"concentration effect" and peak area are two different things.
Since you are dealing with conductivity, which is concentration dependent, the peak area will be the product of analyte concentration times residence time in the flow cell. If you run at constant volumetric flow rate, the linear velocity will vary inversely with the square of the column diameter, hence residence time will increase with the square of the diameter.
If you run at constant linear velocity (i.e., if you decrease the flow in proportion to the square of the column diameter), then the residence time will stay the same.
Samples get diluted as they pass through the column. This dilution is proportional to the column volume. If the column length stays the same, then volume in the smaller column will decrease with the square of the diameter, and sample concentration will *increase* by that same factor.
Sooooo: If you run at constant volumetric flow and keep column length constant, a narrower column will give you a higher analyte concentration but a smaller residence time, and the peak area should be about the same. If you run at constant linear velocity, the narrower column will increase the peak area roughly in inverse proportion to the square of the diameter.
All of the above assumes that you have the same length and roughly the same plate number on the two columns.
