Question $1$

For two countries, Kutreman and Senaseman, Kutreman has a capital$-$labour ratio

that is initially twice as big as that of Senaseman, but neither is yet in a steady state.

Both countries have the same production function, $Y=4(KL{)}^{\frac{1}{2}}.$ Kutreman has a $15\%$

saving rate, $7\%$ population growth rate, and $3\%$ depreciation rate. Senaseman has a

$20\%$ saving rate, $10\%$ population growth rate, and $6\%$ depreciation rate, while

Assume there is no technological progress.

$($a$)$ For each country, calculate the capital$-$labour $(k^{*}),$ output per labour $(y^{*})$ and

consumption per labour $(c^{*})$ in the steady state. Does the initial capital$-$labour

ratios affect your results?

$($b$)$ For each country, determine the growth rate of Y and $(\frac{Y}{L})$ in the steady state.

$($c$)$ Calculate the golden rule level of capital$-$labour ratio for each country and

determine whether the countries have too little or too much capital relative to the

steady state.

$($i$)$

Eleternine the number of years it will take Kutreman and Senaseman to increase

their steady state capital stocks to $40$ and $52$ respectively. Assume constant

growth rates of $5\%$ and $7\%$ respectively.