The Economy-Wide Wage-Setting (WS) Curve Equation

An economic model defines the wage (w) an employer must offer to ensure an employee does not shirk their duties. The initial relationship is given by the equation: w = τ(b + a^N) + (1 - τ)(w - c) + c + rent. Arrange the following algebraic steps in the correct logical order to solve this equation for w.

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

An economic model for determining the wage (w) that prevents employee shirking starts with the equation: w = τ(b + a^N) + (1 - τ)(w - c) + c + rent. If you algebraically isolate the term τw on one side of the equation, what is the resulting expression on the other side?

An initial equation for the wage (w) needed to prevent shirking is w = τ(b + a^N) + (1 - τ)(w - c) + c + rent. This can be algebraically rearranged to τw = τ(b + a^N + c) + rent. What is the most important economic insight revealed by this specific intermediate step in the derivation?

Evaluating Alternative Formulations of a Wage Model

Deriving the Wage-Setting Relationship

True or False: In the algebraic derivation of the wage-setting equation from the initial condition w = τ(b + a^N) + (1 - τ)(w - c) + c + rent, the simplification process involves the term (1 - τ)c being directly cancelled out by the standalone +c term.

The derivation of the wage-setting equation begins with w = τ(b + a^N) + (1 - τ)(w - c) + c + rent. After several algebraic steps, this can be simplified to an intermediate form where τw is isolated on the left side. The right side of this intermediate equation is τ(b + a^N + ____) + rent. What variable or constant fills the blank inside the parentheses?

Evaluating a Model Modification

Adapting the Wage Derivation for a Special Case