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2. Suppose a firm optimizes the two period profit function: Y - wN + [(Y'-w'N')/(1+r)] where...

2. Suppose a firm optimizes the two period profit function: Y - wN + [(Y'-w'N')/(1+r)] where current labor N, and future labor N’ are the only inputs. The production function in the current period is Y = zF(N) The production function in the future period is Y’ = z’F(N’) a) What is the profit maximizing first-order condition with respect to current labor N? b) What is the total differential of this first-order condition? c) What is the expression for the derivative dN / dw? d) What is the expression for the derivative dN / dz? e) What is the sign of the derivative dN / dw (positive/negative/indeterminate)? f) What is the sign of the derivative dN / dz (positive/negative/indeterminate)?

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