ECON 212 Homework #3 Please complete all problems and show work for full credit. 1. Suppose that the economy is on a balanced growth path in the Romer model, and then, in the year 2020, research productivity, z, increases immediately and permanently to a new higher level z' > Z. a. Solve for the new growth rate of knowledge and per capita output, yt. b. Make a graph of yt over time using a ratio or log scale. c. Why might research productivity increase in an economy? 2. Suppose the parameters of the Romer model take the following values: A = 100, = 0.06, z = 1/3,000, and N = 1,000. a. What is the growth rate of output per person in the economy? b. What is the initial level of output per person? What is the level of output per person in 100 years? C. Now consider the following changes, one at a time: a doubling of the initial stock of knowledge A, a doubling of the research share I, a doubling of research productivity Z, and a doubling of the population N. How would your answer to parts (a) and (b) change in each case? d. If you could advocate one of the changes considered in part (c), which would you choose and why? 3. Consider a version of the Romer model with the following production function: Y = A0.5 Lyt In this version of the model the exponent on ideas in the output production function has been reduced so that ideas have diminishing returns in the production of output. a. Provide an economic interpretation of this re-formulation of the problem. b. What is the growth rate of knowledge in this economy? C. What is the growth rate of output per person in this economy? d. Solve for the level of output per person at each point in time.