The Analysis of an Economic Growth Model with Tax Evasion and Delay

In this paper we formulate an economic model with tax evasion, corruption and taxes. In the first part the static model is considered, where there are a representative agent and a public institution. The public institution by its tax collectors detects the tax evasion and enacts a system of tax on capital and fines. The representative agent is endowed with a capital k, k>0, and he has to pay a tax on this capital at a rate t1, t1 being in interval (0,1].The agent can try to evades the tax on capital by concealing a capital e1 of the total capital. The optimal tax evasion level which maximizes expected net profit is determined. In the second part, the dynamic model of tax evasion is presented, where the representative agent chooses at each moment in time the level of tax evasion so as maximize expected net profit on infinite horizon, taking into account of the motion equation for the capital k(t), that depend on k(t-τ) and e1(t-τ). Using the delay t as bifurcation parameter we have shown that a Hopf bifurcation occurs when this parameter passes through the critical value t0. The direction of the Hopf bifurcation, the stability and the period of bifurcating period solution are also discussed and characterized.