### Instructions Answers To Each Of The Following Problems Will Be Evaluated Based O (1)

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 ﬁrm 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 ﬁrm’s objective function?

(b)What are the ﬁrm’s ﬁrst-order conditions?

(c)What are the optimal q and r ?

(d)Under what levels of α does the ﬁrm invest in R&D?