The Theory of the Consumer

Market Baskets

• Definition: A list of specific quantities of one or more goods (also called a bundle).
• Example: A grocery cart with items or monthly quantities of food, clothing, and housing a consumer purchases.

Consumer Preferences

1. Completeness: Consumers can compare and rank all market baskets.
2. Transitivity: If a consumer prefers A to B and B to C, they must prefer A to C.
3. More is better than less: Consumers prefer more goods to fewer, assuming all else is equal.

Indifference Curve

• Definition: A curve showing combinations of market baskets that give a consumer the same satisfaction.

Indifference Map

• Definition: A set of indifference curves showing different combinations of market baskets among which the consumer is indifferent.

Marginal Rate of Substitution (MRS)

• Definition: The maximum amount of one good a consumer is willing to give up for an additional unit of another good.
• Formula:
  $$
  MRS_{xy} = \frac{dy}{dx} = \frac{MU_x}{MU_y}
  $$

Budget Line

• Definition: Combinations of goods for which the total money spent equals income.
• Formula:
  $$
  P_F F + P_C C = I
  $$
  Where:
• ( P_F ) = Price of food, ( F ) = Quantity of food
• ( P_C ) = Price of clothing, ( C ) = Quantity of clothing
• ( I ) = Income

Maximizing Consumer Satisfaction

• Condition: Occurs where the indifference curve and the budget line are tangent.
• Equilibrium Condition:
  $$
  MRS = \frac{P_F}{P_C}
  $$

Substitution and Income Effects

• Substitution Effect: Change in consumption due to a change in price, holding utility constant.
• Income Effect: Change in consumption due to a change in purchasing power, holding relative prices constant.

Consumer Surplus

• Definition: The difference between what a consumer is willing to pay and what they actually pay.

Network Externalities

• Definition: When demand depends on other individuals’ purchases.
• Positive (Bandwagon Effect): More people buying increases demand.
• Negative (Snob Effect): More people buying decreases demand.

Consumer Preferences Toward Risk

1. Risk Averse: Prefers a certain income over a risky one with the same expected value.
2. Risk Loving: Prefers a risky income over a certain one with the same expected value.
3. Risk Neutral: Indifferent between a certain and risky income with the same expected value.

Reducing Risk

1. Diversification: Spreading investments to reduce risk.
2. Insurance: Paying to transfer the risk of uncertain events.
3. Information: Gaining knowledge to reduce uncertainty.

Here is a concise and extensive cheat sheet based on the key ideas from the provided Theory of the Firm document, with mathematical equations and solutions wrapped with $$…$$.

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Theory of the Firm

Firms and Production Decisions:

1. Production Technology: Describes the methods a firm uses to produce goods.
2. Cost Constraints: Factors limiting production due to costs.
3. Input Choices: Decisions firms make regarding the mix of inputs to minimize costs.

Production Function:

• Describes the highest output a firm can produce for a given input combination:
  $$ q = F(K, L) $$
• q: Output
• K: Capital
• L: Labor

Production with One Variable Input:

• Total Product (TP): Output for varying input amounts.
• Average Product (AP): Output per unit of input:
  $$ AP_L = \frac{q}{L} $$
• Marginal Product (MP): Additional output per extra unit of input:
  $$ MP_L = \frac{\Delta q}{\Delta L} $$

Law of Diminishing Marginal Returns:

• With fixed inputs, increasing one input results in smaller output increments over time.

Isoquant & Isocost Lines:

• Isoquant: Curve showing all input combinations that yield the same output.
• Isocost Line: Shows combinations of inputs a firm can afford at a given cost.

Marginal Rate of Technical Substitution (MRTS):

• The rate at which one input can be substituted for another while keeping output constant:
  $$ MRTS = – \frac{\Delta K}{\Delta L} $$

Returns to Scale:

1. Increasing Returns to Scale: Output more than doubles when inputs double.
2. Constant Returns to Scale: Output doubles when inputs double.
3. Decreasing Returns to Scale: Output increases less than double when inputs double.

Costs of Production:

• Accounting Cost: Actual expenses + depreciation.
• Economic Cost: Costs including opportunity cost of resources.

Short-Run vs. Long-Run Costs:

• User Cost of Capital:
  $$ \text{User Cost} = \text{Economic Depreciation} + (r \times \text{Value of Capital}) $$
• Example: If the purchase price is $150 million, depreciation is $5 million/year, and the interest rate is 10%, then:
  $$ \text{User Cost} = 5M + (0.10 \times 150M) = 20M $$

Economies and Diseconomies of Scale:

• Economies of Scale: Output can be doubled for less than a doubling of cost.
• Diseconomies of Scale: Doubling output costs more than doubling the input costs.

Market Structures:

Perfectly Competitive Markets:

• Features:

1. Price-taking behavior.
2. Product homogeneity.
3. Free entry and exit.

Profit Maximization:

• In perfect competition, firms maximize profit where:
  $$ MC(q) = MR = P $$

Short-Run Supply Decision:

• A firm produces where:
  $$ P = MC $$
• The firm shuts down if:
  $$ P < \text{Average Economic Cost} $$

Long-Run Profit Maximization:

• Firms choose output where:
  $$ P = LMC $$

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Competitive Markets

Government Policies and Market Intervention

• Price Ceiling:
• Effect: Increases demand, decreases supply → leads to shortages.
• Impact on Consumers: Some benefit from lower prices, while others cannot buy due to shortages.
• Evaluating Impact: Changes in Consumer Surplus (CS) and Producer Surplus (PS) are key metrics.
• Consumer Surplus (CS):
  $$ \text{CS} = \text{Willingness to Pay} – \text{Actual Price Paid} $$
• Measures the extra benefit consumers receive beyond the price they pay.
• Producer Surplus (PS):
  $$ \text{PS} = \text{Market Price} – \text{Marginal Cost of Production} $$
• Summed over all units produced, PS is the benefit producers get from selling above their cost.
• Deadweight Loss (DWL):
  $$ \text{DWL} = \text{Loss of Total Surplus due to Market Inefficiency} $$
• Price controls (like price ceilings) can cause DWL because the loss in producer surplus often outweighs consumer gains.
  $$ \Delta \text{CS} + \Delta \text{PS} = – B – C $$

Market Efficiency and Failure

• Economic Efficiency:
  $$ \text{Maximization of Total Surplus (CS + PS)} $$
• Occurs in a perfectly competitive market.
• Market Failure:
  Occurs when unregulated markets are inefficient, e.g., externalities (costs/benefits not reflected in prices) or information asymmetry.

Price Supports and Production Quotas

• Price Support:
• Government sets a support price ( P_s ), buying up the excess supply to maintain prices above equilibrium.
• Effect: Reduces consumer surplus, increases producer surplus, but at a cost to the government.
  $$ \Delta \text{CS} = – A – B $$
  $$ \Delta \text{PS} = A + B + D $$
  $$ \text{Cost to Government} = (Q_2 – Q_1) P_s $$
• Production Quotas:
  To sustain higher prices, the government restricts supply via quotas or incentives for producers to reduce output.

Taxes and Subsidies

• Tax:
  $$ P_b = \text{Price paid by buyers (includes tax)} $$
  $$ P_s = \text{Price sellers receive (net of tax)} $$
• Impact: Divided between buyers and sellers, depending on the elasticity of supply and demand.
• Deadweight Loss:
  $$ \text{DWL} = B + C $$
• Subsidy:
  $$ \text{A negative tax, benefits divided between buyers and sellers depending on relative elasticities.} $$

Price Floors (Minimum Prices)

• Effect: Raises prices above equilibrium (e.g., minimum wage laws, agricultural price supports).
  $$ \Delta \text{CS} = – A – B $$
  $$ \Delta \text{PS} = A – C $$
  $$ \text{Total change in surplus} = – B – C $$

Import Tariffs and Quotas

• Elimination of Imports:
• Raises domestic prices, benefiting producers but harming consumers and creating deadweight loss.
  $$ \Delta \text{CS} = – (A + B + C) $$
  $$ \text{DWL} = B + C $$

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Monopoly and Monopsony

Monopoly

• Definition: A market with only one seller who completely controls output and price.
• Average Revenue (AR): The price received per unit sold, which is the market demand curve.
• Marginal Revenue (MR): Change in revenue from a unit change in output. The monopolist uses MR to choose the profit-maximizing output.

Monopoly Power

• P = MC for Competitive Firms: Price equals marginal cost.
• P > MC for Monopoly: A monopolist sets a price greater than the marginal cost.
• Lerner Index: A measure of monopoly power, calculated as the excess of price over marginal cost as a fraction of price. $$ L = \frac{P – MC}{P} $$

Rule of Thumb for Pricing

• Monopolist’s price markup over MC is: $$ P = \frac{MC}{1 + (1/Ed)} $$ where ( Ed ) is the elasticity of demand for the firm.

Markup Pricing Examples

1. Supermarkets: Typically, the price is set about 11% above MC when elasticity is -10. $$ P = \frac{MC}{1 – 0.1} = 1.11 MC $$
2. Convenience Stores: Face less elastic demand, setting prices 25% above MC when elasticity is -5. $$ P = \frac{MC}{1 – 0.2} = 1.25 MC $$
3. Designer Jeans: Markups range from 33% to 50% higher than MC when elasticity is between -3 and -4.

Sources of Monopoly Power

1. Elasticity of Market Demand: The less elastic the demand, the greater the monopoly power.
2. Number of Firms: Fewer firms mean more market control.
3. Firm Interaction: Competitors’ reactions can influence monopoly pricing.

Social Costs of Monopoly Power

• Rent Seeking: Expenditure in socially unproductive efforts to maintain monopoly power, such as lobbying or avoiding antitrust.

Price Regulation

• Eliminating Deadweight Loss: In monopolies, price regulation can prevent deadweight loss unlike in competitive markets.

Natural Monopoly

• Definition: A single firm that can produce the entire market output at a lower cost than multiple firms.

Monopsony

• Definition: A market with a single buyer.

Monopsony Power

• Marginal Value (MV): The additional benefit from purchasing one more unit.
• Marginal Expenditure (ME): The additional cost of buying one more unit.
• Average Expenditure (AE): The price paid per unit of a good.

Sources of Monopsony Power

1. Elasticity of Market Supply: The less elastic the supply curve, the more monopsony power, as ME > AE.
2. Number of Buyers: More buyers reduce the power of any single buyer.
3. Buyer Interaction: Collusion among buyers can increase monopsony power.

Limiting Market Power

• Antitrust Laws: Regulations that prevent actions restraining competition (e.g., Sherman Act, Clayton Act).
• Parallel Conduct: Implicit collusion where one firm follows another.
• Predatory Pricing: Pricing strategies to eliminate competitors.

Philippine Context

• Philippine Competition Act (RA No. 10667): A local version of antitrust regulations to limit market dominance.