Suppose the aggregate demand curve for nurses in an island city is Nd = 300 - 5w, where w is the hourly wage rate for nurses and Nd is the number of nurses demanded in this city. The supply of nurses is NS = 5W - 100, where NS is the number of nurses supplied to the market. In addition, the city government publicly announces that the city needs to hire 125 nurses in order to provide good-quality hospital care to its citizens. Meanwhile, the city government regulates the wage rate for nurses at w = 30. Answer the following questions: a. Use both economic and need-based approaches to calculate the nursing shortage under the current regulated wage rate. Do these two approaches yield the same estimates on the number of nursing shortage? b. If the city government decides to recruit nurses from overseas and this policy shifts the supply of nurse to NS' = 5w - 50, does this policy solve the problem of a nursing shortage or just mitigate the extent of nursing shortage? Does your answer differ according to different definitions of "shortage"? Explain your answer. c. If the city government further announces raising the wage rate for nurses from 30 to 40 and the policy that allows recruiting nurses from overseas remains valid, does the city government solve the problem of nursing shortage or create a new problem? Does your answer differ according to different definitions of "shortage"? Explain your answer.