To have and manage an agricultural fair or exposition for the purpose of promoting and encouraging agriculture and the domestic arts of the information and betterment of the inhabitants of rural communities within the State of Delaware, including the rights to hold competitions for all kinds of products of the soil or of the land, and of horses, cattle, and livestock, and the holding of races, shows and competitions of speed or quality of horses and other animals and the giving of rewards or prizes and the like. To promote the betterment of those engaged in agriculture and horticulture, the improvement of the grade products in these pursuits, and the development of a higher degree of efficiency in these occupations.