1. Nathaniel has an income of $100 per week, which he spends on medicine and all other goods. Assume his medicine costs $10 for each pill.

   1. Suppose the government agrees to pay half of Nathaniel’s medicine bill, so that his pills effectively cost him only $5 each. As a result, he chooses to buy 80 pills. Graphically show how the government program affects Nathaniel’s budget constraint and show his new optimal consumption bundle (labeled P*).

   2. Suppose the government ends the old program described in part (a) and replaces it with a simpler program: Nathaniel would simply get a cash gift of $40 from the government. Graphically show Nathaniel’s budget constraint under the revised government program. Determine if the new budget constraint goes above, below, or through point P.

   3. Of the two government programs in parts (a) and (b), which would Nathaniel prefer and which is more expensive for the government?