As head of the planning division of Eastern Motors, your job is to determine whe

Question

As head of the planning division 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^0.5L^0.5
where S is the tons of steel and L is the units of labor. You can locate your plant
either in country A or in country B. In country A, steel costs $7 a ton and labor
costs $7 per unit. In country B, steel costs $8 a ton and labor costs $6 per unit. In
which country should the company locate its new plant so as to minimize costs per
unit of output

Explanation / Answer

let us first solve MPS/MPL which is the derivative with respect to s/derivative with respect to s (.5s^-.5l^.5)/(.5s^.5l^-.5) =L/S now that we know our outcome, we can plug our numbers in for country A and B and see which yeilds higher returns. Country A 7/7=1 Country B 6/8=3/4 We can now see the higher returns and lower cost per unit is in country A. Hope this helps

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