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A firm’s production function is Q(L,K) = K^1/2 + L. The firm faces a price of...

A firm’s production function is Q(L,K) = K^1/2 + L. The firm faces a price of labor, w, and a price of capital services, r.

a. Derive the long-run input demand functions for L and K, assuming an interior solution. If the firm must produce 100 units of output, what must be true of the relative price of labor in terms of capital (i.e. w/r) in order for the firm to use a positive amount of labor? Graphically depict this firm’s expansion path.

b. In general, explain what an expansion path represents and how it compares to an input demand function.

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