This paper introduces a market size dependent firm entry cost into the Helpman, Melitz and Yeaple (2004) (HMY) version of the Melitz (2003) model. This is a relatively small generalisation, which preserves the analytical solvability of the model. Nevertheless, our model yields several new results that are in line with data. First, the average productivity of firms located in a market increases in the size of the market. Second, the productivity of exporters is U-shaped with reference to export market size. Third, the productivity premium (the difference in average productivity) between exporters and non-exporters decreases in the home country size. Fourth, we derive a set of new results related to trade volume. It is shown that when the fixed entry cost of exporting declines, for instance as the result of economic integration, export shares converge. This prognosis is supported by the empirical section of the paper. Fifth, we use a multicountry version of our model to derive a gravity equation. Our specification yields a gravity equation a la Anderson and van Wincoop (2003), but where GDP per capita enters as an additional explanatory variable.