a) Consider an economy that produces electricity by burning coal, discharging sulphur dioxide into the air in the process. Suppose that the government wants one of the firms to reduce its output of sulphur dioxide by 20%, and it is going to choose the firm in the economy that can do so at the lowest cost. The true adjustment cost of each firm in the economy is given by the table below: Firm: Adjustment Cost: 1 200 2 220 3 240 Suppose that the government knows there are three firms in the economy, but it does not know their true adjustment costs. To elicit the true adjustment costs the government employs a mechanism which has the following features: Each firm has to report an adjustment cost. The firm announcing the lowest adjustment cost will be forced to implement the reduction of sulphur dioxide. The firm announcing the lowest adjustment cost is paid the second-lowest cost, and all other firms are paid 12% of the lowest reported cost. Determine whether a firm can ever profit by deviating from truth-telling. Explain your answer. Propose a mechanism that induces each firm to report its adjustment cost truthfully. Explain your scheme from the standpoint of each firm in the economy. b) There are four individuals (1, 2, 3 and 4) and five feasible outcomes (A,B,X,Y and Z). The table below specifies the utility function for each individual: Y A 1 50 1 50 B 2 0 U U2 US UA 5 100 1 -4 1 2 75 z 3 1 1 1 90 Derive the efficient outcomes Derive the weakly efficient outcomes . a) Consider an economy that produces electricity by burning coal, discharging sulphur dioxide into the air in the process. Suppose that the government wants one of the firms to reduce its output of sulphur dioxide by 20%, and it is going to choose the firm in the economy that can do so at the lowest cost. The true adjustment cost of each firm in the economy is given by the table below: Firm: Adjustment Cost: 1 200 2 220 3 240 Suppose that the government knows there are three firms in the economy, but it does not know their true adjustment costs. To elicit the true adjustment costs the government employs a mechanism which has the following features: Each firm has to report an adjustment cost. The firm announcing the lowest adjustment cost will be forced to implement the reduction of sulphur dioxide. The firm announcing the lowest adjustment cost is paid the second-lowest cost, and all other firms are paid 12% of the lowest reported cost. Determine whether a firm can ever profit by deviating from truth-telling. Explain your answer. Propose a mechanism that induces each firm to report its adjustment cost truthfully. Explain your scheme from the standpoint of each firm in the economy. b) There are four individuals (1, 2, 3 and 4) and five feasible outcomes (A,B,X,Y and Z). The table below specifies the utility function for each individual: Y A 1 50 1 50 B 2 0 U U2 US UA 5 100 1 -4 1 2 75 z 3 1 1 1 90 Derive the efficient outcomes Derive the weakly efficient outcomes