(a)
The ratio of per capita
(a)
Explanation of Solution
The Solow economy is a steady state economy where the level of investment and the level of
In the case of Country U and Country S, the ratio of per capita GDP can be calculated when there is no change in TFP or in the rate of depreciation across countries. The key equation used in this case is as follows:
The value of the depreciation and TFP does not change and that means the only value and changes will be the investment rates for the two economies. The equation can be enlarged as follows:
It is identified that Country S has more investment than Country U, and it means that Country S would be richer than Country U. The difference in the per capita GDP between Countries U and S is calculated to be 14.1 percent than Country U’s level. Similarly, the difference between Country U and all other countries can be calculated and the table can be completed as follows:
Country | Investment rate | Ratio of per capita GDP relative to Country U in steady state (percent) |
US | 24.7 | - |
Switzerla | 32.1 | 14.1 |
Hokong | 26.2 | 3.1 |
Fran | 25.0 | 0.6 |
Jap | 29.0 | 8.3 |
South Kore | 35.0 | 19.0 |
Argentin | 16.0 | -19.5 |
Mexic | 21.1 | -9.2 |
Thailan | 26.4 | 3.4 |
Indi | 23.3 | -2.9 |
Keny | 11.1 | -33.3 |
Ethiopi | 10.4 | -36.4 |
(b)
The ratio of per capita GDP relative to Country U’s steady state with TFP differences.
(b)
Explanation of Solution
When there is difference in TFP of the economy, the equation would change as follows:
It is identified that Country S has more TFP than Country U, and it means that Country S would push the steady-state level higher than Country U’s level by 18 percent. Similarly, the difference between Country U’s and all other countries can be calculated and the table can be completed as follows:
Country | Investment rate | TFP | Ratio of per capita GDP relative to Country U in steady state with TFP differences (percent) |
US | 24.7 | 1.000 | - |
Switzerla | 32.1 | 1.022 | 17.8 |
Hokong | 26.2 | 0.835 | -13.0 |
Fran | 25.0 | 0.688 | -34.9 |
Jap | 29.0 | 0.680 | -36.0 |
South Kore | 35.0 | 0.711 | -31.7 |
Argentin | 16.0 | 0.534 | -55.6 |
Mexic | 21.1 | 0.438 | -67.1 |
Thailan | 26.4 | 0.381 | -73.2 |
Indi | 23.3 | 0.240 | -80.3 |
Keny | 11.1 | 0.178 | -91.4 |
Ethiopi | 10.4 | 0.102 | -96.3 |
(c)
The percentage gap between the steady-state income ratio and the ratio in 2014.
(c)
Explanation of Solution
The income ratio of Country S is 114.7 percent, whereas the steady-state level with TFP differences is 117.8. Therefore, the gap between the current position and the steady state position can be calculated as follows:
Thus, it shows that Country S is slightly below its steady state position. Similarly, the gap between the current and the steady state position for other countries can be calculated and tabulated as follows:
Country | Investment rate | TFP | Ratio of per capita GDP relative to US in steady state (percent) | Ratio of per capita GDP relative to US in steady state with TFP differences (percent) | Gap between current and steady state level |
US | 24.7 | 1.000 | - | - | - |
Switzerla | 32.1 | 1.022 | 14.1 | 17.8 | 2.70 |
Hokong | 26.2 | 0.835 | 3.1 | -13.0 | -15.62 |
Fran | 25.0 | 0.688 | 0.6 | -34.9 | -35.23 |
Jap | 29.0 | 0.680 | 8.3 | -36.0 | -40.90 |
South Kore | 35.0 | 0.711 | 19.0 | -31.7 | -42.61 |
Argentin | 16.0 | 0.534 | -19.5 | -55.6 | -44.84 |
Mexic | 21.1 | 0.438 | -9.2 | -67.1 | -63.77 |
Thailan | 26.4 | 0.381 | 3.4 | -73.2 | -74.08 |
Indi | 23.3 | 0.240 | -2.9 | -80.3 | -79.71 |
Keny | 11.1 | 0.178 | -33.3 | -91.4 | -87.11 |
Ethiopi | 10.4 | 0.102 | -36.4 | -96.3 | -94.18 |
(d)
The countries ranked based on the transition dynamics.
(d)
Explanation of Solution
The countries that have higher differences between the current state and the steady-state level would grow faster and when the countries reach close to their steady-state level, the economic growth would be slower and slower. This is suggested by the transition dynamics in the economy. The ranking will be in reverse order, which means that the economy with the highest growth rate will be Country E and least growth will be Country U.
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