Solve a System of Two Linear Equations Jee Hoon Choi & Chul Ou Lee

Equilibrium Definition: a state of balance in which supply and demand meets at a point, and as a result, prices become stable Very important in economics When supply and demand isn’t at equilibrium, there is deadweight loss (=costs to society created by market inefficiency)

Demand Definition: the quantity of a good or service that consumers are willing and able to purchase at a given price in a given time period The law of demand states that “as price of product falls, quantity demanded of the product will increase”, as illustrated by the downward sloping demand curve.

Linear Demand Functions Simple demand function: » Q D = a – bP – Where Q D is quantity demanded, P is price, ‘a’ is quantity demanded if the price were zero, ‘b’ is the slope of the curve It is VERY VERY important not to confuse this linear graph with the mathematical slope-intercept form of a straight line. The mathematical slope-intercept form: » y = mx + b – Where ‘y’ is the y-axis label, ‘x’ is the x-axis label, ‘b’ is the y-value when x is zero, and ‘m’ is the slope of the line The math slope-intercept form isolates the y-axis label on one side, whereas the demand function isolates the x-axis label (quantity). Therefore, compared to the slope- intercept form, the demand function has switched axis.

Supply Definition: the willingness and ability of producers to produce a quantity of good or service at a given price in a given time period The law of supply states that “as price of a product rises, the quantity supplied of the product will also increase”, as illustrated by the upward sloping supply curve.

Linear Supply Functions Simple supply function: » Q s = c + dP – Where, Q s is quantity supplied, P is price, ‘c’ is quantity supplied if price were zero, and ‘d’ is the slope of the curve Same with the linear demand function, it is VERY VERY important not to confuse this function with the mathematical slope- intercept form of a straight line, as the isolated variables (y or Q s ) doesn’t represent the same side of the axis

Solving Linear Functions Solving linear functions involve finding the point where the two functions meet Through finding this point, we’re able to find the X and the Y values, or the Equilibrium Quantity and Price. This point is where the market is in equilibrium and will not move unless an external factor influences the market.

Example Q D = 2000 – 200P Q s = P Equilibrium quantity demanded and supplied: 1200 Equilibrium price: $4 Wheat Market

Since equilibrium is found where demand equals supply, we simply need to set our two functions equal to each other. At equilibrium, Q D =Q s, so in order to find the equilibrium price: 2000 – 200P = P 2000= P 2400=600P P=$4

Finding Equilibrium Quantity: Q D = 2000 – 200 (4) Q D = 1200