<p>Even if it is a very general result, its implications are not immediately intuitive and actually often quite difficult to accept. Why should the impact of an increase in the price for fresh strawberries on the demand for gasoline, be the same as the impact of a price increase for gasoline on the demand for fresh strawberries (while keeping <span class="math-container">$u$</span> constant) ?
One of the more convincing empirical investigation of Slutsky symmetry is experimental and provided in this paper which is also very closely related to the questions your ask:<br>
Sippel, Reinhard, 1997, "An Experiment on the Pure Theory of Consumer's Behaviour," <em>The Economic Journal</em>, 107, 1431-1444. </p>

CC BY-SA 4.0
2020-02-11T23:10:27.267Z
Thank you for the reference. It's a surprising prediction but I'd say that's what you want in science. A theory that only predicts things you already expect isn't a great theory.
UtilityMaximiser
CC BY-SA 4.0
2020-02-09T10:19:05.917Z
2020-02-09T10:35:40.873Z
2020-02-09T10:35:40.873Z
Bertrand
<p>It is a well known fact in consumer theory that for a Hicksian demand curve the cross-price elasticity of good <span class="math-container">$i$</span> with respect to the price of good <span class="math-container">$j$</span> equals the cross-price elasticity of good <span class="math-container">$j$</span> with respect to the price of good <span class="math-container">$i$</span>. This result (iirc) depends only on the utility function being continuous and so has great generality.</p>

<p>Of course, no consumer is actually Hicksian (though firms of course are) but the vast majority of goods take up only a small portion of a person's expenditure and so we expect the income effect to be small, and so the consumer de-facto Hicksian. What is the empirical status of this prediction? Do economists agree with my claim that most consumers are de-facto Hicksians? If the answer to the second question is no, have similar empirical tests been done for firms?</p>

CC BY-SA 4.0
2020-02-09T06:30:06.210Z
"*the vast majority of goods take up only a small portion of a person's expenditure and so we expect the income effect to be small, and so the consumer de-facto Hicksian.*" Wouldn't this imply that the consumer is de-facto Hicksian for the price changes of most goods, but not all? (E.g., not rent.)
Giskard
<consumer-theory>
Empirical tests for symmetry of cross-price elasticities
UtilityMaximiser
# Empirical tests for symmetry of cross-price elasticities

(Asked by: username_0 on 2020-02-09)

It is a well known fact in consumer theory that for a Hicksian demand curve the cross-price elasticity of good $i$ with respect to the price of good $j$ equals the cross-price elasticity of good $j$ with respect to the price of good $i$. This result (iirc) depends only on the utility function being continuous and so has great generality.

Of course, no consumer is actually Hicksian (though firms of course are) but the vast majority of goods take up only a small portion of a person's expenditure and so we expect the income effect to be small, and so the consumer de-facto Hicksian. What is the empirical status of this prediction? Do economists agree with my claim that most consumers are de-facto Hicksians? If the answer to the second question is no, have similar empirical tests been done for firms?

**Tags:** consumer-theory

> **Comments:**
> **username_1**: "*the vast majority of goods take up only a small portion of a person's expenditure and so we expect the income effect to be small, and so the consumer de-facto Hicksian.*" Wouldn't this imply that the consumer is de-facto Hicksian for the price changes of most goods, but not all? (E.g., not rent.)  

---

## 1 answers

### Answer by username_2 on 2020-02-09. Score: 1

Even if it is a very general result, its implications are not immediately intuitive and actually often quite difficult to accept. Why should the impact of an increase in the price for fresh strawberries on the demand for gasoline, be the same as the impact of a price increase for gasoline on the demand for fresh strawberries (while keeping $u$ constant) ?
One of the more convincing empirical investigation of Slutsky symmetry is experimental and provided in this paper which is also very closely related to the questions your ask:  
Sippel, Reinhard, 1997, "An Experiment on the Pure Theory of Consumer's Behaviour," *The Economic Journal*, 107, 1431-1444.

> **Comments:**
> **username_0**: Thank you for the reference. It's a surprising prediction but I'd say that's what you want in science. A theory that only predicts things you already expect isn't a great theory.  

---

