#$4.$ Suppose two equally productive individuals, Tim and George, each have $10$ hours $of$ labor $to$

devote $to$ producing either ice cream $(x)or$ chicken soup $(Y).$ The utility functions are identical and

are given $by$:

$U_i(x_i,Y_i)=U_t=U_g=x_i^{0\mathrm{.}5}{Y}_i^{0\mathrm{.}5},i=t$ and $g$

These guys have $no$ preference $asto$ which items they produce and the production functions for each

good are given $by$:

$x=2L_x,Y=3L_Y$

where $L_x$ and $L_y$ are the total labor hours devoted $to$ the production $of$ each good respectively. Using

this information:

$At$ the competitive equilibrium, what must the price ratio $\frac{P_x}{P_Y}be?$

$-$Given this price ratio, how much ice cream $(x)$ chicken soup $(Y)$ will Tim and George

demand? Hint: Normalize and set the wage rate equal $to$ one $(w=1).$