Consider an economy where a fraction f of the unemployed find work every period, and a fraction s of the employed are separated from their jobs every period. Let U denote unemployment, E employment and L the fixed labour force. 

a. Derive an expression for the unemployment rate, u = U/L, in the steady state.

 

b. Compute the unemployment rate when s = 0.01 and f = 0.15.

 

c. Suppose that f increases to 0.20. What happens to the unemployment rate? Interpret your results.