Yes and no. In an industrialized society, yes, the efficiency of food production depends on technology which depends on the economy.

But there are other models. Hunter gatherers, for example, can provide for themselves with minimal technology required. They don't (at least very rarely) overuse the land, so they always have more next year.

Organic farming is another example.. still requires technology but a different kind, knowledge of soil biology, pests and predators, etcetera, and it has different effects on the surrounding environment than industrial farming - less pesticide and fertilizer runoff into local watersheds, for example.

Also there is the question: what kind of food do you eat? In the underdeveloped world, herders vs. agricultural societies use the land differently. In the developed world, meat eaters use more land per capita because livestock requires more land and water to feed than the equivalent amount of vegetable protein.

With more wealth, people generally choose to eat more meat, which is more resource intensive, rather than choosing to eat a vegetarian diet and thus becoming more efficient in land usage. So techology and wealth do not necessarily lead to more efficient agriculture.