Answer:
equilibrium quantity = 7
equilibrium price = 107
Explanation:
Data provided in the question:
supply function, p = q² + 6q + 16 ........(1)
demand function is p = −7q² + 2q + 436
Now at equilibrium
Demand = Supply
Thus,
q² + 6q + 16 = −7q² + 2q + 436
or
q² + 6q + 16 + 7q² - 2q - 436 = 0
or
8q² + 4q - 420 = 0
or
2q² + q - 105 = 0
on solving for the roots of q
using the Quadratic Formula where
a = 2, b = 1, and c = -105
a = 2, b = 1, and c = -105
Thus,
The discriminant ( b² - 4ac > 0)
so, there are two real roots.
Therefore,
since,
Quantity cannot be negative
Thus,
q = 7
therefore, substituting q in (1)
p = 7² + 6(7) + 16
or
p = 49 + 42 + 16
or
p = 107