How can I evaluate the extent to which increased competition leads to higher levels of economic efficiency?

Keeping all other factors fixed, increased competition will make the demand curve that firms face flatter due to increased elasticity of the demand. By drawing a diagram depicting a firm's costs and revenues, we can see that this will make the firm move from the profit-maximising output to the allocative-efficient point of production (where price=marginal cost). Therefore overall levels of efficiency will be likely to increase. However, make sure to evaluate this point by arguing that increased competition may reduce profit margins and so, in the long run, it may reduce the extent to which firms can invest in research and development in order to become productively efficient in the long-run.