A typical low-income family has $600 monthly income. They allocate their income between food and other goods. Assume that the price of one unit of other goods is $1 and the price of one unit of food is $6. Each household has usual shaped strictly convex preferences between food and other goods.

The government is planning to provide food support to households with low-income. You have been asked to analyze the following two alternative plans designed for this purpose.

Plan 1. Each family will receive a voucher that can be used to purchase 100 units of food for free. The voucher can only be used to purchase food.

Plan 2. The government will provide a subsidy to low-income families, so that they would only pay $2 per unit of food.

a) Draw the budget constraint for a typical household before the introduction of any government support plan while keeping food on the horizontal axis.

b) Reproduce your diagram from (a) and show how a household's budget constraint changes under Plan 1. Briefly explain your work.

c) Reproduce your diagram from (a) and show how a household's budget constraint changes under Plan 2. Briefly explain your work.

Scenario B: Suppose that a household is offered Plan 2 and it is observed that they consume

150 units of food under that plan.

Reproduce your diagram from part (c) and show this choice on it.

How much is the household spending on food and how much are they

spending on other goods at their optimal bundle under Plan 2?

If this household were offered Plan 1 instead of Plan 2, would they be

better off and would they consume more or less food? Support your answer by doing further diagrammatic work and explanations.