Question 8: Matching-Market Clearing. Let the aggregate matching function m(s, v) be given by the Cobb-Douglas function: m(s, v) = sv^1- where parameter belongs to (0, 1). All variables are defined in the previous two questions. Also let = v/s measure the degree of labour-market tightness or congestions effects.

1. Show how probability p and q depend on . Provide a brief economic interpretation.
2. Draw the matching-market clearing diagram in which labour-market tightness equates LFP (or labour supply) with new job creation ("labour demand")
3. Using the "perfect competitive" labour supply/labour demand diagram describe briefly and qualitatively "how" real wages are determined in the matching framework. (Note: this entire question has nothing to do with labour supply, but nonetheless it is possible to think in terms of this framework).