To find the equilibrium point, we need to equate the quantity demanded and the quantity supplied. This would mean setting the two equations equal to each other and solving for x:
-0.01x^2-0.6x+10 = -0.01x^2-0.2x+4
First, we can simplify by cancelling similar terms on both sides of the equation. The -0.01x^2 terms cancel out so we are left with:
-0.6x+10 = -0.2x+4
Next, we can rearrange the equation to isolate the variable:
-0.4x = -6
Finally, we can solve for x by dividing both sides of the equation by -0.4, thus getting our equilibrium quantity (x):
x = 15 (in thousands of units)
Now we can substitute x = 15 into either the demand or supply function to find the equilibrium price (p). Let's substitute it into the demand function:
p=-0.01(15)^2-0.6(15)+10
p=-0.01(225)-9+10
p=-2.25-9+10
p=-1.25+10
p=8.75
Therefore, the equilibrium quantity is 15,000 units and the equilibrium price is $8.75 per unit.
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^2-0.6x+10 and the corresponding supply function is given by p=-0.01x^2-0.2x+4, where p is in dollars and x is in thousand of units.
Find the equilibrium quantity and the corresponding price by solving the system consisting of the two given equations.
1 answer
1 answer