In 1954, Murphy started his own crisp company, Tayto, in O’Rahilly’s Parade off Moore Street with one van and eight employees, some of whom were to work for him for more than 40 years. His great marketing coup was to invent the world’s first cheese and onion flavour and put paid to the dull crisps of his childhood. The product flourished at home and abroad and within two years the business had moved to Mount Pleasant Avenue in Rathmines. In 1960, the company acquired an additional premises in Harold’s Cross.

Joe ‘Spuds’ Murphy’s marketing flair led him to become one of the first sponsors of a Radio Éireann programme. He also rented space for a neon sign on one of the premier locations in Dublin at the junction of D’Olier Street and Westmoreland Street. The Tayto sign became one of the great landmarks of Dublin in the 1960s and 1970s.

He and his company were well-known in the business abroad and in 1964 Beatrice Foods of Chicago bought a majority stake in Tayto. By the early 1970s Tayto had some 300 employees, most of them at its state-of-the-art factory in Coolock. Tayto acquired the King Crisps company in 1972 and Joe Murphy developed unique and separate marketing and sales strategies for Tayto and King brands. However, he did not rest on his laurels. He continually sought ways to enhance the brand and by now the company was introducing new crisp flavours and snack products to the Irish market. Tayto was the first company to manufacture and market extruded snack products in Ireland. In 1981, Tayto acquired the Smiths Food Group factory at Terenure where a new and extended range of Tayto products was produced.