Since nothing of this scope or sophistication has been developed, only educated guesses, regarding costs, are possible at this incipient stage.

So to precisely reduce the unknown variables we will employ 4 smaller scaled test barrels before commiting ourselves to the full build model.

The greatest Costs are not likely to come from the SpaceGUN barells, but rather the Solar Arrays that power them, as a great deal of power will be neccessary to keep them operational.
The largest fully operational Solar Array System which encompassed just (1) sqkm cost $1.8 Billion, though cost of solar cell manufacture has dropped since, and continues on a steady decline which combined with alternative technologies being applied routinely and our own novel system (yet to be announced) we expect this cost to drop to less than 1/10th of the aforementioned Solar Array, at the very least.

These preliminary test models will be budgeted at $800 Million :
And alloting 1.5 years for this R&D

*        50 meter Aerial Micro Launcher with tube diameter of 5 cm's or less

*        150 meter Suborbital Micro Launcher with tube diameter of 10 cm's or less

*        350 meter Suborbital Launcher with tube diameter of 20 cm's or less

*        1000 meter Orbital Launcher with tube diameter of 30 cm's or less

*        250,000-1,000,000 square meters of 20% efficieny solar panels
producing at least 300 Mwh's DAILY, theoretically sufficient for delivering 33,000 KG's into LEO....we expect electric efficiency of 25% for the Gun...so realistically about 8,250 KG's

*        5-10 Supercomputers to assist in the study of materials, electromagnetic phenomena, aeronautics, astronautics, and barrel design.

A preliminary budget for the final, mountain-bound SpaceGun
...is set at $1 Billion....

The 2 Kilometer Barrel Shouldn't Cost more than $250,000,000
it is the full Solar Array (25 SqKm's) that represents the bulk of the cost....so we will build up as much as we can, based on the best pricepoint at that time, minus a modest 4 year operations budget for essential personnel...once the SpaceGun is operational.

A Half-Year is Allotted for the Final Build and Essential Testing