Consider the welfare program, created to make sure that needy people get adequate income to buy food. The government is offering nontransferable food vouchers to any individual earning less than $980, paying out FV = 294 0.3Y where Y is the income. People have the utility functions U = 1/3 ln(F) + 2/3 ln(X) where F is food and X is other goods. The prices of food and other goods are both normalized to 1, therefore, the budget constraint is F + X = Y

(A) Consider a world WITHOUT food vouchers. Determine the demands for food and other goods for someone with an income of $300

(B) Consider a world WITH food vouchers. Determine the optimal levels of food and other goods consumption for an individual with earned income of $300.

(C)Show the outcome in (b) with a standard budget constraint/indifference curve graph.

(D) Does the food voucher program entail a loss or gain in efficiency compared to a program that pays the same amount as the food voucher program in cash? If so, then calculate the value of the efficiency loss/gain.