4. Consider the Search and Matching model discussed in class. The matching function is given by M(V, U) = AVI-"U" , where A is a parameter representing the efficiency of the matching process. In your answers below, define any additional notation that you introduce. (a) Write an equation for the expected discounted profits for a firm with a filled job (defining your notation appropriately) and provide an intuition for the expression you obtain. (b) Write an equation for the expected discounted profits for a firm with an unfilled vacancy (defining your notation appropriately) and provide an intuition for the expression you obtain. (c) Use the condition that the expected discounted profits from an unfilled vacancy must be equal to zero, along with the equations obtained in parts (a) and (b), to derive the job creation curve. (d) What does the job creation curve imply about the relationship between wages and the value of the marginal product of labour in this model? Explain the intuition for this result. (e) In a steady state equilibrium with free entry, the expected discounted profits from an unfilled vacancy must be equal to zero. Explain intuitively why this must be the case. (f) The equilibrium in the Search and Matching Model is determined by three equations. The first is the Beveridge Curve, which is given by: 1 = 9 + A01-n (BC) where u represents the unemployment rate, q is the separation rate, and 0 represents labour market tightness. The second is the Wage Curve, which is given by: w= vy+ (1 - ) =( + 9)+ ryAg1-n r+q+ yA01-n (WC) where w is the wage, y is labour productivity, y is the workers' bargaining power, z represents unemployment benefits, and r is the discount factor. The third equation is the Job Creation Curve derived above. Suppose that there is an increase in h, the cost of posting a vacancy. Show graphically how the increase in h would impact the equilibrium unemployment rate in the model. Discuss the intuition