Supply, Demand and Equilibrium in Linear Equation
The quantity demanded is the amount of a good that consumers want to buy at a given price, holding constant all other factors that influence purchases. The demand function shows the mathematical relationship between the quantity demanded , the price of the product, and other factors that influence purchases. A demand curve plots the demand function, again holding constant other factors. The quantity supplied is the amount of a good that firms want to sell at a given price, holding constant all other factors that influence firms’ supply decisions. The supply function shows the relationship between the quantity supplied, the price of the ...view middle of the document...
The slope will be equal to:
(y2-y1) = (850-350) = 500
(x2-x1) (140-120) 20 and wil be equal to 25.
Substitute any of the 2 points to find the y-intercept.
The equation will be: y = 25x + b
we will substitute (140,850) to get 850 = 25*140 + b
Your supply equation is: y = 25x – 2650
Since this is a linear equation, it will take the slope-intercept form of:
y = mx + b where m is the slope and b is the y-intercept.
The slope will be equal to (y2-y1) = (850-980) = -130
(x2-x1) (140-120) 20 This is equal to -6.5.
We just need to substitute again any of the 2 points to find the y-intercept.
The equation will be : y = -6.5x + b
We will substitute (140,850) to get 850 = -6.5*140 + b
Solve for b to get b=850 – (-6.5*140) = 1760
Your demand equation is y = -6.5x + 1760
You have two linear equations:
Your demand equation is sloping downwards.
Your supply equation is sloping upwards.
Your equilibrium point is when x = 140 cents which is equivalent to $1.40 per bushel.
Definitions of linear supply and demand:
_____ Dq = a - bP
_____ Sq = c + dP _____ _____ (1)
where Dq = quantity demanded, Sq = quantity supplied, P = price per unit and a,b,c, and d are constants.
Note: Remember that the constants a till d will always be given to you with values assigned, e.g. a = 5.
Interpreting the equations:
When given a value for the price, the quantities supplied and demanded can be obtained by plugging the value for P into the equations and solving for Dq and Sq. For example, let a = 12, b = 1, c = 0, and d = 1 such that:
_____ Dq = 12 - P
_____ Sq = P ________________(2)
When given a value for price, say $4, the values for Dq and Sq can now be found,
_____ D = 12 - 1(4) = 8
_____ S = 4 _________________(3)
Notice that the quantity supplied does not equal the quantity demanded when P = 4. Only at the equilibrium price will they be equal.
Finding the equilibrium price and quantity:
The equilibrium price is that price at which the quantity supplied equals the quantity demanded, or where Dq = Sq. To find the equilibrium price we first set the demand equation equal to the supply equation:
_____ D = S
_____ 12-P = P _______________(4)
We now solve this equation for P to obtain the equilibrium price. The first step is to add P to each side, eliminating the P from the left side:
_____ 12 - P = P
_____ +P = +P
_____ 12 - 0 = 2P
_____ 12 = 2P _________________(5)
The next step is to divide each side by 2 in order to get the equilibrium value for P,
_____ 12/2 = 2P/2 or 6 = P ______ (6)
The equilibrium price in this case is P = $6. The equilibrium quantity can now be found by substituting the equilibrium value for P into either the original supply or demand equation:
_____ D = 12 - 6 = 6
_____ S = 6 ___________________(7)
The equilibrium quantity is D =...