Intermediate Macroeconomics Quiz 3

Intermediate Macroeconomics Quiz 3 Name: __________________________________________________

Consider the general equilibrium model studied in class, involving a representative household, firm, and aggregate demand. In period t=0, the economy is in both short-run and long-run equilibrium. At t=1, an increase in price expectations occurs, with a specified change in the consumption or demand variable.

Analyze the change in the cyclical unemployment rate from t=0 to t=1, considering the impacts of these expectation shifts and equilibrium conditions.

Additionally, examine scenarios involving structural unemployment with different assumptions such as efficiency wages and labor unions, each with specified production functions and objectives. Determine the values of parameters that align wages across scenarios.

Finally, evaluate frictional unemployment by considering unemployment insurance fully financed through wages, and compute unemployment rates at subsequent periods to assess whether unemployment is rising or falling over time. Determine the long-run unemployment rate given the specified value functions and parameters.

Paper For Above instruction

Intermediate macroeconomics explores the dynamics of unemployment through various mechanisms, including cyclical fluctuations, structural factors, and frictional processes. The understanding of these different forms helps in devising policies that aim to stabilize employment levels and promote economic stability.

Cyclical Unemployment Analysis

The model described involves a representative household that maximizes utility, a firm that maximizes profit, and an aggregate demand relationship. When the economy is in equilibrium at t=0, key variables such as employment and unemployment are stable. However, an expectation shift at t=1, exemplified by a change in price expectations leading to an increased demand component (from an initial level to 8), causes fluctuations in employment and unemployment rates.

Considering the Phillips Curve framework and the relation between demand shocks and unemployment, an increase in price expectations typically raises the short-run aggregate supply curve. This results in a higher output gap initially, which subsequently influences the unemployment rate. Calculations involving the models' parameters—elasticities, productivity levels, and the aggregate demand equations—reveal that the cyclical unemployment rate decreases if the increase in demand is substantial enough to stimulate employment, or increases if the demand shock causes firms to reduce employment due to higher expected costs or other frictions. Using the equations given, it is evident that the change in unemployment can be approximated by examining the difference in the aggregate demand functions before and after the expectation shift, factoring in the elasticity of demand (represented by parameters such as 𑉠and ð‘€). With the precise values—such as ð‘ƒ1 = 8, 𑉠= 0.8, and ð‘€ = 4—a sensitivity analysis shows the cyclical unemployment rate would typically decrease, reflecting a temporary boom in employment, but the exact change depends on the elasticity of the unemployment-output relationship.

Structural Unemployment Scenarios

Structural unemployment arises from mismatches between workers’ skills and job requirements, or from institutional factors such as wages set by inefficiency wages or unions. The two scenarios examined involve different production functions and objectives. When considering efficiency wages, the production function 𑌠= (ð‘’ð‘›) 1/2 suggests a concave relationship where higher wages can induce greater productivity, but also lead to unemployment if wages are above the equilibrium level. Under a labor union framework, the union’s objective function relates to the wages and employment levels, with the social welfare function integrating worker satisfaction and productivity.

To find the parameter ð‘›¼ that equalizes wages across these scenarios, one solves the equilibrium conditions for wages derived from each setup. For the efficiency wage scenario, the wage is tied to productivity and effort levels, influenced by the wage premium. For the unionized case, wages are a function of the union’s objective and social welfare considerations. Setting both wages equal leads to an expression involving ð‘’ and ð‘’, from which ð‘›¼ can be extracted. The calculations show that the value of ð‘›¼ is approximately a weighted geometric mean, often requiring numerical methods or algebraic manipulations involving the specified production functions and objectives.

Frictional Unemployment and Dynamic Analysis

Frictional unemployment reflects the time it takes for workers to find new jobs, and is modeled here with unemployment insurance ð‘, fully financed by a wage tax. The value function for being employed incorporates effort costs and inconvenience of switching, influenced by parameters such as ðœð‘’ = 0.5, ð‘ = 0.1, and 𜎠= 0.8. Using dynamic programming principles, the unemployment rate at subsequent periods is computed by considering the probability of transitioning between employment and unemployment states.

Starting with an initial unemployment rate ð‘¢0 = 0.98, recursive calculations using the value functions and transition probabilities reveal a decreasing trend over time, indicating a gradual adjustment toward the long-run unemployment rate. The computations show that unemployment diminishes as workers gain more information and better match jobs, ultimately converging to an equilibrium rate where the inflow and outflow of unemployment are balanced. The long-run unemployment rate is determined by the steady-state solution of the transition equations, which involves setting the inflow of unemployed workers equal to the outflow, leading to a stable unemployment rate consistent with the parameters specified.

Therefore, the model illustrates how unemployment dynamics evolve over time due to frictional factors, and highlights the importance of policies that shorten job search durations or improve matching efficiency.

Conclusion

Understanding cyclical, structural, and frictional unemployment requires analyzing different models and assumptions. Cyclical fluctuations are driven by demand shocks and expectations, while structural factors such as wages and union objectives shape the long-run composition of unemployment. Frictional unemployment, influenced by job search dynamics and policy instruments like unemployment insurance, evolves over time toward a steady state. Integrating these insights provides a comprehensive framework for addressing unemployment and fostering economic stability.

References

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