This economist won a Nobel prize in economics for his work on business cycle theory: a

The correct answer is b.

F.A Hayek is the economist that attained the Nobel Prize due to his efforts to establish the business cycle theory. The significant reason he attained the Nobel Prize is that he came up with practical illustrations that helped individuals organize their plans, which is considered a significant accomplishment in economics. Hayek strongly illustrated the function of information in the economy and how prices are used to convey information and synchronize economic schemes. Hayek used the mentioned illustrations to develop the Mises' business cycles theory and the argumentation over the central organization of economic estimations.