After graduating with an Associate Diploma of Forestry from the VSF in 1953, Arthur joined the FCV and spent three years in the Assessment Section engaged in surveys of forest resources. In 1957/1958 he was awarded a scholarship for two years of study at Melbourne University, graduating with a Bachelor of Science in Forestry (Melb).

In 1959 he was posted to the Division of Forest Operations. Arthur was Officer in Charge of the East Warburton Sub–District and acting District Forester, Upper Yarra Forest District.

In 1962 he transferred to the Research Branch. He was Officer in Charge, Central Division Research Station charged with designing and implementing extensive research in mensuration and silviculture of Ash-type eucalypts.

In 1970 he was promoted to Forest Assessor, Officer in Charge of the Assessment Section, with responsibility for the design and planning of surveys, and reporting, on all aspects of the State's forest resources.

In 1974 Arthur was promoted to Marketing Officer, Officer in Charge of the Sales and Marketing Branch and Deputy Chief, Division of Economics and Marketing. He served in the Division of Economics, through the change in organisation from the FCV to CFL, until his retirement from State Government employment in 1987.

Following his retirement from State Government employment, Arthur established a successful private company, Arthur Webb & Associates Pty Ltd, engaging in consulting to the forest industries, private forest growers, government agencies and tertiary institutions, as well as numerous members of the sawmilling industry in Victoria.

In addition to his Associate Diploma of Forestry and Bachelor of Science in Forestry, Arthur’s other academic qualifications are Master of Science in Forestry (Melb) 1967, for his studies into the thinning of Eucalyptus regnans, Diploma of Forestry (Oxon) 1969, and Graduate Diploma in Agribusiness (CIT) 1979.

In 1968 Arthur was awarded a Churchill Fellowship to study forestry in South Africa and Europe. In 1969 he was awarded a Russell Grimwade Scholarship enabling him, at Oxford University, to undertake an economic analysis of alternate methods of managing Ash-type regrowth.