Gain modulation of neuronal firing rate has been shown to be important for a large number of computations in the brain including attentional selection. Several models can produce gain modulation. One of the features characterizing attentional modulation is that attentional input in the absence of visual input produces little if any change in the mean firing rate of excitatory neurons in early visual cortex. This has been difficult to understand in computational models of gain modulation. Here we expand a previous network model of multiplicative neuron responses  by separating excitatory and inhibitory neuron propulations while keeping the single-neuron models simple. We analyze attentional input and lateral inhibition patterns which best reproduce electrophysiological results. We find that attentional input to excitatory and inhibitory neurons is the same, and, surprisingly, the optimal lateral inhibition connectivity is not Gaussian but needs to have a heavier tail. Addtionally, our model predicts that there is a minimum size of the attentional spotlight above which attentional modulation is multiplicative; below this minimum it becomes additive.