7. Economists like to talk about growth mathematically. The Explore supplement of the previous section introduced a simplified production function of the form:
Output = (Technology coefficient) * (Capital)a * (Labor)1-a
If we divide through by Labor, we get an equation for output per worker, which is productivity:
Output/Labor = (Technology coefficient) * (Capital/Labor)a
According to this equation, what happens to productivity when capital increases? When technology improves? When labor increases? Can you explain the reason for the changed productivity in each case? Can you give real-world examples of each?
8. The story of the Chinese fleet under Admiral Zhang He has been used to illustrate both the technological advancement of the Chinese at the time of European expansion and also the resistance to change of the Chinese government. Find who Zhang He was and how his story illustrates the potential and limitations of the Chinese in the fifteenth and sixteenth centuries.