This seems like a homework question, so I'll just give hints.

By definition, a quasilinear utility has the form $u(x, y) = x + v(y)$ where $y$ is a vector of all other goods and $v(\cdot)$ is strictly concave. In this case, $x$ is called the numeraire.

• From utility maximization, what's the first order condition that relates $MU_x$, $MU_y$, $p_x$, and $p_y$? Write down the equation.
• What's the utility gain from consuming one more unit of $x$?

You should be able to work things out from there.

This seems like a homework question, so I'll just give hints.

By definition, a quasilinear utility has the form $u(x, y) = x + v(y)$ where $y$ is a vector of all other goods and $v(\cdot)$ is strictly concave. In this case, $x$ is called the numeraire.

• From utility maximization, what's the first order condition that relates $MU_x$, $MU_y$, $p_x$, and $p_y$? Write down the equation.
• What's the utility gain from consuming one more unit of $x$?

You should be able to work things out from there.

Edit

$MU_x$ will be constant... more precisely, $MU_x$ is always one (by definition).

You can then plug this into FOC and get that $MU_y = 1/z$. where $z = p_x/p_y$ is simply how many $y$'s you could buy with "additional amount of wealth equal to the cost of one unit of good 1 on all other goods".

Since one more unit of good $y$ will get you $1/z$, you need (approximately) $z$ more of good $y$ to get one more unit of utility increase (which is the same as what you get when you increase $x$ by one unit).