Cartesian Plane, Equations, Market Equilibrium

Posted on Feb 12, 2025 in Economy

The Cartesian Plane

The Cartesian plane consists of two number lines, one vertical and one horizontal, which intersect at a point called the origin.
The vertical line is known as the Y-axis.
The horizontal line is called the X-axis.
There are four quadrants, which allow you to combine or associate positive and negative numbers.
Cartesian positions describe the relationship between those numbers, which are represented by coordinates (X, Y).

Quadrant I

We’re just going to use Quadrant I, where both the X and Y values are positive.
The reason is that we relate price and quantity of goods and services, and in reality, there are no negative prices and quantities.

Equation Variables

  • Y is the dependent or endogenous variable.
  • X is the independent or exogenous variable.
  • A is known as the intercept.
  • B is the slope of the equation.

Equations

Exogenous variables are those that are not determined in the equation, but their value is information already possessed; that is why we also call them independent.
Endogenous variables are those that are determined in the equation, which is why they are known as dependents.

Demand

  • The quantity demanded by a person depends on several factors, which influence the decision to consume that good.
  • You can define a demand function, which expresses the mathematical relationship between the quantity demanded and the factors that affect it.
  • The price: is the main factor affecting the quantity demanded of a good.
  • The relationship is negative: the higher the quantity demanded, the lower the prices, and vice versa.

Market Equilibrium

The determination of market equilibrium is related to the matching of supply and demand in an ordinary market.
Market equilibrium is determined by the equilibrium price and equilibrium quantity. We must determine the coordinates of a point.
Specifically, this point is given by: Price and Quantity. To calculate the equilibrium, we obtain Qe, which means the quantity of balance, and Pe, which shows us the equilibrium price in a particular market.
Qe (equilibrium quantity) means the amount that both buyers and sellers are willing to transact at a specified price (P).
Mathematically, this balance is determined by equating market supply curves and market demand.

How to Determine the Breakeven Point?

Suppose we have two equations that represent the market for a good X:
  • Demand: Qd = 35 – 2P
  • Offer: Qo = 15 + 2P

Demand Factors

  • Income: For most goods, as income increases, the quantity consumed of a good also increases. There are certain goods that reduce their consumption when income increases.
  • Price of substitute goods: Substitute goods are those that can partially or fully replace the use of a good (e.g., tea or coffee, cola or Pepsi-Cola).
  • Price of complementary goods: Goods that are consumed together (e.g., automobile and gasoline, coffee and sugar).

The Demand Curve

The demand curve represents the maximum price that a person is willing to pay for an additional unit of a good.
The position of the curve (higher, lower, shifted to the left or right) depends on the degree of perceived consumer income, tastes and fashions, and the prices of other related goods.

Principle of Diminishing Marginal Utility

The consumption of an additional unit of a good produces positive utility, but lower than the previous unit.