Key words: delayed differential equations, economic growth, tax evasion. JEL Classification: A13, C62, D13, O49. In this paper we formulate an economic mo- del 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, 0 k > and he has to pay a tax on this capital at a rate 1 , t 1 (0,1]. t ∈ The agent can try to evades the tax on capital by concealing a capital 1 e of the total capital. The optimal tax evasion level which maximi- zes expected net profit is determined. In the second part, the dynamic model of tax eva- sion 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 (ݐ) that depends on ( ݐ− ) and  ଵ ( ݐ− ). Using the delay  as bifurcation parameter we have shown that a Hopf bifurcation occurs when this parameter passes through the critical value  ଴ . The direction of the Hopf bifurcation, the stability and the period of bifurcating period so- lution are also discussed and characterized. 1 THE ANALYSIS OF AN ECONOMIC GROWTH MODEL WITH TAX EVASION AND DELAY Olivia BUNDĂU * Mihaela NEAMŢU ** 1. Introduction In this paper, we construct a new economic growth model with tax evasion, taxes and delay. The main feature of our model is that the control variable and the state variable enter with a delay in the motion equation of the state variable. The introduction of the time delay yields a system of mixed functional differential equations. We determine the steady state of this system and we inves- tigate the local stability of the steady state by analyzing the corresponding transcendental characteristic equation of its linearized system. In the following, by choosing of the delay as a bifurcation parameter, we show that this model with a delay exhibits the Hopf bifurcation. Therefore, the dynamics are oscillatory and this is entirely due to time-to-build technology. Then, we discuss the direction and stability of the bifurcating periodic solutions by applying the normal form theory and the center manifold theorem. The outline of this paper is as follows. In Section 2, we present the static model of tax evasion and we determine the optimal tax evasion level which maximizes expected net profit. In Section 3, we formulate the dynamic model of tax evasion. Section 4, by choosing of the delay as a bifurcation parameter, some sufficient conditions for the existence of Hopf bifurcation are derived. In Section 5, the direction of Hopf bifurcation is analyzed by the normal form theory and the center manifold theorem introduced by Hassard and some criteria for the stability of the bifurcating periodic solutions are obtained. In Section 6, the conclusions are discussed. 2. The Model We will consider an economic model with tax evasion, corruption and taxes. In economy of this model 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, 0 k > and he has to pay a tax on this capital at a rate 1 , t 1 (0,1]. t ∈ The agent can try to evades the tax on capital by * Assistant, PhD., Politehnica University of Timişoara, Department of Mathematics, Romania ** Associate Professor, PhD., West University of Timişoara, Faculty of Economics and Business Administration, Timişoara, Romania