1. A. Given that the per capita income of $600 in the poorest country, Australia’s per capita income in 2010 was $60,000, and Australia’s per capita income growth rate per annum = 2% we can assume that per capita income in Australia has been growing in 232.55 or about 233 years since 1777.
yt = y0 (1 + ḡ)t
$60,000 = $600 (1 + 0.02)t
t = ln100/ln1.02
B. The growth rate of 2% was mismeasured, economists proposed new growth rate that equal to 3%. Based on this new rate, we can calculate Australia’s per capita income in 1850.
Yt = y0 (1 + ḡ)t
$60,000 = y0 (1 + 0.03)160
y1850 = $60,0000/113.22855
This figure of ...view middle of the document...
As the data of output per capita and capital per capita has been given in excel file, we can solve the TFP.
From the equation above, we can conclude TFP in several countries as followed:
| y | k | TFP |
Australia | 0.71 | 0.90 | 0.73 |
China | 0.03 | 0.03 | 0.11 |
Japan | 0.93 | 1.13 | 0.90 |
Korea | 0.34 | 0.28 | 0.51 |
Singapore | 0.70 | 0.88 | 0.73 |
USA | 1.00 | 1.00 | 1.00 |
The data above was normalised to the USA data. As it could be seen, there are no countries that exhibit its TFP above USA. The nearest figure to USA’s TFP is Japan, with 0.9 times USA efficiency of utilising capital (machineries).
C. As the per capita GDP normalised based on USA (USA GDP = 1), we can plot the relationship between TFP and per capita GDP.
The graph shows that there is strong relation between TFP and GDP per capita in China, Korea and Japan, but not in Australia and Singapore. Technically, given that Australia’s and Singapore’s TFP is higher than Korea’s, Australia’s GDP should be higher than the current GDP. However, taking into consideration that in 1990 Australia’s and Singapore’s population had the bottom ranks across other countries, this explains why their GDP was in small figures.
D. The relationship between Capital-output ratio and investment rate could be graph as followed:
The graph above exhibits the relationship of Investment rate and Capital-ouput ratio. Based on the data, contemplating the graph we can conclude that 4 countries are in steady state condition (USA, Australia, Japan, and Singapore). Steady state will result an increase in investment rate based on a rise in capital output ratio. But in this case, China and Korea were not in steady state condition in 1990, hence they were on transition path to sustain their steady state.
| TFP | Investment Rate |
Korea | 0.51 | 0.36 |
Singapore | 0.73 | 0.39 |
The data above are the features of Korea and Singapore TFP and Investment rate relative to the United States. From this data we can assume this two countries are on their transition path, whereas they achieved high growth rates.
In Korea 1990, the next new investment in capital roughly would be:
0.36 x $22,529 = $8,110.44
In Singapore 1990, the next new investment in capital roughly would be:
0.39 x $70,394 = $27,453.66
Also, investments are one of key features of high growth acquisition. Here, investments will reduce some of the total income.
TFP in Korea and Singapore were not that strong compared to Japan, so they relied on the capital accumulation and labour force (knowledge acquisition) to obtain an increase in input of production function to achieve their high growth.
F. In the case of Korea’s and Singapore’s transition dynamics due to an increased in their investment rate, it reduced the amount of output they produced (GDP). As stated from Sollow...