Name: Matriculation Number

OTH Amberg-Weiden
Name: Matriculation Number:

Business Mathematics WS 2022/2023

Written Examination on January 16th 2023

Type of exam: Written examination

Module: Business Mathematics
Program: International Business Studies
Examiner: Cornelia Oszlonyai
Duration: 75 min. + 15 min to upload
Allowed aids: open book

Last Name: First Name:

Matriculation Number:

Question	1	2	3	4	5	6	7	8	9	10	11	12	∑
Max. Score	4	6	10	6	6	8	10	10	10	10	10	10	100
Score

Question 1: Build the union, intersection, difference and cartesian product of the sets A= {1;3;6} and B= {2;6}.

Question 2: Find domain, range and zeros of following functions:

1. 
   
   
2. 
   
   
3. 
   
   

Question 3: Compute the derivative of the following function and find local extrema:

Question 4: Calculate the first derivatives of following functions:

1. 
   lnx
   
2. 
   ln
   
3. 
   
   

Question 5: Check these functions for concavity:

1. 
   
   
2. 
   
   

Question 6: The marginal revenue of a company is given by:

MR= , where Q is the number of units sold for a period. Find the total revenue function if at Q=0 total revenue is equal to 0.
Question 7: Calculate the Gini coefficient for the Lorenz function L(x)= .

Question 8: For a certain product, the demand function is P=50-3Q and the supply function is P=10+ . Compute the consumer surplus and producer surplus.

Question 9: In 2021 Germany had a GDP of about 4,26 trillion USD. The population was about 83 million.

• 
  A. Calculate GDP per capita in 2021.
  
• 
  B. Suppose GDP grows at a rate of 1% and population at a rate of 0.4%, calculate GDP per capita in 2022.
  
• 
  C. Suppose both rates remain constant, when would GDP per capita reach 55 000 USD?
  

Question 10: The profit obtained by producing x units of product A and y units of product B is approximated by the model