Consumer Choice and Free Goods:

Suppose poor people spend their money on two goods: booze and food. The government doesn't want low-income welfare recipients to spend the money it gives them on booze, so it gives them food stamps to be used only on food. 

a) Using the consumer choice model, illustrate how, paradoxically, giving people food stamps could lead to an increase in booze-buying. (Hint: First draw the budget constraint without food stamps and then with food stamps.)

b) Using the consumer choice model, illustrate how giving a poor person cash instead of food stamps will result in higher utility.