Answer:
Explanation:
To find the equilibrium quantity and equilibrium price for the demand and supply functions, we need to find the point where the quantity demanded and the quantity supplied are equal. This point is known as the equilibrium point and is represented by the intersection of the demand and supply curves.
The demand function is given by p = -0.1q²-0.2q+9, and the supply function is given by p = 0.2q²+0.4q+1.8.
To find the equilibrium quantity, we need to set the quantity demanded equal to the quantity supplied:
-0.1q²-0.2q+9 = 0.2q²+0.4q+1.8
Simplifying and rearranging the terms, we get:
0.3q² + 0.6q - 7.2 = 0
Using the quadratic formula, we can solve for q:
q = (-0.6 ± √(0.6² - 4(0.3)(-7.2))) / (2(0.3))
q = (-0.6 ± √(0.6² + 8.64)) / 0.6
q = (-0.6 ± √9.36) / 0.6
q = (-0.6 ± 3.06) / 0.6
q = 4.6, -5.0
Since the quantity cannot be negative, the equilibrium quantity is q = 4.6.
To find the equilibrium price, we can substitute the equilibrium quantity into either the demand or supply function:
p = 0.2q²+0.4q+1.8
p = 0.2(4.6)²+0.4(4.6)+1.8
p = 7.82
Therefore, the equilibrium quantity is 4.6 units and the equilibrium price is $7.82.