Optimal tax the optimum. Stipulating this condition results in the following formula for the optimal top tax rate, if incomes are Pareto distributed: formula_1 where: Empirical estimation of the parameters of this equation suggests that the revenue-maximising top tax rate is between approximately 50% and 80%, although this estimate neglects long-run behavioural responses, which would imply higher elasticities and a lower optimal tax rate. Saez's analysis can also be generalised to tax rates other than the top rate. In the late 1970s, Arthur Laffer developed the Laffer curve, which demonstrates that there are two effects of changing tax rates: an arithmetic effect—if
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