Algebraic Proof of the Positive Wage-Employment Relationship
By differentiating the steady-state employment equation with respect to the wage (), the derivative of employment is: Since the weekly matches (), the quit rate (), and the derivative of the acceptance probability () are all positive, the derivative of employment is positive (). This algebraically confirms that the steady-state employment level () is an increasing function of the wage (), which equivalently implies that the wage () is an increasing function of employment ().
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Learn After
In a model where the steady-state employment level (N) is determined by the wage (w), the number of weekly matches (m), and the quit rate (q), the conclusion that employment is an increasing function of the wage relies on key assumptions. Suppose a peculiar market condition arises where offering a higher wage unexpectedly decreases the probability that a worker accepts a job offer. All other factors, such as positive match and quit rates, remain unchanged. What is the logical implication of this specific condition for the wage-employment relationship?
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In the algebraic proof demonstrating the relationship between wage (w) and the steady-state employment level (N), the conclusion that dN/dw > 0 holds true as long as the probability of a worker accepting a job offer increases with the wage, even if the quit rate (q) were zero.
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