Sign of income effect is ambiguous When discussing the standard neoclassical model of labor supply, I have seen it is assumed that the sign of the income effect is ambiguous. Could anyone please explain this assumption, and more generally, how to think about the substitution effect and the income effect in this model?

Kind regards.
Welcome to SE.

The two goods that the consumer consumes in this model are leisure and consumption. If the agent works more, he can consume more, but he has to give up leisure. Similarly, if he undertakes more leisure, he must consume less. All this assumes the wage rate is unchanged.

However, consider an increase in the wage rate. The opportunity cost of lying in the sun (leisure) has increased, as the agent could have worked instead, earned a higher wage as compared to before, and consumed more. Thus, the relative price of leisure has gone up, and the agent substitutes towards consumption, and this is the substitution effect.

Consider the income effect now. A standard model would assume that consumption and leisure are both normal goods, that is, as your wealth increases, you have more of both. At the current optimum point, as the wage has increased, your wealth has increased, and thus you undertake more leisure and also consume more. This is the income effect.

So, what I think you were asking was more about the total effect on working hours, that is, the cumulative result of both the substitution and income effects on the number of hours worked. Because in this example, the substitution effect pushes leisure up and the income effect pushes leisure down, the total effect is indeed ambiguous.

However, just in case you were actually asking about the income effect per se, the ambiguity may be due to letting go of the normality assumption. If leisure isn't normal, but is inferior instead, then the income effect pushes leisure downwards. Here, the total effect isn't ambiguous however, as the total number of hours worked unambiguously increases.