What impact would introducing 15 times more soy worldwide do to the price of soy? Soy is a commodity and the main export of Argentina. It is said Argentina has 40 million of hectares of arable land and it produces food for 400 million persons and that potentially could make food for 600 millions. I can't confirm this is true but it's said by the president of one of the main agrarian organizations of Argentina, probably with statistics made by them and/or data of the national institute of agrarian technology.

Africa it's said to have 600 million hectares of arable land, which is 15 times the arable land of Argentina. What would happen to the prices of soy related commodities if Africa proportionally introduces 15 times more soy related products to the world? Take any soy product you want for the answer, soy bean if you want for example. Can this be calculated? I've heard of prices simulations predictions for other commodities when introduced or retrieved from the market, such as oil, so I suppose this can be calculated.
Roberts and Schlenker (2013) estimate the price elasticity of demand for agricultural commodities to be about -0.08 to -0.05. These are elasticities estimated over much smaller changes in $p$ and $q$ than you are suggesting. Remember that the elasticity is effectively percent change in $q$ for a percent change in $p$, so we can ask what the percent change in $p$ is for a percent change in $q$. 

If production is 15x more soy than there is currently (in total, so globally) then this is a 1500% ((1*15+1 - 1)/1) increase in soy. Using the high end (most elastic), we get that prices have to fall 18,750% (15/-0.08) to clear the market at this new higher quantity. This is impossible, so this tells us that our local elasticity measures won't do to solve this problem. It also suggests that there would be no reason to add so much soy bean production, because demand is likely unable to handle so much soy.