Please Help Me With This Economics Consumer Choice Theory Problem Set?

A family has a yearly income of $30,000 which makes them eligible for $10,000 in food vouchers annually.
1) Illustrate this family’s budget with and without the food vouchers (for simplicity’s sake, assume the price of food as well as all other goods is $1/unit).
2) What needs to be true for the family to be just as well off under this food voucher program as it would be if the government simply sent them $10,000 in cash instead of the food voucher program?
3) Imagine an alternate policy where instead of food vouchers, the government will reimburse 30% of the family’s food expenses. On a separate graph, illustrate the family’s budget constraints with and without this policy.
4) Choose an optimal bundle on this alternate policy budget line and show how much the government is paying to this family (you will need to draw two indifference curves). Call this amount Z.
5) Now suppose the government discontinued this program and instead gives the same amount Z in food vouchers. Add this budget line to your graph. Will this family be happy about the change from the alternate to this new food voucher program?
6) If policymakers seek to increase food consumption by low-income individuals and others want to make low-income individuals happier, will they differ on which policy is best?
7) True or False (illustrate): As the food voucher program becomes more generous, the family will at some point prefer a pure cash check over an equally costly food voucher program.

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