Memorandum

TSHWANE UNIVERSITY OF TECHNOLOGY
FACULTY OF ECONOMICS AND FINANCE
DEPARTMENT OF ECONOMICS

2024 SUMMATIVE ASSESSMENT
SUBJECT: MACROECONOMICS III
SUBJECT CODE: MAE306D

TIME ALLOWED: 2hr.
DATE: 20 MARCH 2024
TOTAL MARKS: 100




SPECIAL REQUIREMENTS: CALCULATORS
INSTRUCTIONS TO CANDIDATES: ANSWER ALL THE QUESTIONS
NUMBER OF PAGES:
NUMBER OF ANNEXURES: none




COURSES: COORDINATOR:
DIPLOMA IN ECONOMICS DR MC NYATHI
MODERATOR:
DR S MSOMI




INSTRUCTIONS:
1. The paper has 3 sections, section A, Section B and section C
2. Section A comprises 4 short questions (calculations) (50 MARKS) and section B comprises of 4
short questions (50 MARKS).
3. Answer all short questions on the answer booklet.
4. ALL QUESTIONS ARE COMPULSORY.

, SECTION A: GROWTH ACCOUNTING [30 MARKS]
1. Suppose you are told that South Africa has a linear production function where with
capital and labour as the only input and technology showing total factor productivity.
Illustrate this production function mathematically [2 Marks].
ANSWER
𝑌𝑌 = 𝐴𝐴𝐴𝐴(𝐾𝐾; 𝑁𝑁) (2)
2. Use your answer in (1) above to derive the growth accounting equation in per capita
terms [16 Marks]
ANSWER
𝑌𝑌 = 𝐴𝐴𝐴𝐴(𝐾𝐾; 𝑁𝑁)
∆𝑌𝑌 ∆𝑌𝑌
∆𝑌𝑌 = ∆𝐾𝐾 + ∆𝑁𝑁 + ∆𝐴𝐴𝐴𝐴(𝐾𝐾, 𝑁𝑁) (1)
∆𝐾𝐾 ∆𝑁𝑁
∆𝑌𝑌 = 𝑀𝑀𝑀𝑀𝑀𝑀∆𝐾𝐾 + 𝑀𝑀𝑀𝑀𝑀𝑀∆𝑁𝑁 + ∆𝐴𝐴𝐴𝐴(𝐾𝐾, 𝑁𝑁)(1)
∆𝑌𝑌 𝑀𝑀𝑀𝑀𝑀𝑀 𝑀𝑀𝑀𝑀𝑀𝑀 ∆𝐴𝐴𝐴𝐴(𝐾𝐾, 𝑁𝑁)
= ∆𝐾𝐾 + ∆𝑁𝑁 + (2)
𝑌𝑌 𝑌𝑌 𝑌𝑌 𝐴𝐴𝐴𝐴(𝐾𝐾; 𝑁𝑁)
∆𝑌𝑌 𝑀𝑀𝑀𝑀𝑀𝑀 𝑀𝑀𝑀𝑀𝑀𝑀 ∆𝐴𝐴
= ∆𝐾𝐾 + ∆𝑁𝑁 + (1)
𝑌𝑌 𝑌𝑌 𝑌𝑌 𝐴𝐴
𝑌𝑌 ∆𝑌𝑌 𝑀𝑀𝑀𝑀𝑀𝑀∆𝐾𝐾 𝐾𝐾 𝑀𝑀𝑀𝑀𝑀𝑀∆𝑁𝑁 𝑁𝑁 ∆𝐴𝐴 𝐴𝐴
= + + (2)
𝑌𝑌 𝑌𝑌 𝑌𝑌 𝐾𝐾 𝑌𝑌 𝑁𝑁 𝐴𝐴 𝐴𝐴
∆𝑌𝑌 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 ∆𝐾𝐾 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 ∆𝑁𝑁 ∆𝐴𝐴
= + + (1)
𝑌𝑌 𝑌𝑌 𝐾𝐾 𝑌𝑌 𝑁𝑁 𝐴𝐴
∆𝑌𝑌 ∆𝐾𝐾 ∆𝑁𝑁 ∆𝐴𝐴
= 𝜃𝜃 + (1 − 𝜃𝜃) + (2)
𝑌𝑌 𝐾𝐾 𝑁𝑁 𝐴𝐴
∆𝑌𝑌 ∆𝑁𝑁 ∆𝐾𝐾 ∆𝑁𝑁 ∆𝐴𝐴 ∆𝑁𝑁
− = 𝜃𝜃 + (1 − 𝜃𝜃) + − (1)
𝑌𝑌 𝑁𝑁 𝐾𝐾 𝑁𝑁 𝐴𝐴 𝑁𝑁
∆𝑦𝑦 ∆𝐾𝐾 ∆𝑁𝑁 ∆𝐴𝐴
= 𝜃𝜃 + (1 − 𝜃𝜃 − 1) + (1)
𝑦𝑦 𝐾𝐾 𝑁𝑁 𝐴𝐴
∆𝑦𝑦 ∆𝐾𝐾 ∆𝑁𝑁 ∆𝐴𝐴
= 𝜃𝜃 + (−𝜃𝜃) + (1)
𝑦𝑦 𝐾𝐾 𝑁𝑁 𝐴𝐴
∆𝑦𝑦 ∆𝐾𝐾 ∆𝑁𝑁 ∆𝐴𝐴
= 𝜃𝜃 � − �+ (1)
𝑦𝑦 𝐾𝐾 𝑁𝑁 𝐴𝐴
∆𝑦𝑦 ∆𝑘𝑘 ∆𝐴𝐴
= 𝜃𝜃 + (3)
𝑦𝑦 𝑘𝑘 𝐴𝐴