In Korea, newspaper companies are prohibited to offer premiums more than 20% of annual subscribing price by regulations. Since offering premiums is one of price discrimination strategies in newspaper industry, it is known that offering premiums - gift coupon, rebates, etc. - raises consumer welfare. I theoretically show that if the government keeps the regulation without knowing consumer preference on newspaper and the rate of informed consumer, it might reduces consumer welfare in the newspaper market. On the other hand, Korea's Newspaper Law prescribes that the newspaper companies are presumed as market dominating enterprisers which are prohibited to abuse own market-dominant positions, if one company shares 30% of newspaper market or three companies hold 60% of market share. The regulation of the Newspaper Law is taken the criticism that the law reduces the market effectiveness, because even Korea's general competition law, Monopoly Regulation and Fair Trade Act, stipulates that companies which shares 50% of newspaper market or three of which companies hold 75% of market share are presumed as market dominating enterprisers. I point out the problem of the Newspaper Law's regulation on presumption of market-dominant positions.