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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

your answers assume that 6 ? ?? ? 0.

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)

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Tags:

Dependent Variables

Math equation

value of x

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