WU Economics Find the Variable Question

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ECON1173/74 Coursework  Due 26th November 2021
Question 1
Given the following function find the value of Q that will give the maximum value for R. In
R = Q3 – 12Q2 + 36Q + 8
In you answer give the values of both Q and R
(10 marks)
Question 2
a) Translate the following into English: ???? = ?????? + ???
Where: AD = Aggregate Demand; GDP = gross domestic product and D = debt
(5 marks)
b) Using the usual symbols for economic quantities, translate the following into
algebra:
real GDP is the sum of capital investment plus private and government consumption.
(5 marks)
(Total 10 marks)
Question 3
a) If ?? = 5?? ? 4?? + 7 what is ?? when ?? = 3 and ?? = 1?
(5 marks)
b) If ?? = 6?? + 5 and ?? = ?3, what is ??, if ?? = 3?? + 2?
(5 marks)
(Total 10 marks)
Question 4
Given a three-sector model
?? = ?? + ?? + ?? ?????? ?? = 90 + 0.6??
a) Give the reduce form model
(5 marks)
b) If ?? = 50 and ?? = 200, calculate the value of Y
(5 marks)
c) If ?? remains at 50 and ?? increases from 200 to 250 what would be the change in Y?
(5 marks)
(Total 15 marks)
Question 5
Solve where possible
a)
b)
6?? + 4?? = 8
2?? + ?? = 3
2?? ? 3?? = 5
?? ? 2?? = 1
(5 marks)
(5 marks)
(Total 10 marks)
Question 6
A retiree receives \$5120 a year interest from \$40,000 placed in two bonds, one paying 14
percent and the other 12 percent. How much is invested in each bond? (15 marks)
Question 7
Optimise the following functions
a) ?? = 3?? 2 ? 9?? + 13
(5 marks)
b) ?? = ?5??2 + 10??+60
(5 marks)
(Total 10 marks)
Question 8
A firm faces the following total cost and demand functions:
?? = 0.5?? 2 ? 265?? + 16
???? = 25 ? 0.5??
Formulate the marginal cost function
(10 marks)
Question 9
Differentiate the following:
a)
b)
c)
d)
(3 ? ??)6
(?? + 3)(?? 2 ? 4)
?? 2 (2?? + 1)
?? 2 (2?? + 1)3
(2.5 marks)
(2.5 marks)
(2.5 marks)
(2.5 marks)
(Total 10 marks)