= Solution
In $2+1$ spacetime dimensions, the dimensionless <action> gives $[\mathcal L]=3$ and $[\partial_\mu]=1$. The scalar <kinetic term> requires $2[\phi]+2=3$, whereas the fermion <kinetic term> requires $2[\psi]+1=3$. Thus the <engineering dimensions of relativistic fields> are
$$
[\phi]=\frac12,\qquad[\psi]=[\bar\psi]=1.
$$
Matching each interaction to <mass dimension> three gives
$$
\boxed{[g_1]=3-(2[\phi]+2[\psi])=0,\quad[g_2]=3-4[\phi]=1,\quad[g_3]=3-6[\phi]=0.}
$$
Here the brackets mean exponents of mass in <natural units>. The coefficients $g_1,g_3$ are <marginal couplings> by classical <power counting>, and $g_2$ is a <relevant coupling>.
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