Apart from the fallacy of assuming that the demand curve for food is constant under changing conditions, your professor’s conclusion does not follow from his stipulations.
If an entrepreneur is selling a product at a price for which demand is inelastic, he can raise his price and increase his revenues even though he sells less output. No entrepreneur will price his product in the inelastic portion of his demand curve. Instead, regardless of how steep or flat the demand curve is for his product, he will price it at the unit elastic point (which is the midpoint) of his (linear) demand curve. At that point, his revenues will be as large as possible.
If the farmer’s costs are falling as he raises his price to take advantage of the inelastic demand, then his profit will skyrocket. As a consequence, other entrepreneurs will invest in farming and production will increase. Increased production by more entrepreneurs will reduce the demand curves for existing farmers and they will lower their prices to render the greatest revenue under the new conditions. This process of adjustment will continue until there is no more additional profit to be earned by further expansion in production.
Moreover, technology is not a force of nature that automatically lower costs. A particular technology is chosen by entrepreneurs as efficient, given his circumstances. New technologies are brought forth by saving-investing in research and development. Entrepreneurs will only invest in technologies that they anticipate will render their production more profitable.
Elasticity is discussed in the lecture on Competition and Monopoly.