Weak complementarity, path independence, and the intuition of the Willig condition

Weak complementarity is usually invoked for valuing public goods using information on private goods. However, using uncompensated demands requires a second condition, the Willig condition. This paper present an intuitive explanation of the Willig condition and shows that the alternative versions are equivalent to a path-independence condition for line integrals. This condition is fulfilled for compensated demands but not uncompensated demands except in restrictive special cases. It is shown that this is a type of quasi-homotheticity and requires that the income flexibility of quality must equal the income elasticity of the weak complement. The importance and restrictiveness of the Willig condition are shown using three alternative functional forms.