Math Review, Economics Foundations, Demand, Supply, and Price Determination -- ECON 323, Chapters I-II

Source: Lecture Notes of Prof. Guoqiang Tian, Texas A&M University

Tags: microeconomics, scarcity, resources, opportunity cost, demand, supply, equilibrium, price ceiling, price floor, ceteris paribus, normal goods, inferior goods, PPF, positive statements, normative statements


TL;DR

This section covers the foundational building blocks of microeconomics: the scarcity problem, how markets allocate resources through demand and supply, and how equilibrium prices emerge. It also introduces government price controls (ceilings and floors) and their effects on markets. The maths needed is limited to solving two linear equations simultaneously.


Key Terms

Economics

The study of how limited resources are allocated among competing uses.

Scarcity

The fundamental economic problem: resources are limited but society has unlimited wants.

Land

All natural resources, e.g. soil, forest, minerals, water.

Labour

The mental and physical skills provided by workers, e.g. teachers, managers, steel workers.

Capital

Man-made aids to production, e.g. machinery, buildings, tools.

Opportunity cost

The cost of a unit of a good measured in terms of other goods that must be forgone to obtain it. Equal to the sum of explicit and implicit costs.

Explicit costs

Payments made for resources purchased or hired from outside sources, e.g. wages, interest on borrowed money, rent paid to an outside party.

Implicit costs

Costs of resources used but neither purchased nor hired from outside sources, e.g. salary the owner could earn elsewhere, interest that could be earned by lending money.

Production possibility frontier (PPF)

A curve showing all the different combinations of goods a rational individual (or economy) can produce with a fixed amount of resources.

Positive statements

Claims about what is, was, or will be. Disputes can be settled by looking at facts. E.g. "Decreasing unemployment will result in higher inflation."

Normative statements

Opinions or value judgements about what should or ought to be. Disputes cannot be settled by facts alone. E.g. "It would be better to have low unemployment than low inflation."

Microeconomics

The study of individual consumers, firms, and markets, and how markets are organised.

Absolute (nominal) price

The price of a good without adjusting for the changing value of money.

Relative (real) price

The price of a good adjusted for the changing value of money. E.g. a first-class Titanic ticket in 1912 cost $7,500, roughly equivalent to $80,000 in 1997 dollars.

Demand (D(p))

A schedule showing the maximum amounts of a good or service a consumer is willing and able to purchase at each price, ceteris paribus.

Ceteris paribus

"All other things remaining constant" (preferences, income, prices of other goods, environmental conditions, expectations, market size).

Law of demand

An inverse relationship between price and quantity demanded: the lower the price, the greater the quantity demanded, and vice versa.

Supply (S(p))

A schedule showing the maximum quantities of a good or service sellers are willing and able to sell at each price, ceteris paribus.

Law of supply

A direct relationship between price and quantity supplied: the higher the price, the greater the quantity supplied, and vice versa.

Equilibrium price (pe)

The price at which quantity supplied equals quantity demanded. We say pe "clears the market."

Surplus

Occurs when quantity supplied exceeds quantity demanded (price is above equilibrium).

Shortage

Occurs when quantity demanded exceeds quantity supplied (price is below equilibrium).

Price ceiling

A maximum legal price, above which buying or selling is prohibited. Aimed at helping consumers.

Price floor (price support)

A minimum legal price, below which buying or selling is prohibited. Aimed at helping producers. Examples include agricultural price supports and minimum wage.


Core Content

Three Basic Assumptions of Economics

  • Self-interest behaviour: individuals pursue their personal goals.

  • Rational decision-making: market participants make rational decisions.

  • Scarcity of resources: market participants face scarce resources.

Economic Systems

  • Decentralised (price/market) system: consumption and production decisions are made through markets; consumers and producers are motivated by self-interest.

  • Centralised system: all production and consumption decisions are made by a central planning board; no unemployment, no inflation, no free enterprise.

Math Foundations

The course requires only straight-line equations and solving two equations with two unknowns.

A linear equation takes the form y = ax + b, where a is the slope and b is the y-intercept.

To find the intersection of y = 60 - 3x and y = 5 + 2x, set them equal: 60 - 3x = 5 + 2x, giving x = 11 and y = 27.

Demand

A linear demand function: D(p) = ap + b, where a < 0 (inverse relationship).

Economists traditionally plot price on the vertical axis and quantity on the horizontal axis.

A change in quantity demanded is caused by a change in price and is represented by a movement along the demand curve. A change in demand is caused by a change in something other than price and is represented by a shift of the entire demand curve.

Market demand is the horizontal sum of all individual demands.

Factors That Shift the Demand Curve

  • Size of market: e.g. city growth or better marketing increases the number of consumers.

  • Income: for normal goods, demand rises as income rises; for inferior goods, demand falls as income rises (e.g. potatoes, cheap bread).

  • Prices of related goods: substitute goods (butter and margarine) move demand in the same direction as the other good's price; complementary goods (hamburgers and buns) move demand in the opposite direction.

  • Tastes and preferences: e.g. a health scare about saccharin reduces its demand.

  • Expectations: e.g. an expected sale next week reduces demand this week.

  • Environmental conditions: e.g. weather affects demand for air conditioners, ice cream, winter coats.

Supply

A linear supply function: S(p) = ap + b, where a > 0 (direct relationship).

The direct relationship exists because of substitution in production: as the price of a good rises, producers shift resources into that higher-priced good and away from lower-priced goods. Alternatively, producers have an incentive to hire extra resources.

Market supply is the horizontal sum of all individual firm supplies.

Factors That Shift the Supply Curve

  • Number of firms

  • Prices of related goods

  • Technology (advancement lowers costs, increases supply)

  • Expectations

  • Environmental conditions

  • Price of resources (e.g. wage increases raise costs, decrease supply)

Equilibrium and Market Adjustment

When p > pe: surplus arises, producers cut prices, qs falls, qd rises, until qs = qd at pe.

When p < pe: shortage arises, consumers compete and push prices up, qd falls, qs rises, until qs = qd at pe.

Shift effects on equilibrium:

  • Demand increase: pe rises, qe rises.

  • Supply increase: pe falls, qe rises.

  • Both supply and demand increase: qe rises, but the effect on pe depends on relative magnitudes.

Government Price Controls

Price ceiling effects: shortage, tendency to form a black market, bad service and quality, reduced production, wrong signals about production and consumption. Consumers may also be worse off.

Price floor effects: surplus, unnecessary service, over-investment, wrong information about production and consumption. Methods to maintain: government purchases the surplus, or output is restricted to the quantity demanded at the floor price.


Formulas / Diagrams

  • Linear demand: D(p) = ap + b, a < 0

  • Linear supply: S(p) = ap + b, a > 0

  • Equilibrium condition: D(pe) = S(pe)

  • Straight line: y = ax + b (slope a, intercept b)


Why It Matters / Exam Flags

⚠️ Distinguish between a change in quantity demanded (movement along the curve, caused by own-price change) and a change in demand (shift of the curve, caused by non-price factors). This is a classic exam question.

⚠️ The equilibrium condition D(pe) = S(pe) is fundamental. Be able to solve for pe algebraically.

⚠️ Know the effects of price ceilings and price floors, not just the definition but the consequences (shortage vs. surplus, black markets, welfare losses).

⚠️ Understand the difference between positive and normative statements.

⚠️ Opportunity cost = explicit costs + implicit costs. Do not forget implicit costs.


Practice Q&A

Q: What is the difference between a change in quantity demanded and a change in demand?

A: A change in quantity demanded is a movement along the demand curve caused by a change in the good's own price. A change in demand is a shift of the entire demand curve, caused by a change in income, tastes, prices of related goods, expectations, market size, or environmental conditions.

Q: If the demand function is D(p) = 90 - 20p and the supply function is S(p) = -15 + 10p, what is the equilibrium price and quantity?

A: Set D(pe) = S(pe): 90 - 20pe = -15 + 10pe, so 105 = 30pe, giving pe = 3.5. Substituting: qe = 90 - 20(3.5) = 20.

Q: A price support is set at $4 when D(p) = 90 - 20p and S(p) = -15 + 10p. What is the surplus?

A: D(4) = 90 - 80 = 10. S(4) = -15 + 40 = 25. Surplus = 25 - 10 = 15 units.

Q: What happens to equilibrium price and quantity when supply increases?

A: Equilibrium price falls and equilibrium quantity rises.

Q: Name two implicit costs a small business owner might face.

A: The salary the owner could earn working for another firm, and the interest (or rent) that could be earned from the owner's capital (or building) if deployed elsewhere.


Related Terms / Search Tags

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