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A  firm’s production function is Q = K^0.5L^0.5. The prices of the applied inputs are pK =...

A  firm’s production function is Q = K^0.5L^0.5. The prices of the applied inputs are pK = $2, pL = $2. The firm would like to know the maximum output that can be produced for $8,000. Find the combination of inputs that maximizes output for a cost of $8,000, the amount of output that can be produced, and identify the expansion path.
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Answer #1

expansion path is the locus of the tangency point of the isoquant curve and the iso cost curve.

Expansion path equation can be written as : K = w/r × L

In this case w = r hence, w/r = 1

Therefore, L = K

Which mean , if prices of two factors of production are the same , in the given Cobb Douglas production function then equal qualities of factors will be used .

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