Simulations of the electron acoustic instability are conducted with plasma parameters based on the DE 1 observations near the polar cusp. The cusp plasma is assumed to consist of hot electrons, cold electrons, a warm electron beam, and a neutralizing background. The electron acoustic mode, a relatively unknown electrostatic mode, is found to be driven unstable by an electron beam in the presence of a two-temperature electron plasma. We use a particle-in-cell code to examine the temporal behavior of this instability over a range of parameters, including the beam speed and the cold electron density. The simulation results are shown to agree with the linear theory with regard to the wave frequency, the growth rate, and the electrostatic nature of the instability. It is found that the heating rate for each electron component determined from the simulations is in agreement with second-order theory and that the saturation level of the fluctuations is consistent with nonlinear theory. The simulations demonstrate that the instability saturates by either trapping the beam, trapping the cold electrons, or forming a plateau on the beam distribution. Under some conditions the instability can strongly heat the cold electrons. By comparing the simulation results with the DE 1 plasma and wave observations, we conclude that the observed low-energy electron beam can generate broadband electrostatic emissions in the frequency range of cusp hiss by means of the electron acoustic instability. However, the simulations also indicate that a more detailed examination of the plasma observations is needed to explain the origin of the electromagnetic component of cusp auroral hiss.