Muqaddimah empires to collapse, with the result that lower revenue was collected from high rates." He wrote: Ibn Khaldun introduced the concept now popularly known as the Laffer curve, that increases in tax rates initially increase tax revenues, but eventually the increases in tax rates cause a decrease in tax revenues. This occurs as too high a tax rate discourages producers in the economy. Ibn Khaldun used a dialectic approach to describe the sociological implications of tax choice (which now forms a part of economics theory): This analysis is very similar to the modern economic concept known as the Laffer curve.
Optimal foraging theory items that an animal should carry back to its nesting site or the optimal size of a food item that an animal should feed on. Figure 1, shows an example of how an optimal decision rule could be determined from a graphical model. The curve represents the energy gain per cost (E) for adopting foraging strategy x. Energy gain per cost is the currency being optimized. The constraints of the system determine the shape of this curve. The optimal decision rule (x*) is the strategy for which the currency, energy gain per costs, is the greatest. Optimal foraging models can