Why do consumer price react less than import prices to exchange rates?

It is well-known that the extent of pass-through of exchange rate changes to consumer prices is much lower than to import prices. One explanation is local distribution costs. Here we consider an alternative, complementary, explanation based on the optimal pricing strategies of firms. We consider a model where foreign exporting firms sell intermediate goods to domestic firms. Domestic firms assemble the imported intermediate goods and sell final goods to consumers. When domestic firms face significant competition from other domestic final goods producing sectors (e.g., the non-trade goods sector) we show that they prefer to price in domestic currency, while exporting firms tend to price in the exporter's currency. In that case the pass-through to import prices is complete, while the pass-through to consumer prices is zero.