where y is output per worker and k is capital per worker. Suppose that the marginal propensity to save s = 20%, the rate of population growth n = 3% and the depreciation rated = 2% (a) Using Excel, calculate how y varies as k increases from 1 to 21. Ploty as a function of k on a graph and comment on the shape of the intensive production function. Consider three economies which share the same underlying characteristics of s, n and d but at a given time I = 0 they are at different stages of growth. At 7 = 0, economy 1 has 1 unit of capital per worker, economy 2 has 5 units of capital per worker and economy 3 has 10 units of capital per worker. (b) For each of the economy (1,2,3), i. calculate the level of output per worker at I = 0; ii. use the Solow growth formula to calculate the amount by which capital per worker will increase between 7 = 0 and the next period I = 1. iii. calculate the new level of capital at I = 1 and use this to calculate the level of per-capita output atI = 1. (c) Now calculate the growth rate of each economy between 7 = 0 and I = 1 (recall what is meant by the term growth rate). How do the three economies' growth rates compare and what is the main reason that they differ? (d) Calculate the steady state level of capital per worker and output per worker for each of the economy. Are they the same or are they different? What type of convergence would these economies display? (e) Suppose that there is a fourth economy which shares all the same features as the first three but in which capital per worker at 7 = 0 is 20. What will happen to this economy's capital stock over time? Explain with a diagram. 2. You are given the following data for two countries. All variables (except the factor shares) are in percent per annum. % Country change ratio change V change wages on 9% change TFP V Fiji 3.5 1.9 2.1 0.70 1.5