The government of the island nation of Autarka has become increasingly concerned aboutthe health and wellbeing of low income households. Medical experts stress the importanceof a healthy diet in this regard. They have determined that, ideally, a household wouldconsume at least 5kg of fresh fruit and vegetables each week.The government has proposed implementing a new voucher scheme to ensure that the5kg per week consumption target is met. Under the government’s proposal, the voucherswould be redeemable for fresh fruit and vegetables, but could not be used for other typesof 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 household’s income.Community groups in Autarka have expressed concern that a voucher scheme is unnec-essarily paternalistic; depriving low income households of the choice of how to spend theirincome. These groups argue that the government’s consumption targets could be metjust as well using transfers (monetary payments from the government to the low incomehouseholds). Transfers, they argue, would empower low income households to make theirown consumption decisions. Your task is to determine the optimal voucher value as a function of household income.The voucher must implement the government’s target of 5kg of fresh fruit and vegetablesconsumed per week, while minimising the cost of the vouchers to the government. Youare also to assess the community groups’ claim that a transfer scheme would implementthe government’s targets just as well.Do you think that the community groups aremotivated by the health outcomes associated with a good diet? Or might they haveanother objective? Using data from household surveys, you have determined that the ‘typical’ household’spreferences are represented by the utility function,U= (x+ 24)y ,wherexrepresents the quantity of fruit and vegetables consumed, andyrepresents thequantity of the composite good consumed. The associate marginal utilities are,MUx=yandMUy=x+ 24.The price of fruit and vegetables isPx= $10 per kg, and the price of the composite goodis normalised toPy= 1. Suppose that, instead of transfers, the government decides to use vouchers re-deemable for fruit and vegetables. What value of voucher would the government need inorder to achieve the 5kg consumption target? Hint: Your answer will be a function of thehousehold’s incomeI. You should assume that vouchers cannot have a negative value.
The government of the island nation of Autarka has become increasingly concerned aboutthe health and wellbeing of low income households. Medical experts stress the importanceof a healthy diet in this regard. They have determined that, ideally, a household wouldconsume at least 5kg of fresh fruit and vegetables each week.The government has proposed implementing a new voucher scheme to ensure that the5kg per week consumption target is met. Under the government’s proposal, the voucherswould be redeemable for fresh fruit and vegetables, but could not be used for other typesof 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 household’s income.Community groups in Autarka have expressed concern that a voucher scheme is unnec-essarily paternalistic; depriving low income households of the choice of how to spend theirincome. These groups argue that the government’s consumption targets could be metjust as well using transfers (monetary payments from the government to the low incomehouseholds). Transfers, they argue, would empower low income households to make theirown consumption decisions.
Your task is to determine the optimal voucher value as a function of household income.The voucher must implement the government’s target of 5kg of fresh fruit and vegetablesconsumed per week, while minimising the cost of the vouchers to the government. Youare also to assess the community groups’ claim that a transfer scheme would implementthe government’s targets just as well.Do you think that the community groups aremotivated by the health outcomes associated with a good diet? Or might they haveanother objective?
Using data from household surveys, you have determined that the ‘typical’ household’spreferences are represented by the utility function,U= (x+ 24)y ,wherexrepresents the quantity of fruit and vegetables consumed, andyrepresents thequantity of the composite good consumed. The associate
Suppose that, instead of transfers, the government decides to use vouchers re-deemable for fruit and vegetables. What value of voucher would the government need inorder to achieve the 5kg consumption target? Hint: Your answer will be a function of thehousehold’s incomeI. You should assume that vouchers cannot have a negative value.
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