Label each of the following statements true, false, or uncertain. Explain briefly.

a. Writing the production function in terms of capital and effective labor implies that as the level of technology increases by \(10 \%\), the number of workers required to achieve the same level of output decreases by \(10 \%\).

b. If the rate of technological progress increases, the investment rate (the ratio of investment to output) must increase to keep capital per effective worker constant.

c. In steady state, output per effective worker grows at the rate of population growth.

d. In steady state, output per worker grows at the rate of technological progress.

e. A higher saving rate implies a higher level of capital per effective worker in the steady state and thus a higher rate of growth of output per effective worker.

f. Even if the potential returns from research and development (R\&D) spending are identical to the potential returns from investing in a new machine, \(R \& D\) spending is much riskier for firms than investing in new machines.

g. The fact that one cannot patent a theorem implies that private firms will not engage in basic research.

h. Because eventually we will know everything, growth will have to come to an end.

i. Technology has not played an important part in Chinese economic growth.