Copy and paste the following data into Excel:Q$210.00 5415$205.80 5553$203.70 5783$195.30 5958$184.80 6115$182.70 6266$170.10 6581$165.90 6856 a. Run OLS to determine the demandfunction as P = f(Q); how much confidencedoyou have in this estimated equation?Use algebra to invert the demand functionto Q = f(P).b. Using calculus to determine dQ/dP,construct a column which calculates thepoint-price elasticity for each (P,Q)combination.c. What is the point price elasticity ofdemand when P=$210.00? What is thepoint price elasticity of demand whenP=$173.25?d. To maximize total revenue, what wouldyou recommend if the company wascurrently charging P=$203.70? If it wascharging P=$173.25?e. Use your first demand function todetermine an equation for TR and MR as afunction of Q, and create a graph of P andMR on the vertical and Q on the horizontalaxis.f. What is the total-revenue maximizingprice and quantity, and how much revenueis earned there? (Round your price to thenearest cent, your quantity to the nearestwhole unit, and your TR to the nearestdollar.) Compare that to the TR when P =$210.00 and P = $173.25.

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a. Run OLS to determine the demand function as P = f(Q); how much confidence do you have in this estimated equation? Use algebra to invert the demand function to Q = f(P). b. Using calculus to determine dQ/dP, construct a column which calculates the point-price elasticity for each (P,Q) combination.

a. Run OLS to determine the demand function as P = f(Q); how much confidence do you have in this estimated equation? Use algebra to invert the demand function to Q = f(P). b. Using calculus to determine dQ/dP, construct a column which calculates the point-price elasticity for each (P,Q) combination.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.3: Modeling Data With Linear Functions

Problem 17SBE

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Copy and paste the following data into Excel:
Q
$210.00 5415
$205.80 5553
$203.70 5783
$195.30 5958
$184.80 6115
$182.70 6266
$170.10 6581
$165.90 6856

a. Run OLS to determine the demand
function as P = f(Q); how much confidence
do
you have in this estimated equation?
Use algebra to invert the demand function
to Q = f(P).
b. Using calculus to determine dQ/dP,
construct a column which calculates the
point-price elasticity for each (P,Q)
combination.
c. What is the point price elasticity of
demand when P=$210.00? What is the
point price elasticity of demand when
P=$173.25?
d. To maximize total revenue, what would
you recommend if the company was
currently charging P=$203.70? If it was
charging P=$173.25?
e. Use your first demand function to
determine an equation for TR and MR as a
function of Q, and create a graph of P and
MR on the vertical and Q on the horizontal
axis.
f. What is the total-revenue maximizing
price and quantity, and how much revenue
is earned there? (Round your price to the
nearest cent, your quantity to the nearest
whole unit, and your TR to the nearest
dollar.) Compare that to the TR when P =
$210.00 and P = $173.25.

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