What if White declines the Volga Gambit? rnbq1rk1/p3ppbp/3p1np1/1ppP4/2P2B2/2N2N1P/PP2PPP1/R2QKB1R b KQ - 0 8


In the above position, Black gets a solid initiative and easy play on the weak White queenside pawns after 1.cxb5 (1. Nxb5? Ne4!).

But White can decline with 1.e3, intending 2.Be2, 3.O-O. Should Black respond with 1...Nbd7, waiting for White to take the pawn?
The position you've shown looks at first glance to be a poor side-line of the Benko (Volga) gambit for white, both the timing of h3 and Nc3 seem out of place. For instance let's reach that position (somewhat sensibly) by the following line: (annotated)

 [title "A path to OP's Benko gambit sideline"]
 [fen ""]
 1.d4 Nf6 2.c4 c5 3.d5 b5 4.Nf3 g6 5.Bf4 Bg7 6.h3 {h3 is well unnecessary here, in Benko the c8 bishop doesn't target the g4 square anyway, and if the f6 knight wants to re-route to e5 it doesn't have to go via g4, but d7. Thus, h3 is a waste of a tempo when white is already behind in development} (6.Nbd2 O-O 7.e4 {is much more to the point if you don't want to accept the gambit}) (6.e3 {yet another possibility, Nbd2 Be2 O-O are in queue unless black does something active} d6 {black cannot allow d6}) d6 7.Nc3 O-O 8.e3 {this is your suggestion: it doesn't really work here as you c3 knight is misplaced if you don't want to accept the gambit, now b4 comes with a tempo and your knight will end up either on the rim or hindering your own pieces} (8.Nxb5 {seems to be the most sensible choice, not damaging your pawn structure and not offering black to play a6 getting rid of its weak pawn and activating the bishop via a6-f1 diagonal.} Ne4 9.Nd2 {Not giving black chance to take on b2} Qa5 {pinning the knight and preventing Nc3 and preparing to take on b2 again} 10.Qc2 {sure visually it doesn't look great for white, but we're holding for the moment.}) (8.cxb5 a6 {accepts the gambit again but allows for the usual follow-up with a6-bxa6-Qb6 etc}) b4 {when the knight is on d2, b4 is less dangerous because you'll still be able to challenge it with a3 in time} 9.Ne2 Ne4 {g7 bishop alone is dominating the position, white lacks in development and dark square control, without any real other compensation to speak of} 10.Nd2 Nxd2 11.Qxd2 a5 {I think at this point black's advantage is quite clear.}


To conclude the above analysis in short key takeaways:


This is generally not a desirable Benko line for white. 6.h3 seems well out of place, white should be pushing to complete development (so that you can quickly start challenging black's queen-side or creating play in the center, none of which is possible with your king still on e1.)
7.Nc3 is not the way to go if you don't want to accept the gambit, you're allowing b4 without any repercussions for black, and your knight will be mis-placed. 7.Nbd2 is a much better try. If you want to stick to 7.Nc3 then it's best to start considering accepting the gambit, either 8.Nxb5 or 8.cxb5 each with their own merit and far more playable than 8.e3.
After 8.e3 b4 white is objectively behind: the knights seem out of coordination, the bishop on f4 is staring at a wall, there are no clear pawn breaks for white, the queen-side is permanently weak and there are no quick ways of creating counter-play on the king-side as we're far behind in any attempt to challenge the g7 bishop (Qd2-Bf4 battery is not possible with e3, nor is there any re-routing for the bishop to return to d4-g7 diagonal). This also answers your main question: Black should not respond by Nbd7 after 8.e3, instead 8...b4 is the main move to consider, exploiting the mis-placed c3 knight while increasing your grip on the dark squares, leaving no real ways for white to challenge the g7 bishop (note b4 is also stopping any future attempts at Bd2-Bc3)
Small recommendation (for the white side): avoid the Bf4 side-lines, none of them are really interesting for white, in fact in many of the Benko variations the bishop belongs to its original c1 square for a long time as b2 is continuously under pressure. Instead consider the 5.Qc2 variation if you don't want to accept the gambit, which can roughly go as follows: 5.Qc2 Bg7 6.e4 d6 7.Be2 O-O 8.O-O. I think after going through some of the possible side-lines of this variation, you can convince yourself that this is a much more sound continuation for white. Alternatively, accepting the gambit is known to yield the best play for white, namely lines such as 5.cxb5 a6 6.bxa6 Bxa6 7.Nc3 (black does have a different kind of compensation now, but by accepting the gambit we've prevented b4 altogether and revived chances to challenge the dark-squares) 7...Bg7 and many ways for white to continue.


Welcome to ask additional questions, either regarding the analysis or more related to the black side of the Benko gambit.