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Suppose a firm optimizes the two period profit function: Y-wN+Y*-w*N* /1+r where current labor N, and...

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 sign of the derivative dN/dw (positive/negative/indeterminate)? b) What is the sign of the derivative dN/dz (positive/negative/indeterminate)? c) What is the profit maximizing firt-order condition with respect to future labor N? d). What is the total differential of this first-order condition? e) What is the expression for the derivative dN*/dw* ? f) What is the expression for the derivative dN*/dr? g) 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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