3. Question 3 (25 marks) In the following exercise we consider the production and the long run growth of different economies. Our starting point is a simple model of the Cobb-Douglas production technology with a capital share in production of 1/3. and a labor share in production of 2/3. (a) First. let's consider the simplest Cobb-Douglas technology as l; = 1951.5. Convert the Cobb-Douglas production function into per capita terms. Why might we be more concerned about per capita output rather than total output when discussing the welfare impacts of economic growth? [5 marks] Show how the adjusted production function looks like if we also consider total factor productivity (TFP). How does the production function look like in per capita terms? Why do we think that it is a good idea to augment the production function with the TFP? [5 marks] 4QQMN13G em 4QQMN14G (c) Now consider the general Solow model with per capita production function given by y, = Alf. to determine which country has the hight steady-state level of capital and output using the following data in Table 1. Assume that labor is xed and we can dene the population of any country in such a way that it is equal to one. Which country has the highest steady-state per capita capital stock and output per capita? Which country has the lowat? [5 marks] 4 s 6 r1 China 0.79 0.32 0.05 035 Hungary 0.95 0.20 0.04 0.40 South Korea 0.84 0.35 0.06 0.45 Table 2: Parameter values (d) Explain the likely driving forces behind your answers in (c). [5 marks] (e) Let's focus on Hungary and assume that the economy is in its steady-state represented by the capital and output per capita levels that were calculated in (c). Now consider that TFP in Hungary increases from 0.95 to 1. Using the Solow Diagram. show how the economy adjusts to this structural change. How do capital per capita and output per capita evolve over time? [5 marks]