c)
When workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before, the break-even investment remains unchanged. The actual investment is increased since:
\(f(k)=k^\alpha=(\frac{K}{AL})^\alpha\) , an increase in \(\frac{K}{AL}\) means an increase in \(f(k)\). It also increase actual investment since it equals \(sf(k)\).
The balanced growth path level of capital goes from \(k^\star_1\) to \(k^\star_2\).