $Q^*$.

• Shut down if $P^* < AVC(Q^*)$.

9.2 Monopoly II

Section 1: Welfare Effects of Monopoly

• Monopoly reduces total surplus compared to perfect competition due to underproduction (deadweight loss).

• Perfect price discrimination eliminates deadweight loss; all surplus goes to the producer.

Section 2: Sources of Monopoly

• Exclusive control of inputs, economies of scale (natural monopoly), government licenses, patents.

• Patents trade off innovation incentives against short-term deadweight loss.

Section 3: Addressing Monopoly

• Price ceilings can restore competitive outcomes if the competitive price is known, but implementation is challenging.