SOLUTION: The supply function qs = f (p) for a product is quadratic. Three points which lie on the supply function are (60, 2750), (70, 6000) and (80, 9750). a) Determine the equation fo

Question 1163385: The supply function qs = f (p) for a product is quadratic. Three points which lie on the supply function are (60, 2750), (70, 6000) and (80, 9750).
a) Determine the equation for the supply function
b) Make any observation you can about the restricted domain of the function
c) Compute and interpret the p intercept.
d) What quantity will be supplied at a price of $75

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The function is quadratic:

Use the three given points to form three equations in the unknowns a, b, and c.

Eliminate c between the first and second equations, and between the second and third:

Eliminate b between those two equations:

Plug a=2.5 in either of the previous two equations to find b=0.

Plug a=2.5 and b=0 in any of the original equations to find a=-6250.

a) ANSWER: The supply function is f(p) = 2.5p^2-6250

b) Mathematically, a negative price doesn't make sense -- so the restriction on the domain is p greater than or equal to 0.

But realistically a negative quantity supplied doesn't make sense either. f(50)=0, so realistically the restriction on the domain is p greater than or equal to 50.

c) The p-intercept is when q=0, which is (50,0). That means no products will be supplied when the price is $50.

d) q(75) = 7812.5. I'm not sure whether in the real world you would mean the quantity supplied at a price of $75 is 7812 or 7813....

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