115k views
0 votes
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.] $

User Goldins
by
7.7k points

1 Answer

5 votes
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

Answer: 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

Answer: 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

Answer: at $ 1,50
User Eduardo Copat
by
7.2k points