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Even the cheapest things are, by definition, not available in famine. Being fat is pretty clear indicator that you have not been recently suffering from famine.

Look at sumo wrestlers for a striking example of muscle mass and high (subcutaneous) body fat.

Sumo wrestlers are certainly strong. However the extra bulk causes a significantly increased risk of many health problems.

You can be malnutrished and fat, but that is different situation. War and famine typically means it is impossible to find enough calories no matter what source. It means that sugar is expensive and so are carbs.