Quasilinear Utility Functions
Is that first claim right? I guess it depends what you mean by an income effect. 

Say your quasi-linear utility form is:
$$U(x,v) = x + \ln(v)$$
Say $P_v = P_x=1$ and so for wealth $w = P_v\cdot v + P_x \cdot x = x + v$. 
If $0&lt;w\leq 1$ the household strictly prefers to buy $v$ to $x$ and buys no $x$ but $w&gt;1$ is then exclusively $x$ is purchased beyond that. So demand for $x$ looks like this:
$$w&lt;1: x^* = 0$$
$$w&lt;1: v^* = w$$
$$w\geq1: x^* = w-1$$
$$w\geq1: v^* = 1$$

So the marginal demand for $x/v$ depends on $w$.