U.S. drugmaker AbbVie stepped up the pursuit for the London listed bio-pharmaceutical giant, Shire. AbbVie offered $51.5 billion to acquire Shire. Its executives called and wrote to Shire's top shareholders directly asking them to push Shire's management into an agreement. Per U.K. regulations, if the two sides cannot reach a deal by July 18, the bidder must walk away for six months. AbbVie wants to access Shire's growth and to reach different patients. Currently, the only star AbbVie has is the rheumatoid arthritis drug Humira. Shire, on the other hand, manufactures a number of widely used drugs for different patients. Its number one drug is Vyvanse, an amphetamine to treat attention deficit hyperactivity disorder. The American Psychiatric Association estimated that 5% of children in the U.S. have ADHD and the symptoms don't necessarily disappear when the young patients become adults. Doctors prescribe more than $1 billion worth of Vyvanse to treat ADHD every year. Because Shire is based in Europe, AbbVie could change its address to overseas and enjoy better tax treatment if the acquisition is successful. It is estimated AbbVie's tax rate could drop to as low as 13% from the current 22%.