The Giffen Paradox

The attribution is a mess

Alfred Marshall introduced the phenomenon in the third edition of his Principles of Economics (1895):

There are however some exceptions. For instance, as Mr Giffen has pointed out, a rise in the price of bread makes so large a drain on the resources of the poorer labouring families and raises so much the marginal utility of money to them, that they are forced to curtail their consumption of meat and the more expensive farinaceous foods: and, bread being still the cheapest food which they can get and will take, they consume more, and not less of it.

That is the whole of it — one paragraph, no citation, no data. Sir Robert Giffen was a distinguished statistician: head of the statistical department of the Board of Trade, president of the Royal Statistical Society, knighted the same year Marshall's third edition appeared. He was exactly the kind of authority whose name would settle a question. But no one has found the passage.

George Stigler went looking in 1947, in "Notes on the History of the Giffen Paradox", and reported that nothing in Giffen's published writings states the proposition Marshall credits to him. Giffen wrote a great deal about working-class budgets and about the price of bread, and some of it gestures in the vicinity, but the specific claim is not there. The most likely explanation is that Marshall was reporting something Giffen said in conversation or in a lecture, which was normal practice at the time and leaves no record.

The honest position: the phenomenon is named after a man who may never have asserted it in print. This is worth stating plainly, because textbooks have repeated the attribution for over a century without the qualification.

The Irish potato story is probably false

The most commonly repeated illustration — that during the Irish famine of the 1840s the rising price of potatoes caused the poor to eat more potatoes — appears to be wrong on its own terms.

Gerald Dwyer and Cotton Lindsay laid out the case in 1984. The famine was caused by potato blight, which destroyed the crop: there were dramatically fewer potatoes to eat, so consumption fell for reasons that have nothing to do with demand curves. Sherwin Rosen reached a similar conclusion in 1999. Whatever the Irish famine demonstrates, it is not a Giffen good.

The story survives in teaching because it is memorable, which is a good reason to be suspicious of memorable economic anecdotes generally.

Was it ever more than a theoretical curiosity?

For most of the twentieth century, serious economists split into three camps, and the split is worth understanding because it is a general one about how theory and evidence interact.

The possibility is fine, the example is missing. The majority view. Giffen goods are perfectly consistent with utility maximisation — the Slutsky equation permits them and no axiom rules them out — so they belong in the theory, and the absence of examples is an empirical fact about the world rather than a defect in the analysis.

The absence is itself informative. A minority, including some who took the "as if" methodology seriously, argued that a phenomenon with no confirmed instance in a century of looking should be dropped from teaching, whatever its logical status. Textbook space is scarce and students overweight what they are shown.

The search was badly designed. A third view, which Jensen and Miller essentially vindicated, was that nobody had looked in the right place with the right method. Giffen behaviour requires very poor households, a staple with a huge budget share, a real fallback good to give up, and a price change you can attribute cleanly. Historical price series from rich countries satisfy none of those conditions.

What was found before 2008

Two earlier results deserve credit, and neither is a field observation.

Raymond Battalio, John Kagel and Carl Kogut demonstrated a Giffen good in the laboratory in 1991, using rats choosing between quinine-flavoured water and root beer under a budget of lever presses. The design was clean and the upward-sloping demand was real. What it establishes is that the mechanism works in a system with the right structure — not that human markets contain such goods.

Various historical studies claimed to detect upward-sloping demand in price series for bread, potatoes and rice. These were consistently vulnerable to the same objection: in observational data, price and quantity are jointly determined, and a supply shock that raises price while reducing quantity looks nothing like a demand curve. Identification, not economics, was the binding constraint. This is precisely why the randomised subsidy in Jensen and Miller's design was decisive.

1890. Alfred Marshall published the first edition of Principles of Economics. It contains no Giffen passage.

1895. The third edition adds the paragraph quoted above. Marshall attributes the observation to Robert Giffen without a citation. Later editions kept it, and it entered the standard curriculum through Marshall's near-total dominance of English-language economics teaching for the next thirty years.

1915. Eugen Slutsky, working in Kyiv, published the equation that separates the substitution and income effects in "Sulla teoria del bilancio del consumatore" in an Italian journal. The paper was ignored, partly because of the war and partly because of where it appeared.

1934. John Hicks and R. G. D. Allen rediscovered and popularised the decomposition in "A Reconsideration of the Theory of Value". From this point the Giffen good ceased to be a puzzle and became a corner of a general theory: an exception you can locate exactly, on a specific sign condition.

1947. George Stigler published "Notes on the History of the Giffen Paradox" in the Journal of Political Economy, documenting that the attribution to Giffen cannot be traced to Giffen.

1984 and 1999. Dwyer and Lindsay, and later Rosen, dismantled the Irish potato illustration.

1991. Battalio, Kagel and Kogut published the laboratory demonstration in the American Economic Review.

2008. Robert Jensen and Nolan Miller published "Giffen Behavior and Subsistence Consumption" in the American Economic Review, reporting the randomised subsidy experiments in Hunan and Gansu. It remains the standard citation for the claim that Giffen goods exist.

It is the cleanest case of a "law" that is really a strong tendency. The law of demand is not a theorem of consumer theory. It follows from utility maximisation only with an extra assumption — that the good is not too inferior and not too large a share of spending. The Giffen good marks exactly where the assumption bites. Knowing that boundary is more useful than believing the law is unconditional.

It sharpened how economists think about welfare for the poor. The mechanism is not a curiosity about demand curves; it is a statement about how households near subsistence actually make decisions. Jensen and Miller's practical point was this: subsidising a staple can reduce consumption of that staple among the poor, because the subsidy makes them richer and they spend the gain on better food. Whether that is a good or a bad outcome depends on what the programme was for. If the goal is calories, the subsidy may be self-defeating; if the goal is nutrition, it may be working exactly as it should. Either way, designing food policy without the income effect in view will produce surprises.

It is a case study in the cost of a missing counterexample. For 113 years the profession taught a phenomenon with no confirmed instance. That is defensible — the theory permitted it and the theory was right — but it also meant a century of textbook diagrams whose empirical content was unknown. The resolution came from a change in method: a randomised price change in a population selected because theory said the effect should be there. The lesson generalises well beyond Giffen goods.

It is why identification matters. Every pre-2008 attempt failed for the same reason: observational price and quantity data cannot distinguish a demand curve from a supply shock. That the definitive answer came from an experiment rather than from better econometrics on old data is part of why the credibility revolution reshaped empirical economics.

Food policy and subsistence. Staple price shocks in low-income countries — the 2007–08 and 2010–11 food price spikes among them — raise exactly this question: does a rise in the price of the staple reduce staple consumption, or increase it while destroying dietary diversity? The measured answer determines whether a price shock shows up as a calorie crisis or a nutrition crisis, and those call for different responses.

Cash transfers versus in-kind subsidies. The Giffen mechanism is one reason the two are not interchangeable. An in-kind subsidy changes relative prices and therefore triggers substitution; a cash transfer changes income only. Where the income effect on a staple is strongly negative, the two policies move staple consumption in opposite directions.

Behavioural pricing generally. Upward-sloping demand appears in modern markets for reasons that are not Giffen effects and should not be confused with them: Veblen goods, where price signals status; quality signalling, where price is read as evidence of quality in the absence of other information; and speculative assets, where a rising price is read as a forecast of further rises. All three work by changing what the price means to the buyer. A Giffen good involves no such reinterpretation. Preferences are fixed, the good is understood perfectly, and the arithmetic of the budget does all the work. Keeping these apart is the main practical use of the concept today.

The Slutsky decomposition

Let the consumer choose a bundle $x \in \mathbb{R}^n_+$ to maximise $u(x)$ subject to $p \cdot x \le m$. Write $x_i(p,m)$ for the Marshallian demand and $h_i(p,u)$ for the Hicksian (compensated) demand. The Slutsky equation is

$$\frac{\partial x_i(p,m)}{\partial p_i} ;=; \underbrace{\frac{\partial h_i(p,u)}{\partial p_i}}{\text{substitution effect}} ;-; \underbrace{x_i(p,m),\frac{\partial x_i(p,m)}{\partial m}}{\text{income effect}}$$

The substitution term is the own-price derivative of compensated demand. Because the Slutsky matrix is negative semi-definite — a consequence of the weak axiom of revealed preference, not of any further assumption — its diagonal entries satisfy

$$\frac{\partial h_i}{\partial p_i} \le 0$$

So the substitution effect can never be positive. Every Giffen good must therefore get its upward slope entirely from the income term, which requires

$$x_i \frac{\partial x_i}{\partial m} < \frac{\partial h_i}{\partial p_i} \le 0$$

and in particular $\partial x_i / \partial m < 0$: the good is inferior. Inferior is necessary, not sufficient.

The elasticity form

Divide through by $x_i / p_i$ and let $s_i = p_i x_i / m$ be the budget share. Writing $\varepsilon_{ii}$ for the uncompensated own-price elasticity, $\varepsilon^h_{ii}$ for the compensated one, and $\eta_i$ for the income elasticity:

$$\varepsilon_{ii} = \varepsilon^h_{ii} - s_i \eta_i$$

A Giffen good is one with $\varepsilon_{ii} > 0$, which requires

$$s_i,\eta_i < \varepsilon^h_{ii} \le 0 \quad\Longleftrightarrow\quad s_i , |\eta_i| > |\varepsilon^h_{ii}| ;\text{ with }; \eta_i < 0$$

This makes the empirical requirement precise and shows why the search was so hard. The compensated elasticity for a staple food is small in magnitude but not zero — say $|\varepsilon^h_{ii}| \approx 0.1$ to $0.3$. So Giffen behaviour needs the product of budget share and the magnitude of a negative income elasticity to exceed that. With a budget share of 0.5, an income elasticity of about $-0.3$ or steeper would do it. Both numbers are extreme, and they must occur together.

Why the effect vanishes at both ends

Model the household as choosing rice $r$ and a preferred fallback food $f$ subject to a budget $p_r r + p_f f \le m$ and a subsistence calorie constraint $c_r r + c_f f \ge \bar{c}$, with rice the cheaper source of calories ($c_r/p_r > c_f/p_f$), maximising consumption of the preferred food.

When both constraints bind, the solution is

$$r = \frac{m c_f - p_f \bar{c}}{p_r c_f - p_f c_r}, \qquad f = \frac{p_r \bar c - c_r m}{p_r c_f - p_f c_r}$$

Differentiating $r$ with respect to $p_r$ over the region where $f > 0$ gives a positive derivative: rice demand rises with the rice price. The upward slope is not an approximation — it is exact in this model, and it is driven entirely by the calorie constraint forcing a substitution back into rice as the fallback is surrendered.

The behaviour terminates when $f$ hits zero, at the price $p_r^{} = c_r m / \bar c$. Above $p_r^{}$ the calorie constraint can no longer be met, the household spends everything on rice, and $r = m/p_r$ falls hyperbolically. In the worked example, $p_r^{*} = 3600 \times 30 / 14000 \approx 7.71$ yuan per kg, which is where the table above turns over.

At the other end, as $m$ grows the budget constraint stops binding, the calorie floor is met with room to spare, and rice demand behaves normally. Jensen and Miller emphasised this non-monotonicity in poverty as a testable prediction of the theory, and it is the pattern they found: Giffen behaviour among the poor, but not the poorest.

Aggregation

A final constraint worth stating: not everything can be a Giffen good at once. Adding up the budget constraint gives the Engel aggregation condition $\sum_i s_i \eta_i = 1$, so the budget-share-weighted income elasticities must average to one and cannot all be negative. Giffen goods are necessarily a small part of any consumer's spending in the aggregate, however large a share the single good takes.