Consider an autarky Specific Factors model with two goods: $x$ and $Y.$ Labor is mobile. $K_x=1$ is specific to industry $x$ and $K_Y=1$ is specific to industry $Y.$ There are $17$ units of labor in the economy. Production functions are as follows:

$Q_x=L_x^{0\mathrm{.}5}{K}_x^{0\mathrm{.}5},Q_Y=4L_Y^{0\mathrm{.}5}{K}_Y^{0\mathrm{.}5}.$

If the utility function is $U=C_x^{}{C}_Y^{1-},$ what is the value of $$ at which $\frac{p_x}{p_Y}=1$ in equilibrium?

$($a$)\frac{1}{17}.$

$($b$)\frac{1}{4}.$

$($c$)\frac{1}{2}.$

$($d$)\frac{3}{4}.$

$($e$)\frac{16}{17}.$