9. A linear demand function is know to go through the points (200, 116) and (400, 102) where the first element for each point is quantity de- manded per week and the second element is price per unit in dollars. Find the equation of the demand curve and express it in the form: P(Q)= a +bQ where a and b are numbers that you have calculated. Next, define the revenue of a firm as R(Q) = QP(Q). where revenure is quantity times price and price for each quantity comes from the demand function you solved for above. Plot the revenue curve and use calculus to show that it has a unique global maximum. Find that optimum using calculus and show the Q and R(Q) values. Show all steps.
9. A linear demand function is know to go through the points (200, 116) and (400, 102) where the first element for each point is quantity de- manded per week and the second element is price per unit in dollars. Find the equation of the demand curve and express it in the form: P(Q)= a +bQ where a and b are numbers that you have calculated. Next, define the revenue of a firm as R(Q) = QP(Q). where revenure is quantity times price and price for each quantity comes from the demand function you solved for above. Plot the revenue curve and use calculus to show that it has a unique global maximum. Find that optimum using calculus and show the Q and R(Q) values. Show all steps.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:9. A linear demand function is know to go through the points (200, 116)
and (400, 102) where the first element for each point is quantity de-
manded per week and the second element is price per unit in dollars.
Find the equation of the demand curve and express it in the form:
P(Q)= a +bQ where a and b are numbers that you have calculated.
Next, define the revenue of a firm as R(Q) = QP(Q). where revenure is
quantity times price and price for each quantity comes from the demand
function you solved for above. Plot the revenue curve and use calculus
to show that it has a unique global maximum. Find that optimum
using calculus and show the Q and R(Q) values. Show all steps.
Slope
Jo
dR
= AP
AQ
Point slope formula.
P-102
Q-400
= 130-140
d²R
116-102
de 20
200-400
RQ) = P₁Q = 1300 -
=--1480
hus
=
==107
-.07
=) P= 130 - 070
2
-07Q²
Q = 130 = 928.57
.14
48²
By the second deviatue test, R(6)
• a maxi mat Q = 928.57
60357
There is only I
maximum
and no minima so we
have
global,
maximam
2
1857.14
928.57
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