Total energy required per cow per year is 31,500 MJ Energy yielding 5,850 liters of milk - that makes 5.38 MJ of energy consumed per liter of Milk.
Per hectare of grass/clover we will therefore be able to produce 13,382 liters of milk.
Per hectare of corn we will produce 16,431 liters
Now lets look at how much food that yields for human consumption in terms of energy and protein. According to our helpful book, one liter of milk has 1,970 kJ of energy and an average of 3.2% protein content.
The one hectare of grass/clover will therefore yield 26,362 MJ of energy (6.3 million calories) and 428 kg of Protein. The same calculation for the corn will yield 32,369 MJ energy (7.74 million calories) and 525 kg of protein.
Obviously we also have a calf born each year and I have counted that energy into the energy per liter of milk as well - what happens to that calf afterwards is another calculation.
Now lets have a look at how much we will be able to produce if we grow either potatoes or wheat.
Wheat will yield an average of 5 tons per hectare (organic) or 25 tons of potatos.
Wheat has 8.5 MJ energy (2,031 calories) per kg and an average protein content of 14%. That yields a total 42,500 MJ of energy (10,157 million calories) and 700kg of protein.
Potatoes have 2.76 MJ energy (660 calories) per kg and an average protein content of 1.4%. One hectare of potatoes will therefore yield 68,750 MJ of energy (16,430 million calories) and 350 kg of protein.
Our book also informs us that on average 20% of our wheat and potato harvest will "not be fit for sale for human consumption" - the quality is too bad and it should therefore be used as animal fodder - so the above numbers would need to be revised downwards accordingly.
According to WebMD the average adult needs about 50g or protein per day or 18.25kg per year and about 2,500 calories (10.5 MJ) energy per day or 912,500 calories (3,817 MJ) per year.
I will now roughly calculated (average between energy and protein needs) how many people one hectare of each of the above will be able to sustain for one year:
Grass/clover -> milk -> human: 26.2 people
Corn -> milk -> human: 32.2 people
Wheat -> human: 42.2 people
Potato -> human: 47.1 people
It becomes quite clear that producing milk is not nearly as inefficient a way of producing food as it has been so widely propagated (in movies like Cowspiracy).
What I have to mention each and every time I talk about this topic is that of the 4 options above, the grass/clover is the only one which builds up soil fertility rather than depleting the soil's reserves. That is why it is important to practice crop rotation where grass/clover is grown for 2 or 3 years before growing potatoes, grains and vegetables for 3-4 years.
Some vegans argue that we do not need cows in order to practice crop rotation - we could just use the grass/clover as green manure (mulching it into the soil). They are right. But it would be a hell of a waste, considering how much high-quality food those cows can produce for us out of that grass. Additionally, long-term studies by the Swiss Research Institute for Organic Agriculture has shown that when the same crop rotation with cows (the cows eat the grass and the manure is used as fertiliser) is significantly better for soil fertility than without cows (grass/clover is used as green manure). And we know that the world's soils store twice as much carbon as we have in our atmosphere. As Michael Pollan tells us, building up our soil fertility is our greatest chance to tackling climate change.