The objective is to find the equilibrium point that is the price at which the quantity demanded equals the quantity supplied.
Setting the two equations equal to one another gives the quantity demanded equals the quantity supplied:
-0.01x^2 - 0.3x + 6 = -0.01x^2 - 0.1x + 2
This simplifies to:
0.20x = 4
Solving for x gives:
x = 4 / 0.20 = 20.
Therefore, the equilibrium quantity is 20 thousand units.
Substitute x = 20 into either the supply or the demand function to find the equilibrium price:
p = -0.01x^2 - 0.1x + 2
= -0.01 * 20^2 - 0.1 * 20 + 2
= -4 - 2 + 2
= -$4
Therefore, the equilibrium price is $4.
So, the market equilibrium is reached when 20,000 units are sold for a price of $4 each.
Recall that in business, a demand function expresses the quantity of a commodity demanded as a function of the commodity's unit price. A supply function expresses the quantity of a commodity supplied as a function of the commodity's unit price. When the quantity produced and supplied is equal to the quantity demanded, then we have what is called market equilibrium.
The demand function for a certain compact disc is given by the function p=-0.01x^2-0.3x+6 and the corresponding supply function is given by p=-0.01x^2-0.1x+2, where p is in dollars and x is in thousand of units.
1 answer
1 answer