Problem 3. (Midterm Exam, Fall 2017). Consider the Romer model: Y = A Lyt, AA +1 = 2A Lat Lyt + Lat = 1 La = (L. Lyt = (1 - 7), 2 where A, is the initial stock of ideas. 1. Assume that the total labor force in the economy is equal to 100 workers and that 10% of them are employed in the ideas production sector. Assume in addition that 2 = 0.01 and g = 10. Calculate the growth rate of output per capita in this economy. Find the approximate value of output per capita in period t = 14. 2. Assume that the economy starts off at time t = 0 and is growing at the rate found in part 1. In period t = 7, the government decides to maximize food production in this economy by permanently allocating all of the available workers to that sector. How much output per person (approximately) will be produced in period 7 as a result of this policy? What about period t = 14? Sketch the evolution of output per capita over time starting with t = 0, which shows the effects of the government's policy (use the ratio scale).