There are a few approaches you'll have to take if you want to get a complete view of the economic history of the Civil War. Unfortunately I don't know of a single volume that looks at all three.

The first in Northern economic ideology, meaning you want to look at free labor ideology. For that check out Eric Foner's Free Soil, Free Labor, Free Men.

The second is southern economic ideology, specifically the ways that Southerners tried to embrace capitalism through their management of slavery. A decent book on the economic side would be Brian Schoen's Fragile Fabric of Union. That book's arguments are passable for this purpose but not that great overall. A better general investigation of slaveholders themselves is James Oakes' The Ruling Race, though it probably has less detail on the economic side specifically.

Lastly, you need to see the effects of the war on the postwar economy, specifically the overall triumph of free labor in the wake of Reconstruction and emancipation. For this a great place to go is again Eric Foner, with his Reconstruction: America's Unfinished Revolution or you can do his smaller Short History of Reconstruction which is basically the same book.

Lastly, if you ever hear Mark Egnal's Clash of Extremes: the Economic Origins of the Civil War mentioned, run away. That book's title sounds like it's exactly what you're looking for but it's also laughably wrong about almost everything. Do NOT go for that book.