In each of the following questions please write the a match with the worker or student first and order matches within a matching by the worker's subscript or student number. 1. Consider the following matching problem with four firms and five workers. The pref- erences are as follows, PA = W1, W5, W4, W3, W2 Pw1 = f4, f2, f1, f3 Pf2 = W1, W3, W5, W2, WA Pw2 = f1, f2, f3, f4 Pf3 = WA, W2, W3, W5, W1 Pw3 = f1, f3, f4, f2 Pf = W5, W3, W2, W1, WA PwA = f4, f2, f1, fa Pus = f4, f2, f3, f1 (a) Write down an unstable matching for this market where all firms are matched. What is the blocking pair? (b) Write down the steps and outcome of the firm-proposing deferred acceptance algorithm. (c) Write down the steps and outcome of the worker-proposing deferred acceptance algorithm. d) What are the worker- and firm-optimal stable matchings? (e) Suppose the worker-proposing deferred acceptance algorithm is run. Does any worker or firm have an incentive to misrepresent true preferences (when everybody else is truthful)