state whether the monopolist would increase or decrease output:

a. Marginal revenue exceeds marginal cost at the output produced.

b. Marginal cost exceeds marginal revenue at the output produced.

To determine whether a monopolist would increase or decrease output in these scenarios, we need to consider the relationship between marginal revenue (MR) and marginal cost (MC). Marginal revenue refers to the additional revenue generated from selling one more unit of output, while marginal cost refers to the additional cost incurred in producing one more unit.

a. If the monopolist's marginal revenue exceeds marginal cost at the output produced, the monopolist would increase output. In this case, each additional unit sold brings in more revenue than it costs to produce, resulting in greater profits. By expanding output, the monopolist can maximize its profits by continuing to produce as long as MR > MC.

b. Conversely, if the monopolist's marginal cost exceeds marginal revenue at the output produced, the monopolist would decrease output. In this situation, each additional unit sold brings in less revenue than it costs to produce, resulting in diminishing profits. By reducing output, the monopolist can avoid losses by decreasing production as long as MC > MR.

In summary, the monopolist would increase output if MR > MC and decrease output if MC > MR.