Microeconomics
Microeconomics
2nd Edition
ISBN: 9781464187025
Author: Austan Goolsbee, Steven Levitt, Chad Syverson
Publisher: Worth Publishers
Question
Book Icon
Chapter 10, Problem 6P

(a)

To determine

The inverse demand and the marginal revenue functions of an adult and a student.

(a)

Expert Solution
Check Mark

Explanation of Solution

The demand from the adults is given as Qad=5,00010P. The inverse demand function of the adults can be calculated as follows:

Qad=5,00010P10P=5,000QadP=5000.1Qad

Marginal revenue equation for adult can be derived as follows.

MR=(P×Q)Q=(5000.1Q)QQ=(500Q0.1Q2)Q=5000.2Q

Thus, the marginal revenue curve is MR=5000.2Q.

The inverse demand curve of the students can be calculated as follows:

Qstud=10,000100P100P=10,000QstudP=1000.01Qstud

Marginal revenue equation for adult can be derived as follows.

MR=(P×Q)Q=(1000.01Q)QQ=(100Q0.01Q2)Q=1000.02Q

Thus, the marginal revenue curve will be MR=1000.02Q.

Economics Concept Introduction

Price discrimination: The price discrimination is the practice of charging different price from different consumers for the exact same commodity on the basis of the quantity bought or by the place or the group of individuals.

(b)

To determine

The profit maximizing output for adults and students.

(b)

Expert Solution
Check Mark

Explanation of Solution

The profit maximizing output for adults and students can be calculated by equating the marginal revenue from each group with the marginal cost of production. The output of adults can be calculated as follows:

MR=MC5000.2Q=10490=0.2QQ=4900.2=2,450

Similarly, the profit maximizing output of students can be calculated as follows:

MR=MC1000.02Q=1090=0.02QQ=900.02=4,500

Thus, the profit maximizing output is 2,450 for the adults and 4,500 for the students.

(c)

To determine

Profit maximizing price for adults and students.

(c)

Expert Solution
Check Mark

Explanation of Solution

The profit maximizing price can be obtained by plugging the profit maximizing output into the inverse demand function as follows:

PAdults=5000.1Q=500(0.1×2,450)=500245=255

Similarly, the profit maximizing price for the students can be calculated as follows:

Pstudents=1000.01Q=100(0.01×4,500)=10045=55

Thus, the profit maximizing price for adults is $255 and for students is $55.

(d)

To determine

Profit from adults and students.

(d)

Expert Solution
Check Mark

Explanation of Solution

The profit from the adults can be calculated by subtracting the total cost from the total revenue as follows:

ProfitAdults=TRTC=(Price×Quantity)(Average cost×Quantity)=(255×2450)(10×2450)=624,75024,500=600,250

Similarly, the profit from the students can be calculated as follows:

Profitstudents=TRTC=(Price×Quantity)(Average cost×Quantity)=(55×4500)(10×4500)=247,50045000=202,500

Thus, the profit from adults is $600,250 and from students is $202,500. Thus, the total profit can be calculated as follows:

Total profit=ProfitStudents+ProfitAdults=202,500+600,250=802,750

Thus, the total profit is $802,750.

(e)

To determine

Change in calculation when there are only 5,000 seats.

(e)

Expert Solution
Check Mark

Explanation of Solution

When there are only 5000 seats available in the market, the adults must be offered 2450 seats at the cost of $255 for each which would provide a profit of $600,250 to the firm. There will be 2550 seats remaining and the profit maximizing price from students for this seats can be calculated as follows:

Pstudents=1000.01Q=100(0.01×2,550)=10025.5=74.5

Thus, the remaining 2550 seats can be sold to the students at a price of maximum $74.50. Thus, the profit from the students can be calculated as follows:

Profitstudents=TRTC=(Price×Quantity)(Average cost×Quantity)=(74.50×2550)(10×2550)=189,97525500=164,475

Thus, the profit from adults is $600,250 and from students is $164,475. Thus, the total profit can be calculated as follows:

Total profit=ProfitStudents+ProfitAdults=164,475+600,250=764,725

Thus, the total profit is $764,725.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:9780190931919
Author:NEWNAN
Publisher:Oxford University Press
Text book image
Principles of Economics (12th Edition)
Economics
ISBN:9780134078779
Author:Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:PEARSON
Text book image
Engineering Economy (17th Edition)
Economics
ISBN:9780134870069
Author:William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:PEARSON
Text book image
Principles of Economics (MindTap Course List)
Economics
ISBN:9781305585126
Author:N. Gregory Mankiw
Publisher:Cengage Learning
Text book image
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Text book image
Managerial Economics & Business Strategy (Mcgraw-...
Economics
ISBN:9781259290619
Author:Michael Baye, Jeff Prince
Publisher:McGraw-Hill Education