Consider the following welfare program, designed to ensure that needy people get adequate income to buy food. The government offers cash assistance to any worker earning more than $100 and less than $980, according to the following schedule:

Income Cash …………… Assistance Received

$100 ………………………………. $264

$200 ………………………………. $234

$300 ………………………………. $204

$400 ………………………………. $174

$500 ………………………………. $144

$600 ………………………………. $114

$700 ………………………………. $84

$800 ………………………………. $54

$900 ………………………………. $24

$980 ..………………………………. $0

There are two types of consumption goods, food (F) and “other” goods (X), and people have utility functions

U = 1/3ln(F) + 2/3ln(X)

over these goods. The prices of food and other goods are both normalized to 1; therefore, the budget constraint is

F + X = Y

a. Determine the optimal levels of food and other-good consumption for an individual with earned income of $300.

b. Now consider replacing the cash-welfare program with a food stamps program. Instead of receiving the cash amount indicated in the table above, workers would receive an equal amount of stamps that they could spend only on food. Determine the optimum level of food and other-good consumption for the individual with $300 in earned income. Does this make the individual better or worse off than the cash welfare system?

c. Repeat 17a and 17b for an earned income of $900 and explain any differences in outcomes.