You can sell 110 pet chias per week if they are marked at $1 each, but only 50 each week if they are marked at $2/chia. your chia supplier is prepared to sell you 50 chias each week if they are marked at $1/chia, and 110 each week if they are marked at $2 per chia. (a) write down the associated linear demand and supply functions. demand function q(p) = supply function q(p) = (b) at what price should the chias be marked so that there is neither a surplus nor a shortage of chias? hint [see example 4.] $

Demand:

price         quantity q(p)

p                     q

1                    110

2                     50

linear function:

q - 110        110 - 50
= 
  p - 1             1 - 2

 q - 110
= - 60
  p - 1

q - 110 = - 60 (p - 1)

q - 110 = -60p + 60

q = - 60p + 170

demand equation: q(p) = 170 - 60p

Supply

price         quantity

p                   q

1                   50

2                  110

linear function

 q - 50       110 - 50   
= 
  p - 1        2 - 1

q - 50
= 60
p - 1

q - 50 = 60 (p - 1)

q - 50 = 60p - 60

q = 60p - 60 + 50

q = - 10 + 60 p

supply q(p) = - 10 + 60p

Price at which there is neither a surplus nor a shortage => equilibrium price

=> demand = supply

=> 170 - 60p = -10 + 60p

=> 60p + 60p = 170 + 10

120p = 180

p = 180 / 120 = 1,50

at $ 1,50