A.) Suppose the price setting equation is given by P= (1+m)W where m is the markup. The wage-setting equation is given by W =p(z/u) are unemployment benefts and is the unemployment rate.

1. Derive the real wage and unemployment consistent with equilibrium in the labor market in the medium run. Is this the natural rate of unemployment? Does the equilibrium rate of unemployment change if unemployment benefits decrease?

2. Draw the wage-setting and price setting lines on a diagram with u on x-axis and W/P on y-axis. In the diagram, show the change of the natural rate of unemployment if unemployment benefits decrease.

3. Derive the aggregate supply relation. What happens to the AS curve if unemployment benefits decrease? How will the change affect the AS-AD equilibrium? Draw the AS- AD curves.

Suppose that the price setting equation also takes into account the price of energy (another input in production). In particular, P = (1 + m)Wq^1-a where q is the price of one unit of energy. The wage-setting equation is given by W= P(z/u)

1. Derive the real wage and unemployment consistent with equilibrium in the labor market in the medium run. How does the equilibrium unemployment rate change when the price of energy decreases? What is the intuition for this result?

2. Draw the wage-setting and price-setting lines on a diagram with u on x-axis and W/P on y-axis. In the diagram, show the change of the natural rate of unemployment if the price of energy decreases.

3. Derive the aggregate supply relation? What happens to the AS curve if the price of energy decreases? How will the change affect the AS-AD equilibrium? Draw the AS-AD curves