Here's the abstract from the paper:

Sustainable diets, in particular vegetarianism, are often promoted as effective measures to reduce our environmental footprint. Yet, fewconclusions take full-scale behavioral changes into consideration. This can be achieved by calculating the indirect environmental rebound effect related to the re-spending of expenditure saved during the initial behavioral shift. This study aims to quantify the potential energy use and greenhouse gas emission savings, and most likely rebound effects, related to an average Swedish consumer's shift to vegetarianism. Using household budget survey data, it estimates Engel curves of 117 consumption goods, derives marginal expenditure shares, and links these values to environmental intensity indicators. Results indicate that switching to vegetarianism could save consumers 16% of the energy use and 20% of the greenhouse gas emissions related to their dietary consumption. However, if they re-spend the saved income according to their current preferences, they would forego 96% of potential energy savings and 49% of greenhouse gas emission savings. These rebound effects are even higher for lower-income consumers who tend to re-spend on more environmentally intensive goods. Yet, the adverse effect could be tempered by purchasing organic goods or re-spending the money on services. In order to reduce the environmental impact of consumption, it could thus be recommended to not only focus on dietary shifts, but rather on the full range of consumer expenditure.

I'd argue that eating vegetarian isn't really that much cheaper in the first place.

In the paper, there's also section 4.6.2.1 about organic food consumption:

If a vegetarian diet is chosen for its environmental value, it is possible that consumers will simultaneously choose organic instead of conventional products for their perceived improved impact on the environment. Organic products however are often associated with a price premium, which can fundamentally change the conclusions on re-spending and environmental impacts occurred.

and a few paragraphs later:

"Therefore, not only would we avoid any rebound behavior, we find virtuous cycle effects in that consumers will save 111% of both the potential energy and the potential greenhouse gas emission savings thatwere predicted from only foregoing meat alone."

So, if you go vegetarian, go organic while you're at it!

PS: The paper isn't so bad, you should probably read it in full (you know where). https://doi.org/10.1016/j.ecolecon.2015.04.030