Assumption of sufficient wealth in quasi-linear preferences Whenever we talk about quasi-linear preferences, we assume that the consumer is sufficiently wealthy. As far as I understand is that we need that assumption in order to obtain an interior solution.
But what would the economic intuition behind that premise be? Is it that the consumer would not consume anything of the nonlinear good in case of insufficient wealth?
This depends on the exact preferences, but usually the utility function
$$
U(x,y) = v(x) + y
$$
is such that
$$
\lim_{x \to 0} |MRS(x,y)| = \lim_{x \to 0} \frac{\text{d}v(x)}{\text{d} x} = \infty.
$$
In this case it is the consumption of an additional marginal unit of the nonlinear good $x$ that is infinitely useful compared to the consumption of an additional marginal unit of the linear good $y$. Hence the consumer will consume some units of $x$ before buying any of $y$. If the consumer is not 'wealthy enough', the corner solution will be such that $x &gt; 0$, $y = 0$.