Ec301 (Ngai)solution To Class Exercise 4

This study source was downloaded by 100000867488176 from CourseHero.com on 05-22-2023 12:09:54 GMT -05:00https://www.coursehero.com/file/198374603/EC301-LT-PS4-Solutionspdf/ EC301 (Ngai)Solution to Class Exercise 41. Romer R&D model (a) Prot of nal good rm =L1 Y ZA0 xj djwLY ZA0 pjxjdjMaximization, Taking rst order condition: @ @ LY = 0,(1)L Y ZA0 xj djw = 0 ,(1) Y LY =w@ @ xj = 0, pj +L 1 Y x 1j = 0,p(xj) =LY xj 1 1. (a) Perfect competition implies zero prot, so the intermediate good sector cannot pay any positive price to buy the design from the R&D sector.(b) The monopoly takes demand for xj from part (a) as given and maximizeprot: j maxxj (p (xj) r) xjTaking rst order conditionp(xj) r+ p0(xj)xj = 0, r p(xj) = 1 +p0(xj)xj p(xj)using the demand function in part (a), p(xj) =LY xj 1 ;the elasticityp 0(xj)xj p(xj) = 1so, the price charged by the monopoly is pj =r=:The symmetry results from and cost of producing intermediate goods beingthe same across all j:(c) There are three reasons: (1) knowledge spillover ( >0), this generate dy-namic ine ciency, current researcher ignore the positive externality it gen-erates for future researcher. (2) stepping on toe ( r =M C for