1. If x; and x2 are both “bads,” will the tangency condition of -p1/p2 = MR5 lead to an Optimal
consumptive level of goods x1 and x2? Show on a diagram and explain.
2. Governments often have programs to help the poor. A common way of doing this is for the
government to subsidize the purchase of specific goods. Some economists have suggested that
a better way would be to take the money that is spent on the subsidy and just give it as a grant
to each affected (poor) person, though this approach usually has little political support.
Assume that both x1 and x2 are normal superior goods. Let x; be the subsidized good under the
government program and x2 is the Numeraire. Graph the initial situation before the subsidy
(using prices p1 and p2) and then show how the subsidy on the purchase of x1 affects the optimal
consumption of x1 and x2. Now, suppose that the same amount of money as was spent on the
subsidy is just given to the poor people instead of the subsidy. Show how that affects the
optimal consumption of x; and x; (in comparison to both the subsidy and the initial situation
where the government was not involved). Which of these methods to assist the poor make
them the best off? [Hintz this is very similar to the situations described in section 5.6 of your
textbook: you can think of a subsidy as a “negative quantity tax,” and the money grant as a
negative income tax.”]
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