Q10. Efficiency wages and unemployment. The firm's cost per worker is the direct wage cost plus the turnover cost per worker: + [+ () ] Where is the cost of hiring and training a new worker as a fraction of the wage. The (profit-maximising) firm should (of course) set wages to minimize this total cost.

(a) When the wage is set so that this cost is minimized, the derivative with respect to the wage is zero. Derive this condition. (Hint: Note that according to the chain rule, the derivative of () with respect to is ().)

(b) Assume that we are in a symmetric equilibrium where all firms set the same wage. Solve for the job-finding rate in equilibrium and explain the result.

(c) Set the job finding rate as = (+) and solve for the equilibrium rate of unemployment. What factors affect unemployment and why?

(d) Numerically, what happens to unemployment if doubles? Explain intuitively.

(e) Numerically, what happens to unemployment if s becomes twice as high? Explain intuitively.