Introduction to Microeconomic Theory

Introduction to Microeconomic Theory
Key concepts, definitions, and analytical tools that form the foundation of microeconomics.

1. What Is Microeconomics?

2. Fundamental Assumptions

1. Rationality – Agents maximize a well‑defined objective (utility for consumers, profit for firms).
2. Complete Information – All relevant data about prices, technologies, and preferences are known to decision‑makers.
3. Perfect Competition (in baseline models) – Many buyers and sellers, homogeneous products, free entry/exit, no single agent can influence price.
4. Scarcity – Resources (time, money, inputs) are limited, forcing trade‑offs.

Note: Real‑world deviations (imperfect information, market power, externalities) are studied by extending the basic framework.

3. The Consumer: Choice Theory

3.1 Preferences & Utility

• Preference Relations: (\succ) (strictly preferred), (\sim) (indifferent).
• Utility Function: (U(x_1, x_2, …, x_n)) assigns a real number to each consumption bundle (x).
• Key Properties
  • Completeness: Any two bundles can be compared.
  • Transitivity: If (A \succ B) and (B \succ C), then (A \succ C).
  • Monotonicity: More of a good is (weakly) better.
  • Convexity: Preference for diversified bundles (diminishing marginal rate of substitution).

3.2 Budget Constraint

[ p_1x_1 + p_2x_2 + \dots + p_nx_n \leq I ]

• (p_i) = price of good (i)
• (I) = consumer income (or wealth)

3.3 Optimal Choice (Utility Maximization)

[ \max_{x} U(x) \quad \text{s.t.} \quad p\cdot x \le I ]

First‑order conditions (Lagrange method): [ \frac{\partial U/\partial x_i}{\partial U/\partial x_j} = \frac{p_i}{p_j} \quad \forall i,j ] Interpretation: Marginal Rate of Substitution (MRS) equals the price ratio.

3.4 Derived Demand Functions

• Marshallian (Uncompensated) Demand: (x_i(p, I)) – quantity demanded as a function of prices and income.
• Hicksian (Compensated) Demand: (h_i(p, u)) – quantity demanded when utility (u) is held constant (used for welfare analysis).

4. The Firm: Production Theory

4.1 Production Function

[ q = f(L, K, \dots) ]

• (q) = output
• (L, K) = inputs (labor, capital)

Properties