4. The country of Androde is currently using Method 1 for its production function. By chance, scientists stumble onto a technological breakthrough that will enhance Androde’s productivity. This technological breakthrough is reflected in another production function, Method 2. The accompanying table shows combinations of physical capital per worker and output per worker for both methods, assuming that human capital per worker is fixed.
| Method 1 | Method 2 | ||
| Physical capital per worker | Real GDP per worker | Physical capital per worker | Real GDP per worker |
| 0 | 0.00 | 0 | 0.00 |
| 50 | 35.36 | 50 | 70.71 |
| 100 | 50.00 | 100 | 100.00 |
| 150 | 61.24 | 150 | 122.47 |
| 200 | 70.71 | 200 | 141.42 |
| 250 | 79.06 | 250 | 158.11 |
| 300 | 86.60 | 300 | 173.21 |
| 350 | 93.54 | 350 | 187.08 |
| 400 | 100.00 | 400 | 200.00 |
| 450 | 106.07 | 450 | 212.13 |
| 500 | 111.80 | 500 | 223.61 |
Using the data in the accompanying table, draw the two production functions in one diagram. Androde’s current amount of physical capital per worker is 100. In your figure, label that point A.
Starting from point A, over a period of 70 years, the amount of physical capital per worker in Androde rises to 400. Assuming Androde still uses Method 1, in your diagram, label the resulting point of production B. Using the Rule of 70, calculate by how many percent per year output per worker has grown.
Now assume that, starting from point A, over the same period of 70 years, the amount of physical capital per worker in Androde rises to 400, but that during that time period, Androde switches to Method 2. In your diagram, label the resulting point of production C. Using the Rule of 70, calculate by how many percent per year output per worker has grown now.
As the economy of Androde moves from point A to point C, what share of the annual productivity growth is due to higher total factor productivity?