Consider the Romer model of Chapter 6. The final good is produoed using ideas (or technology), A; and labor which is specifically assigned to nal good production, Ly; according to the following formula: YE = AELJII (1) The equation for new ideas is given by At+1 A: = EAtLat (2) Where Lat is the amount of labor employed at the labs trying to come up with new technologies, and E = 0.0025 Also, assume that in the initial period, An = 10000 The total supply of labor in this economy is fixed and given by E = 200. Finally, this economy allocates 95% of its labor force to the production of final good, that is: L3,; = 0.95:. a. What is the growth rate of technology (or the stock of ideas) in this economy? What is the growth rate of output per person on a balanced growth path? (10 points) b. What is the value of per person output in the economy at t = 10? How many years (from t = 0) will it take for output per person to double? (15 points)