Question 131193
{{{Q[1] = (10*K^.5)*(L^.5)}}}
{{{Q[2] = (10*K^.6)*(L^.4)}}}
I used subscripts because {{{Q}}} in the 1st equation
will not necessarily equal {{{Q}}} in the 2nd equation
The problem says {{{K}}} is the same in both cases
and {{{L}}} is the same in both cases
How does {{{Q[1]}}} compare with {{{Q[2]}}}?
I will set up the ratio {{{j = Q[1] / Q[2]}}}
{{{j = (10*K^.5)*(L^.5) / (10*K^.6)*(L^.4)}}}
{{{j = (10*K^.5)*(10^(-1))*K^(-.6))*(L^.5)*(L^(-.4))}}}
{{{j = (K^(-.1))*(L^.1)}}}
{{{j = L^.1 / K^.1}}} or
{{{Q[1] / Q[2] =  L^.1 / K^.1}}}
Suppose {{{Q[1] = Q[2]}}}
{{{L^.1 = K^.1}}}
{{{L = K}}}
If {{{L > K}}} then, {{{Q[1] > Q[2]}}}
If {{{K > L}}} then, {{{Q[2] > Q[1]}}}