4. (Ch. 11, Q6) Suppose that the production function is given by: Y = 0.5VKVN a. Derive the steady-state levels of output per worker and capital per worker in terms of the savings rate, s, and the depreciation rate, 6. b. Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of s and . c. Suppose that 6=0.05. With your favorite spreadsheet software, compute steady- state output per worker and consumption per worker for s=0; s=0.1; s=0.2; s = 1. Explain the intuition behind your results. d. Use your favorite spreadsheet software to graph the steady-state level of output per worker and consumption per worker as a function of the savings rate (i.e. measure the saving rate on the horizontal axis of your graph and the corresponding values of output per worker and consumption per worker on the vertical axis.). e. Does the graph show that there is a value of s that maximizes output per worker? Does the graph show that there is a value of s that maximizes consumption per worker? If so, what is that value? 5. (Ch. 12, Q6) Suppose that the production function is given by: Y = 0.5VKVAN that the savings rate, s, is equal to 16%, and that the depreciation rate, 3, is equal to 10%. Suppose further than the number of workers grows at 2% per year and the rate of technological progress is 4% per year. a. Find the steady-state value of the variables listed in (i) through (v). i. The capital stock per effective worker. ii. Output per effective worker. iii. The growth rate of output per effective worker. iv. The growth rate of output per worker. v. The growth rate of output. b. Suppose that the rate of technological progress doubles to 8% per year. Recompute your answers to part (a). Explain. c. Now suppose that the rate of technological progress is still equal to 4% per year, but the number of workers now grows at 6% per year. Recompute your answers to (a). Are people better off in (a) or in (c)? Explain. 6. Describe the potential relationships between technology and income inequality. a. Give an example where technology is likely to increase income inequality and one where technology is likely to decrease income inequality. b. Assume that a robot is invented with general artificial intelligence and is able to perform all productive actions (i.e. working) better than almost all humans. What is the likely economic outcome of this