Profitable gray market with asymmetric costs

When manufacturers sell their branded goods at different prices in different markets or channels, gray marketers buy goods in the low-priced market and resell them in the high-priced market to compete with the manufacturers' authorized sellers. Conventional wisdom suggests the lost sales in the high-priced market resulting from the gray market's diversion always make manufacturers worse off. However, by purely considering the marginal production cost in the high-priced market is higher than the low-priced market, we show that the manufacturer can gain from gray markets, which contradicts to the conventional result. It happens when the production is significantly less efficient in the high-priced market than in the low-priced market.