Innovation and Technology Diffusion PDF

[Innovation and Technology Diffusion] 1. Consider the version of the Romer model presented in class but now suppose that there are two economies (economy 1 and economy 2) instead of just one. The two economies do not interact in any way. Each conducts R&D, develops its technologies whi...

[Innovation and Technology Diffusion] 1. Consider the version of the Romer model presented in class but now suppose that there are two economies (economy 1 and economy 2) instead of just one. The two economies do not interact in any way. Each conducts R&D, develops its technologies which are sold only domestically and benefits from the knowledge created domestically only. Technology in each country c evolves as [*A*~*ct* + 1~ − *A*~*ct* + 1~ − *A*~ct~ = *aA*~ct~*S*~*c*~]{.math.inline} where [*A*~ct~]{.math.inline} is the stock of technologies developed in c, [*a*]{.math.inline} is the productivity parameter of R&D and [*S*~*c*~]{.math.inline} is the number of scientists in country c. Suppose that both economies have the same productivity of R&D, devote the same number of workers to R&D but, for reasons not relevant, one economy (e.g., economy 1) has a greater stock of technology at time zero ([*A*~10~ \> *A*~20~)]{.math.inline}. A. Which economy will display a larger growth rate of technology? Show algebraically and provide the intuition. B. Suppose that time T, the two economies open up and ideas flow freely across borders from that moment onwards. Suppose further that the number of scientists in each economy does not change. Derive an expression for the evolution of the total stock of technologies in the newly integrated economy. Plot the evolution of [*A*~1*t*~ + *A*~2*t*~]{.math.inline}  before T, at T and after T and explain the key features of the evolution. 2. Consider the technology diffusion model developed in class. The world technology frontier At grows at a constant rate g. Suppose that an economy c with an adoption rate λ0 is in its steady state. At time T, the adoption rate increases to λ1\> λ0. Draw the evolution over time of the stock of technologies in c **relative** to the world technology frontier (Act/At). Start before T and go all the way until the infinite future. Using the model equations, briefly explain your answer. 3. In the Romer model, suppose two countries are identical other than for the fact that one has a greater level of technology (At) than the other. Then, a. The country with greater At grows faster b. We cannot tell which country grows faster c. The country with smaller At grows faster d. They both grow at the same rate 4. In the Romer model, if we increase the share of population that work in R&D: e. The long-run growth of output is not changed, but technology grows faster f. The growth rate of technology accelerates from the beginning. g. Technology grows more slowly at the beginning but faster later on. h. Output is higher in the long run, but does not change at the moment when the share of scientists goes up. 5. A(t+1)=A(t)+a\_bar\*s\_bar\*L\_bar Where a\_bar is a parameter that affects the productivity of R&D, s\_bar is the share of the population that works in R&D, and L\_bar is the fixed population. a. This model displays long-run growth at an increasing rate. b. This model displays long-run growth at a constant rate c. This model does not display long-run growth d. This model displays long-run growth but at a non-constant rate 6. In the technology diffusion model, two countries differ in the adoption rate. Then which of the following is true. i. The country with greater adoption rate grows faster in the long run j. The country with greater adoption rate has higher level of technology and grows faster in the long-run k. The country with greater adoption rate has higher level of technology in the long-run l. We cannot tell 7. 8. 9. Consider an economy where the stock of technologies, A, follows the law of motion: A(t+1)-A(t)=abar\*Ls where abar is a constant and Ls is the number of scientist in the economy. Which of the following is true? m. abar does not affect growth in the long-run n. This economy sustains positive growth in the long run o. The growth of this economy in the long-run is greater the higher is abar. p. The growth of this economy in the long-run is greater the higher is the population in the economy