Consider the following production function no technology:

$Y(t)=F(K(t),L(t))=K(t{)}^{}L(t{)}^{1-}$

where $$ is the share of capital in production as is less than $1$

Where $Y$ is output, $K$ is physical capital, and $L$ is labor. Labor grows at a rate of $n$

In addition, physical capital is accumulated from the domestic country at a rate of $s,$ after the country has fulfilled its commitment to send a fraction of its output $()$ to foreign countries as foreign aid, and tax credits have been paid out to firms with the express condition that these credits are used to purchase more capital, enabling firms add YK to capital stock each period. This implies that the resulting change of capital stock over time is

$K^{}=s(1-)F(K(t),L(t))-K(t)+K(t)$

With $k=\frac{K}{L},$

Match the following shocks to the effect on the steady state level of $k$

increase in rate of foreign aid commitment $$

increase in savings rate s

$q,$

increase in population growth rate $n$

$q,$

increase in depreciation rate $$

$[$Choose $]$

change in steady state level of $k$ cannot be determined increase in steady state level of $k$

no saddle path stable steady state level of $k$ can be determined no change in steady state level of $k$ decrease in steady state level of $k$

increase in tax credits causing $$ to increase