and

= = Consider an economy described by the Romer model, where Yt = AtLyt is the production function of output and AAt+1 = 0.05 A+Lat is the production function of new ideas. Say that 1 every period, there are 20 workers in this economy, and 10% of them are employed in the idea sector. a. What is the growth rate of ideas? Ideally you should be able to both write down the expression and solve for a numerical value. b. How fast does output per capita grow? How do you know this? c. Describe what would happen if the percentage of workers employed in the idea sector fell to 5% (with no other changes). yt Y = AK1/3-2/3 AAt+1 = 2 Atlat Lyt + Lat = Lat = li Assume 7 = 0.1, 2 = 0.01, and I = 3,000. (Recall go - = ) 9 AXt+1 Xt Using the Romer model, assume that the economy is on its balanced growth path. Say that there is a one-time, permanent, increase in the fraction of labor working in research (1). Describe what happens to: a. The growth rate of GDP per capita (growth rate of Y/L) b. The growth rate of knowledge (growth rate of A) c. The level of GDP per capita over time (here, the short and long run effects are different) = = Consider an economy described by the Romer model, where Yt = AtLyt is the production function of output and AAt+1 = 0.05 A+Lat is the production function of new ideas. Say that 1 every period, there are 20 workers in this economy, and 10% of them are employed in the idea sector. a. What is the growth rate of ideas? Ideally you should be able to both write down the expression and solve for a numerical value. b. How fast does output per capita grow? How do you know this? c. Describe what would happen if the percentage of workers employed in the idea sector fell to 5% (with no other changes). yt Y = AK1/3-2/3 AAt+1 = 2 Atlat Lyt + Lat = Lat = li Assume 7 = 0.1, 2 = 0.01, and I = 3,000. (Recall go - = ) 9 AXt+1 Xt Using the Romer model, assume that the economy is on its balanced growth path. Say that there is a one-time, permanent, increase in the fraction of labor working in research (1). Describe what happens to: a. The growth rate of GDP per capita (growth rate of Y/L) b. The growth rate of knowledge (growth rate of A) c. The level of GDP per capita over time (here, the short and long run effects are different)