$*6\mathrm{.}3$ A U$.$S$.$ synthetic rubber manufacturer is considerin$$ moving its production to a Japanese plant. Its esti mated production function is $q=10L^{0\mathrm{.}5}{K}^{0\mathrm{.}5}($Flath $2011).$ In the United States, $w=10=r.$ At it: Japanese plant, the firm will pay a $10\%$ lower wag! and a $10\%$ higher cost of capital: $w^{**}\frac{10}{1\mathrm{.}1}$ anc $r^{**}=1\mathrm{.}110=11.$ What are $L$ and $K,$ and wha is the cost of producing $q=100$ units in both coun tries? What would be the cost of production in Japar if the firm had to use the same factor quantities as it the United States? M