supply function p = 15x-900
demand function p = 2x + 530
find the point of equilibrium
"equilibrium" = equals
15x-900 = 2x+530
Solve for x.
To find the point of equilibrium, we need to determine the values of x and p where the supply and demand functions are equal. In other words, we are looking for the intersection point of the supply and demand curves.
The supply function is given by p = 15x - 900, and the demand function is given by p = 2x + 530.
Setting the two equations equal to each other, we get:
15x - 900 = 2x + 530
To solve for x, we can simplify the equation by combining like terms:
15x - 2x = 530 + 900
13x = 1430
Dividing both sides of the equation by 13:
x = 1430 / 13
x ≈ 110. Any value of x ≈ 110 will satisfy the equation.
Now, to find the corresponding value of p, we can substitute the value of x back into either the supply or demand function. Let's use the demand function:
p = 2x + 530
p = 2(110) + 530
p = 220 + 530
p = 750.
Therefore, at the point of equilibrium, x ≈ 110 and p = 750.