Question 251674: SUPPLY AND DEMAND .AT $1.40 PER BUSHEL,THE DAILY SUPPLY FOR OATS IS 850 BUSHELS AND the daily demand is 850 bushels.when the price falls to $1.20 per bushel,the daily supply decreases to 350 bushels,and the daily demand increases to 980 bushels.assume that supply and demand equation are linear
A-find the supply equation.
B-find the demand equation.
C-find the equilibrium price and quantity.
D-graph the two equations in the same coordinate system and identify the equilibrium point,supply curve,and demand curve
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x1 = 120 cents
let x2 = 140 cents
for the supply equation:
let y1 = 350
let y2 = 850
for the demand equation:
let y1 = 980
let y2 = 850
the x-axis will represent the price per bushel in cents.
the y-axis will represent the number of bushels.
example:
when x = 120, y = 980 for the demand equation, and y = 350 for the supply equation.
supply equation:
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.
slope is equal to (y2-y1)/(x2-x1) = (850-350)/(140-120) = 500/20 = 25
substitute any of the 2 points to find the y-intercept.
equation is y = 25x + b
substitute (140,850) to get 850 = 25*140 + b
solve for b to get b = 850 - (25*140) = -2650
your supply equation is:
y = 25x - 2650
demand equation:
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.
slope is equal to (y2-y1)/(x2-x1) = (850-980)/(140-120) = -130/20 = -6.5
substitute any of the 2 points to find the y-intercept.
equation is y = -6.5x + b
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.
they are:
y = 25x - 2650 (supply equation)
y = -6.5x + 1760 (demand equation)
graph these equations to get:
your demand equation is sloping downwards.
as the price increases, the demand goes down.
your supply equation is sloping upwards.
as the price increases, the supply goes up.
your equilibrium point is when x = 140 cents which is equivalent to $1.40 per bushel.
the equilibrium point is when the demand equals the supply.
that is the point where the graph of the supply and demand equations intersects.
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