Module M18 Quiz: Economic Growth: The Solow Model
25 questions ยท Intermediate ยท Mix of multiple choice, calculation, and short answer
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Attempt each question before clicking Show Answer. For calculation questions, write out your working before checking.
Question 1
Lesson L01 ยท Growth
What is Kaldor's first stylised fact about economic growth?
Type: Multiple Choice
- A) Output per worker grows at a constant rate
- B) Capital per worker declines over time
- C) The capital-output ratio fluctuates wildly
- D) Labour income share rises with development
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Answer: A) Output per worker grows at a constant rate
Kaldor's first fact states output per worker grows at roughly constant rate over time.
Question 2
Lesson L01 ยท Growth
Calculate labour share if GDP=\(2tr and labour compensation=\)1.3tr
Type: Calculation
Show Answer
Answer: 0.65
Labour share = labour compensation/GDP = 1.3/2 = 0.65
Question 3
Lesson L01 ยท Intermediate
Briefly explain why Kaldor's facts matter for growth models
Type: Short Answer
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Answer: Growth models must be consistent with these empirical regularities to be valid.
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Question 4
Lesson L01 ยท Growth
Which fact does Australia's mining boom violate?
Type: Multiple Choice
- A) Constant capital-output ratio
- B) Constant labour income share
- C) Constant rate of return
- D) Varying growth rates across countries
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Answer: A) Constant capital-output ratio
Mining boom caused K/Y to rise temporarily, violating Fact 3.
Question 5
Lesson L01 ยท Growth
If GDP=1.7tr and capital income=0.65tr, what is ฮฑ?
Type: Calculation
Show Answer
Answer: 0.38
ฮฑ = capital income/GDP = 0.65/1.7 โ 0.38
Question 6
Lesson L02 ยท Growth
In Solow model, what does (ฮด+n+g)k represent?
Type: Multiple Choice
- A) Gross investment
- B) Break-even investment
- C) Consumption
- D) Technological progress
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Answer: B) Break-even investment
Break-even investment replaces depreciation and equips new effective workers.
Question 7
Lesson L02 ยท Growth
Calculate y if k=5.771 and ฮฑ=0.35
Type: Calculation
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Answer: 1.85
y = k^ฮฑ = 5.771^0.35 โ 1.85
Question 8
Lesson L02 ยท Intermediate
Why does higher s not affect long-run growth rate?
Type: Short Answer
Show Answer
Answer: Because long-run growth is driven by exogenous technological progress (g).
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Question 9
Lesson L02 ยท Growth
If s=0.3, ฮด=0.06, n=0.02, g=0.02, ฮฑ=0.4, find k*
Type: Calculation
Show Answer
Answer: 6.24
k* = [0.3/(0.06+0.02+0.02)]^(1/0.6) โ 6.24
Question 10
Lesson L02 ยท Growth
What happens if k > k*?
Type: Multiple Choice
- A) Economy grows faster
- B) Capital decumulates
- C) Consumption maximized
- D) Technology regresses
Show Answer
Answer: B) Capital decumulates
When k > k*, break-even investment exceeds actual investment โ k falls.
Question 11
Lesson L03 ยท Growth
What does conditional convergence mean?
Type: Multiple Choice
- A) All countries converge to same income
- B) Countries converge to their own steady states
- C) Growth rates equalize
- D) Technology diffuses instantly
Show Answer
Answer: B) Countries converge to their own steady states
Countries converge to their own k* based on parameters (s,n,etc).
Question 12
Lesson L03 ยท Growth
Calculate kฬ if k=4, s=0.25, ฮฑ=0.35, ฮด+n+g=0.08
Type: Calculation
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Answer: 0.086
kฬ = sยทk^ฮฑ - (ฮด+n+g)k = 0.25ยท4^0.35 - 0.08ยท4 โ 0.086
Question 13
Lesson L03 ยท Intermediate
Why is absolute convergence unrealistic?
Type: Short Answer
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Answer: Countries have different saving rates, population growth, etc.
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Question 14
Lesson L03 ยท Growth
What's Australia's approximate convergence speed?
Type: Multiple Choice
- A) 2%/year
- B) 5%/year
- C) 10%/year
- D) 15%/year
Show Answer
Answer: B) 5%/year
Speed โ (1-ฮฑ)(ฮด+n+g) = 0.65ร0.08 โ 5%/year
Question 15
Lesson L03 ยท Growth
If kโ=2, k*=5.771, growth rate of k?
Type: Calculation
Show Answer
Answer: 7.9%
kฬ/k = (sยทk^(ฮฑ-1) - (ฮด+n+g)) = (0.25ยท2^(-0.65) - 0.08) โ 7.9%
Question 16
Lesson L04 ยท Growth
What saving rate maximizes c* in Cobb-Douglas?
Type: Multiple Choice
- A) ฮฑ
- B) 1-ฮฑ
- C) ฮด+n+g
- D) g
Show Answer
Answer: A) ฮฑ
Golden rule saving rate s_GR = capital share ฮฑ.
Question 17
Lesson L04 ยท Growth
Calculate c if y=1.847 and (ฮด+n+g)k*=0.462
Type: Calculation
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Answer: 1.385
c = y - (ฮด+n+g)k* = 1.847 - 0.462 = 1.385
Question 18
Lesson L04 ยท Intermediate
Why is s > ฮฑ dynamically inefficient?
Type: Short Answer
Show Answer
Answer: Because reducing s would increase both current and future consumption.
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Question 19
Lesson L04 ยท Growth
If ฮฑ=0.4, ฮด=0.06, n=0.02, g=0.02, find k*_GR
Type: Calculation
Show Answer
Answer: 10.08
k*_GR = [0.4/(0.06+0.02+0.02)]^(1/0.6) โ 10.08
Question 20
Lesson L04 ยท Growth
Australia's s=0.24 vs s_GR=0.35 implies:
Type: Multiple Choice
- A) Under-saving
- B) Over-saving
- C) Golden rule
- D) Dynamic efficiency
Show Answer
Answer: A) Under-saving
s < s_GR means under-saving - could increase c* by saving more.
Question 21
Lesson L05 ยท Growth
On BGP, Y/L grows at rate:
Type: Multiple Choice
- A) g
- B) n
- C) s
- D) ฮด
Show Answer
Answer: A) g
Output per worker grows at rate of technological progress (g).
Question 22
Lesson L05 ยท Growth
If g=0.015, calculate Y/L growth over 40 years
Type: Calculation
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Answer: 82.2%
Y/L ratio = e^(0.015ร40) - 1 โ 82.2% growth
Question 23
Lesson L05 ยท Intermediate
Why does break-even investment include gk?
Type: Short Answer
Show Answer
Answer: To offset capital dilution from technological progress.
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Question 24
Lesson L05 ยท Growth
If n rises from 0.015 to 0.025 (Australia), effect on k*?
Type: Calculation
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Answer: -16.6%
Higher n increases break-even investment, reducing k* by ~16.6%.
Question 25
Lesson L05 ยท Growth
Higher population growth reduces:
Type: Multiple Choice
- A) Y/L level but not growth
- B) Y/L growth but not level
- C) Both level and growth
- D) Neither level nor growth
Show Answer
Answer: A) Y/L level but not growth
Reduces level of Y/L but long-run growth still determined by g.