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 shown as a curve of energy gain per time spent in a patch (Figure 3). The curve starts off with a steep slope and gradually levels off as prey becomes harder to find. Another important cost to consider is the traveling time between different patches and the nesting site. An animal loses foraging time while it travels and expends energy through its locomotion. In this model, the currency being optimized is usually net energy gain per unit time. The constraints are the travel time and the shape of the curve of diminishing returns. Graphically, the currency (net energy gain per