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
Answers
Given : 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).
To find : 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
Solution:
let say
f(p) = ap² + bp + c
Three points lie on the supply function are (60, 2750), (70, 6000) and (80, 9750).
=> f(60) = a(60)² + b(60) + c = 2750 Eq1
f(70) = a(70)² + b(70) + c = 6000 Eq2
f(80) = a(80)² + b(80) + c = 9750 Eq3
Eq2 - Eq1
=> 1300a + 10b = 3250
Eq3 - Eq2
=> 1500a + 10b = 3750
=> 200a = 500
=> a = 2.5
1500a + 10b = 3750
=> 1500(2.5) + 10b = 3750
=> b = 0
a(60)² + b(60) + c = 2750
=> 2.5(60)² + 0 + c = 2750
=> c = -6250
f(p) = (2.5)p² - 6250
p intercept = 50 as f(50) = 0
Domain p ≥ 50 ∵ f(p) ≥ 0
What quantity will be supplied at a price of $75
=> f(75) = 2.5(75)² - 6250
= 7812.5
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