Fundamental Economic Equations to Know for Intro to Mathematical Economics

These notes cover key economic equations that help explain how markets function. Understanding concepts like supply and demand equilibrium, production functions, and consumer behavior is essential for grasping the mathematical foundations of economics and making informed decisions in real-world scenarios.

1. Supply and Demand Equilibrium

   • The point where the quantity supplied equals the quantity demanded in a market.
   • Determines the market price and quantity of goods sold.
   • Shifts in supply or demand curves can lead to new equilibrium points, affecting prices and quantities.

2. Cobb-Douglas Production Function

   • A mathematical representation of production that shows the relationship between inputs (capital and labor) and output.
   • Typically takes the form Q = A * L^α * K^β, where Q is output, L is labor, K is capital, and A, α, β are constants.
   • Exhibits constant returns to scale when α + β = 1, indicating proportional increases in output with proportional increases in inputs.

3. Marginal Rate of Substitution

   • The rate at which a consumer is willing to give up one good for another while maintaining the same level of utility.
   • Represents the slope of the indifference curve in consumer choice theory.
   • A key concept in understanding consumer preferences and optimizing consumption choices.

4. Elasticity of Demand

   • Measures the responsiveness of quantity demanded to changes in price, income, or other factors.
   • Price elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price.
   • Helps businesses and policymakers understand consumer behavior and set pricing strategies.

5. Profit Maximization

   • The process by which firms determine the price and output level that leads to the highest possible profit.
   • Occurs where marginal cost equals marginal revenue (MC = MR).
   • Involves analyzing cost structures and market conditions to optimize production decisions.

6. Cost Minimization

   • The strategy firms use to produce a given level of output at the lowest possible cost.
   • Involves choosing the optimal combination of inputs based on their prices and the production function.
   • Essential for maintaining competitiveness and profitability in the market.

7. Utility Maximization

   • The principle that consumers aim to achieve the highest level of satisfaction (utility) from their consumption choices.
   • Occurs when consumers allocate their budget in a way that maximizes their total utility given their preferences and constraints.
   • Involves understanding indifference curves and budget constraints.

8. Marginal Revenue and Marginal Cost

   • Marginal revenue (MR) is the additional revenue gained from selling one more unit of a good, while marginal cost (MC) is the additional cost incurred from producing one more unit.
   • Profit maximization occurs when MR = MC.
   • Understanding these concepts is crucial for firms in making production and pricing decisions.

9. Income and Substitution Effects

   • The income effect refers to the change in quantity demanded due to a change in consumer income, while the substitution effect refers to the change in quantity demanded due to a change in the price of a good relative to others.
   • Together, they explain how consumers adjust their consumption in response to price changes.
   • Important for analyzing consumer behavior and demand curves.

10. Consumption Function

    • A mathematical relationship that describes how total consumer spending varies with changes in disposable income.
    • Typically expressed as C = a + bY, where C is consumption, Y is income, a is autonomous consumption, and b is the marginal propensity to consume.
    • Helps economists understand consumer behavior and predict changes in aggregate demand.