Deriving the Wage-Setting Relationship
An economic model establishes the wage (w) a firm must pay to prevent workers from shirking, based on the following equation, where τ is the expected duration of unemployment, b is the unemployment benefit, a^N is the utility of the marginal worker, c is the cost of effort, and rent is the employment rent:
w = τ(b + a^N) + (1 - τ)(w - c) + c + rent
Show the algebraic steps required to rearrange this initial equation into the intermediate form:
τw = τ(b + a^N + c) + rent
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Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.6 The firm and its employees - The Economy 2.0 Microeconomics @ CORE Econ
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Related
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 forw.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 forw:Initial Equation:
w = τ(b + a^N) + (1 - τ)(w - c) + c + rentBelow 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 + rentLine 2:0 = τ(b + a^N) - τw + τc + rentLine 3:τw = τ(b + a^N) + τc + rentLine 4:w = b + a^N + c + rentAn 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 termτwon 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 isw = τ(b + a^N) + (1 - τ)(w - c) + c + rent. This can be algebraically rearranged toτw = 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)cbeing directly cancelled out by the standalone+cterm.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 whereτwis isolated on the left side. The right side of this intermediate equation isτ(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