### Exploring Productivity

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.

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Copyright
Robert Schenk