Equilibrium in the Labor Market Suppose labor demand in the economy is given by…

Equilibrium in the Labor Market
Suppose labor demand in the economy is given by the equation
, labor supply is given by the equation
, and the price level
. Explain the components of both equations. What is the equilibrium condition in the labor market?
(a) Calculate the equilibrium level of the real wage
and the equilibrium quantity of labor
. Show the situation on the labor market graph.
(b) Suppose with the constant labor supply the demand for labor changes and its equation becomes:
. What would be the new value of the equilibrium level of the real wage and of the equilibrium quantity of labor. Show the change on your graph from point (a).
(c) Suppose now that labor demand is unchanged, but there is the ehange in the labor supply, which equation becomes:
. What would be the new value of the equilibrium level of the real wage and of the equilibrium quantity of labor. Redraw the graph from point (a) and show this change.
(d) Now suppose that in the initial situation the price level has fallen by
. Calculate the new equilibrium level of the real wage and the equilibrium quantity of labor. Redraw the graph from point (a) and show the change.
(c) Describe what will happen in the long run. Show the changes on your graph from point (d).
(f) Suppose the production function for this economy is
, where
and
. Calculate the short-run and the long-run levels of output.
(g) Derive the long-run aggregate supply (LRAS) curve and the short-run aggregate supply (SRAS) curve graphically, using the production function graph, the labor market graph from point (c), and the
graph, putting figures from your calculations.