Instructions: Answers to each of the following problems will be evaluated based on accuracy, complete-ness and clarity. Unsupported answers will receive no credit. Any assumptions you make in answering the questions below should be clearly stated.
1.Suppose a monopoly must decide on a level of R&D along with production levels. R&D is expensive initially, but lowers the marginal cost of production. Suppose the ?rm faces costs C(q, r) = αr2 + (c - r)q, and must decide on a level of R&D expenditure and how much of the good to produce, q. Inverse demand is given by p(q) = a - bq.
(a) What is the ?rm's objective function?
(b) What are the ?rm's ?rst-order conditions?
(c) What are the optimal q and r ?
(d) Under what levels of α does the ?rm invest in R&D?