6of6 Consider the Romer model of Chapter 6. The nal good is produced using ideas (or technology), A, and labor which is specically assigned to nal good production, Ly, according to the following formula: t = at.yr (I) The equation for new ideas is given by Ac+1 A: = man: (2) where Lat is the amount of labor employed at the labs trying to come up with new technologies, and z? = 0.0025 Also, assume that in the initial period, An = 10000 The total supply of labor in this economy is fixed and given by L = 200. Finally, this economy allocates 95% of its labor force to the production of nal 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) c. Suppose that that in t = 10, the portion of the labor force that is allocated to the production of new ideas becomes 0.025. Depict this situation in a graph with time in the horizontal axis and output per person in the vertical axis [degicted In a ratio L816). (15 points) d. Consider the economy described in part (c) and describe the value of 3:30. Compare that value with the one that per capita output would have obtained if the event described in part (c) had never happened. [ 10 points)