An economist is deriving an equation for the wage (w) that a firm must offer to prevent employees from shirking. They begin with the following relationship and attempt to solve for w:
Initial Equation: w = τ(b + a^N) + (1 - τ)(w - c) + c + rent
Below are the steps of their derivation. Which line contains the first algebraic error?
Line 1: w = τ(b + a^N) + w - c - τw + τc + c + rent
Line 2: 0 = τ(b + a^N) - τw + τc + rent
Line 3: τw = τ(b + a^N) + τc + rent
Line 4: w = b + a^N + c + rent
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