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As head of the planning commission of Eastern Motors, your job is to determine where to locate a new plant. The only inputs used in your cars are steel and labor and the production function is Cobb-Douglas where $$f(S,L) = S^{0.5} L^{0.5}$$ where $S$ is tons of steel and $L$ is units of labor.

You can locate your plant either in country A or country B. In country A, steel costs 7\$ and labor costs 7\$. In country B, steel costs \$8 and labor costs 6\$. In which country should the company locate its new plant so as to minimize costs per unit of output, minimize the cost of production?

F(L,S) = L^.5 S^.5 MRTS= MP (S)/ MP(L)=Price of steel/price of labour

COUNTRY A
L/S=1 L=S TCost =7L+7S

Country B l/s=8/6 L=4S/3

T cost = 8S+6L

i dont know what to do next?

gul
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  • Are you looking to minimize the production costs or maximize the production output? Not sure what production function means in this context... – gt6989b Mar 20 '17 at 20:18
  • Minimize the cost of production, as in minimize the cost per unit of output, asmentioned in the question – gul Mar 20 '17 at 20:22
  • So would you not compute the minimization functions and conditions in each country and minimize? Can you update teh question with minimization function and conditions you get for every country? – gt6989b Mar 20 '17 at 20:25
  • Welcome to Math.SE! In general, please provide more context to your question (in particular where it comes from - class exercise, book exercise, ...?) and take care of grammar and formatting. Proper formatting will make is easier to read and understand your question. – mlc Mar 21 '17 at 14:58

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