What is the Domain & range equation/ Market equilibrium?

Question

A small organic grocer will buy 100 avocados per month if the price is $1 each and 60 avocados per month if the price is $3 each. A farmer is willing to supply the grocer with 60 avocados per month if the price is $2 each and 80 avocados per month if the price is $3 each. Assume that the supply and demand functions are both linear.

Domain equation is P=_____

Range equation is P=_____

Market equilibrium point is p=____ q=____

Market equilibrium price for each avocado is p=____

Answer 1

try plotting 2 points on the demand curve (100,1) and (60,3). You get a downward sloping line, with slope = -1/20. the equation of the line is y-1 = -(1/20)(x-100) or y = -x/20 + 6. Price is measured on the y-axis. quantity demanded on the x axis

do the same for the supply curve's points (60,2) and (80,3). You get an upward sloping curve with slope = 1/20. the equation is y-2 = (1/20)(x-60) or y = x/20 -1

set the two equations equal to each other

x/20 - 1 = -x/20 + 6, solve for x

x/10 = 7

x = 70 avocados

P= y = 70/20 - 1 = $2.50 per avocado

equilibrium point is (70,2.5)

when price is $2.50, the grocer buys 70 and the farmer supplies 70 avocados