Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low-income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally , a household would consume at least idkg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met Under the government's proposal , the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the households income. Community groups in Autorka have expressed concern that a voucher scheme is unnecessarily paternalistic depriving low-income houscholds of the choice of how to spend their income. These groups argue that the governmerit's consumption targets could be met just as well using transfers (monetary payments from the government to the low-income households). Transfers, they argue would empower low-income households to make their own consumption decisions. Task Your task is to determine the optimal voucher value as a function of household income The voucher must implement the governments target of 10kg of fresh fruit and vegetables consumed per week while minimising the cost of the vouchers to the government. You are also to assess the community groups claim that a transfer scheme would implement the government's targets just as well. Do you think that the community groups are motivated by the health outcomes associated with a good diet? Or might they have another objective Household preferences Using data from household surveys, you have determined that the typicall households preferences are represented by the utility function U=(x 3bly where X represents the quaritity of fruit and vegetables consumed and y represents the quantity of the composite good consumed. The associate marginal utilities are. MAX-yad May-x+3%. The price of fruit and vegetables is px - $12 per kg and the price of the composite good is normalised to Py = 1 QUESTION 1. Suppose that the government decides to implement its target consumption of fruit and vegetables using transfers. How much would the government need to transfer to a household each week to achieve the log consumption target? Hint Your answer will be a function of the households income L. You should assume that transfers camot be negative