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 5kg of fresh fruit and vegetables each week.

The government has proposed implementing a new voucher scheme to ensure that the 5kg 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 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 their income. These groups argue that the government'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.

Using data from household surveys, you have determined that the 'typical' household's preferences are represented by the utility function,

U = (x + 24)y ,

where x represents the quantity of fruit and vegetables consumed, and y represents the

quantity of the composite good consumed. The associate marginal utilities are, MUx=y and MUy=x+24.

The price of fruit and vegetables is Px = $10 per kg, and the price of the composite good is normalised to Py = 1.

Suppose that, instead of transfers, the government decides to use vouchers re- deemable for fruit and vegetables.

Question: What value of voucher would the government need in order to achieve the 5kg consumption target? Hint: Your answer will be a function of the household's income I. You should assume that vouchers cannot have a negative value.