Suppose a relatively low income family has a monthly budget of $1,000 to allocate between food and a non-food composite good. In this problem, assume food is aggregated into a "composite food" good that is modeled on the horizontal axis, and the non-food composite good is denominated in "dollars of other consumption". The price of food is $10 per unit. Suppose further that this family's tastes exhibit kinks in indifference curves, with one such indifference curve graphed below.


a. Draw the family's budget constraint and label the optimal consumption

bundle.
b. Due to unexpected droughts, the price of food rises to $20. A cash subsidy S that leaves our family with the same level of happiness as it enjoyed prior to the price increase is proposed. How much would this subsidy cost for this family?
c. An alternative proposal suggests a price subsidy s that lowers the price of food for this family from $20 to ($20-s), with s set sufficiently high to allow the family to reach its original utility level.
d. Yet a third proposal suggests a price subsidy that leaves in tact the new price of $20 for the first 20 units of food bought by the family but then lowers the price for this family to $(20-s') while also making the family just as happy as it was before. How high does s' have to be to accomplish this?
e. If cost is all you care about, how would you rank these three policies? What if you care about food consumption for this family and believe a policy is better if it results in more food consumption?

What will be an ideal response?

b. This would change the slope of the budget from -10 to -20 -- which is steeper than the portion of the indifference curve that connects A and B. Bundle A will therefore be the optimum under the cash subsidy -- and the family will need $1,400 to reach A at the new price. Thus, S=$400.



c. For the family to reach its original indifference curve, the price of food would have to go back to $10 for the family -- with B again optimal. Thus, s=10.

d. This is pictured in the last panel -- where the least cost way of reaching the original indifference curve now implies getting the family to bundle C. The slope of the dashed line is -5 -- implying that s'=15.

e. The cash subsidy program costs $400; the straight subsidy costs $500; and the modified subsidy (in part d) is $900. If all you care about is cost, you would prefer the cash subsidy to the straight subsidy to the modified subsidy. If, however, you care about how much food the family eats -- and you think more is better, the preference ordering over the three policies would be reversed.