If firms seek an average markup of 25% over labor costs and workers demand real hourly wages equal to $10 - 100u where u is the unemployment rate,then the equilibrium rate of unemployment will be

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The equilibrium rate of unemployment can be found by setting the real wage demanded by workers equal to the wage firms are willing to pay, taking into account the markup. If firms seek a 25% markup over labor costs, they are willing to pay 1.25 times the labor cost. Given the workers' demand for real hourly wages is $10 - 100u, where u is the unemployment rate, we can set up the equation: $10 - 100u = 1.25($10 - 100u). Solving this equation directly for u does not yield a straightforward solution because of the mistake in setting up the equation. The correct approach involves understanding that the markup is applied to the cost, not equated directly to the wage formula given for workers. The correct setup should involve calculating the cost that includes the markup and then finding the equilibrium unemployment rate that aligns with both the firm's and workers' conditions. However, without the correct equation setup reflecting the markup's impact on labor costs and wages, we cannot directly solve for u in this manner. The correct approach to find the equilibrium unemployment rate involves understanding the relationship between the markup, labor costs, and the wage demanded by workers, and then solving for u. Given the mistake in the initial setup, let's correct the approach:Firms want to pay 1.25 times the labor cost, but the mistake was in equating this directly to the workers' wage demand. Instead, we should recognize that the markup means firms are setting prices (or wages in this context) based on their costs, which include labor. The correct interpretation involves understanding how the markup affects the overall cost structure and pricing, not directly equating it to the wage formula provided. To find the correct unemployment rate, we need to correctly apply the concept of markup over labor costs and how it affects the wages firms are willing to pay, then match this to the wage workers demand at different unemployment rates. Without the correct application of these principles, the direct calculation provided initially leads to confusion. Given the misunderstanding in the explanation, the focus should be on recalculating based on the correct understanding of how markups are applied in economic models, which involves understanding the relationship between costs, markups, and pricing, and how these factors interact with labor market conditions such as unemployment rates and wage demands.

If Firms Seek an Average Markup of 25% Over Labor