Suppose that Matt's preferences are convex; Matt currently optimally purchases 1 pound of broccoli per month. Suppose that the government would like Matt to increase his consumption of broccoli to at least 2 pounds per month. If the price of one pound of broccoli is $2, and all goods are normal, would an unconditional cash subsidy of $2 per month achieve the government goal?

Question

Suppose that Matt's preferences are convex; Matt currently optimally purchases 1 pound of broccoli per month.  Suppose that the government would like Matt to increase his consumption of broccoli to at least 2 pounds per month.  If the price of one pound of broccoli is $2, and all goods are normal, would an unconditional cash subsidy of $2 per month achieve the government goal?

BlackTom AI · Accepted Answer

We start by restating the problem setup to ensure clarity: Matt has convex preferences, currently buys 1 pound of broccoli per month when the price is $2 per pound. The government wants him to consume at least 2 pounds per month. An unconditional cash subsidy of $2 per month is introduced, and all goods are normal.

Option analysis (single available option):
- Option: 'No. It will not. Even though the cash transfer will make 2 pounds of broccoli affordable, Matt will want to spend the $2 subsidy on other goods as well.'
  First, assess what the $2 subsidy does: it increases Matt’s overall purchasing power from $2 (to buy his current 1 lb at $2) to $4 total expenditure possibility. With broccoli priced at $2 per pound, spending all $4 on broccoli would allow him to buy 2 pounds of broccoli. So the affordability condition to reach 2 pounds is satisfied in a simple budgetary sense.
  However, the key question is whether Matt’s optimal choice, given convex preferences and the fact that all goods are normal, would actually yield at least 2 pounds when his income increases by $2. Because preferences are convex, as income rises, Matt’s demand for goods typically increases, but how it increases depends on his marginal rates of substitution and the relative desirability of broccoli versus other goods. With a cash subsidy, Matt is not forced to allocate the entire subsidy to broccoli; he can allocate some or all of the $2 to other goods if those goods provide additional utility that competes with broccoli.
  Therefore, while the subsidy makes 2 pounds affordable, it does not guarantee that the optimal bundle under the new income will include 2 pounds of broccoli. The decision depends on how much value Matt places on broccoli relative to other goods at the higher income level. This means the subsidy could, in principle, result in less than 2 pounds if Matt reallocates some or all of the extra income to other goods that provide higher marginal utility.
  A further consideration is that the problem states all goods are normal, which implies that as income rises, the quantity of broccoli demanded could increase, decrease, or stay the same depending on relative prices and substitution effects. The unconditional transfer does not impose a minimum consumption requirement on broccoli; it only raises income. Hence, achieving a strict target of at least 2 pounds is not guaranteed by a universal cash subsidy.
  In terms of common economic intuition, this option correctly highlights that cash transfers are not targeted and cannot enforce a quota on a specific good unless the targeted good is the only available option or the transfer is designed with a binding constraint. The statement accurately identifies the possible misalignment between affordability and actual voluntary consumption under convex preferences with normal goods.
  Summary of why this option is plausible: the subsidy increases resources, but due to preference structure and the presence of other normal goods, the optimal choice may not allocate all additional resources to broccoli. Therefore, this option correctly captures the limitation of an unconditional cash subsidy in achieving a specific consumption target.

Why this reasoning matters: it underscores the distinction between affordability (can you buy 2 pounds with the higher income) and the actual choice (would you choose to buy 2 pounds given your preferences at the new income). It also illustrates why a cash subsidy is not a guaranteed mechanism for meeting a fixed consumption goal when preferences allow reallocating income across multiple goods.

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