Estimating the effects of goods and labor market power on firm pricing behavior is difficult since firm-level output and employment are jointly determined. We exploit the variation in the sets of destination countries across exporting firms, which enables us to separately identify the effects of goods and labor market power on pass-through rates by reducing the comovement of firm size across specific sales markets and in its local labor market. We present a theoretical framework in which multi-destination exporters are oligopolists in their goods markets and oligopsonists in their local labor market. Combining firm-level trade data per product-destination with establishment-level balance sheet data and employment zone identifiers for the universe of French firms from 1995 to 2015, we construct theoretically sound proxies for labor and goods market power and jointly estimate their effects on export prices using exchange rate shocks as the source of identifying variation in firm demand. Consistent with the model's predictions, we provide robust evidence that firms with stronger labor market power have a lower pass-through of changes in their effective exchange rate into export prices conditional on their goods market power. The findings indicate a sizable degree of labor market power for French exporters.