Lesson preview · Consumer Optimization
Applications
~6 min · Free to read
Consumer optimization isn’t just textbook geometry — it explains why certain policies make people better or worse off. When markets are free, consumers reach their highest feasible indifference curve. But interventions like rationing, taxes, and subsidies can alter the budget set in ways that move consumers to lower indifference curves, even if the policy is well-intentioned.
A striking example came after Hurricane Sandy in 2012. New Jersey and New York imposed gas rationing — odd/even license plate rules limited when you could buy fuel, and some stations set their own 10-gallon limits. Economically, rationing adds a constraint on top of the budget constraint: even if you can afford 20 gallons, a cap may hold you to 10. The consumer can no longer reach the indifference curve they’d freely choose, and may end up on a strictly lower one.
Tip
Rationing vs. Free Markets
Without rationing, the consumer picks the bundle where . With rationing, a maximum quantity constraint may force them to a bundle where . At the rationed bundle, the consumer would prefer to buy more of the rationed good but is not allowed to. The resulting utility loss is called the deadweight loss of rationing.
Another classic application is lump-sum taxes vs. equivalent quantity taxes. A quantity tax on good X raises its price (rotating the budget line inward). An equal-revenue lump-sum tax (a fixed dollar amount) shifts the budget line inward in parallel. It can be shown that the lump-sum tax always leaves the consumer on an indifference curve at least as high as — and usually higher than — the quantity tax that raises the same revenue, because the lump-sum tax doesn’t distort relative prices.
Rationing can never improve the consumer’s outcome if they were already optimizing freely. Adding constraints can only reduce (or at best leave unchanged) the maximum utility attainable.
Check yourself · no marks
After Hurricane Sandy, some stations limited sales to 10 gallons per visit. A consumer who would freely choose 18 gallons is forced to buy only 10. What’s true about their MRS at the rationed bundle?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Worked Example
A consumer optimally buys 15 gallons of gas and spends 85 dollars on other goods (total income 100 dollars, gas at 1 dollar/gallon). The government rations gas to 8 gallons max. (a) What is the consumer forced to do? (b) Why is this worse than the free-market outcome?
Practice · 1 / 4
A quantity tax on good X raises its effective price. How does this change the budget line?
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