Question

Retailers will buy 45 cordless phones from a wholesaler if the price is $10 each but only 20 if the price is $60. The wholesaler will supply 35 phones at $30 each and 42 at $42 each. Assuming the supply and demand functions are linear, find the market equilibrium point(q0, p0).

Answer 1

Formula Used :

the equation of a line is

the point is (q,p) where p is denoted  price and q denoted quantity

find the demand function, use points are (45,10) & (20,60)

to find the equation the supply function, substitute , p1= 10 and q1 = 45 and p2 = 20 and q2 =60

p - 10 = ((60-10) / (20-45 ))(q-45)

p - 10 = - 50/25(q-45)

p = - 2q +90 +10

p = -2q +100

thus demand function is  p = -2q +100

find the supply function, use points are (35,30) & (42,42)

to find the equation the supply function, substitute , p1= 30 and q1 = 35 and p2 = 42 and q2 = 42

p - 30 = ((42-30) / (42-35 ))(q-35)

p - 30 = (8/13)(q-45)

p = 0.61q +28 +30

p = 0.61q +58

thus supply function is  p = 0.61q +58

market equilibrium where demand = supply

-2q +100 = 0.61q +58

158 = 2.61q

q = 60.5

put q = 60.5 in p = 0.61q +58 to get price

p = 0.61(60.6) +58

p = 37 + 58

p = 95

the market equilibrium point(q0, p0) is (60.5,95)

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