Question 2 (Two variations of the Romer model) In the analysis of economic growth driven by knowledge accumulation (i.e. the Romer model without capital), we have assumed that production happens via the following production function: Y? = A,Ly, where A, is knowledge (i.e. ideas) and Ly, is the number of workers in manufacturing. This is an extreme assumption, and we will try to understand the implications of a less extreme one. Assume that the production function is now Y, = A;/Ly,. The rest of the model is unchanged. a. Explain the economic meaning of this assumption. b. Does the growth rate of A, change with respect to our baseline case? How? Why? c. Calculate the growth rate of GDP per worker. d. Assuming knowledge in year 0 was Ao, derive the equation for GDP per capita in year t . Now assume that the production function is Y = A,Ly,, but the knowledge accumulation equation is given by AA +1 = ZA? Lar. The rest of the model is unchanged. e. Explain the economic meaning of this assumption. f. Does the growth rate of A, change with respect to our baseline case? How? Why? g. Calculate the growth rate of GDP per worker