(Requires calculus) Let patents be the number of patents applied for by a firm during a given year. Assume that the conditional expectation of patents given sales and RD is
E(patents | sales, RD) = exp [β0 + β1 log(sales) + β2RD + β3RD2],
where sales is annual firm sales and RD is total spending on research and development over the past 10 years.
(i) How would you estimate the βj? Justify your answer by discussing the nature of patents.
(ii) How do you interpret βj?
(iii) Find the partial effect of RD on E(patents\sales, RD).