Question 1: Fact I: Consider the following setup that follows the standard Solow model in Country A. There are N consumers, each endowed with one unit of available time. Consumers do not value leisure and they divide output between consumption and savings according to the following rule: a fraction s of output is saved, and the rest is consumed. There is a representative firm that has a Cobb- Douglas production technology of the form Y = zF(K,N), where K denotes capital, N denotes Labour, z is (Total Factor Productivity (TFP). Initially country A had 100 units of Capital, 144 units of labour and population growth rate was 0.01. Suppose you are given the fact that in this economy depreciation d is 0.09 and at steady state, the output per-capita could be expressed as y" = (k*). Now, consider the unfortunate situation where a disease took several lives, reducing the number of labour force equal to 81 units. 1.1 Describe and explain changes/effect of this disease on country A's per-capita output, and per capita capital in the steady state, comparing these with the initial steady state that was prevailing before the disaster. (Note: you are supposed to describe and explain changes in detail, following Solow Model. The numbers are provided to give you more details about the economy, but you are not required to provide mathematical derivationsumbers for this question). 1.2 If you were illustrating the old and new steady state in a diagram, with per-capita capital In x-axis, describe how your graph would change before and after the disease. Would you expect the growth rate of output per worker in country A smaller or greater than it was before the disease? Question 2: Consider country B, where every citizen is identical (like clones of each other) and each individual has one unit of labour to supply. The country produces only one commodity, food. Current aggregate output of food, Y, is produced using current inputs of land, L. and current labour, N, that is Y = zF(L.N), where z is total factor productivity (TFP). Future population is N", population grows at a rate n - 0.01, and depends on consumption per worker, c = C/N. There is no money, wage payment is provided solely in terms of foods. In equilibrium all foods produced in the economy are consumed and this is a closed economy without any government, net export or savings. Consider the Malthus model in the context of country B. Suppose the economy is currently at steady state. Now suppose considerable amount of land is destroyed due to an earthquake in country B. Describe and explain changes/effect of this incidence on steady state land per capita, and standard of living. Explain how wage would be determined in country B and how this process (of determining wage in Mathus model) is different compared to the competitive equilibrium models we studied in Chapter 4 and 5. Explain if you think wage would be higher or lower in country B after the earthquake.Question 2 : Solow Growth Model [35 marks] Consider the following numerical example using the Solow growth model. Suppose that F(K, N) = KI/13N9/13, Y = =F(K.N). Furthermore, assume that the capital depreciation rate is d = 0.04, the savings rate is s = 0.3, the population growth rate is n = 0.035, and the productivity is = = 1.75. Suppose Ko = 200 and No = 100. 1. Compute the values ki, vi, and e of the per-worker capital, output and consumption in period one. [05 marks] 2. Find the steady state per-capita capital stock (k*), output per capita (y"), and consumption per capita (c"). [10 marks] 3. Assume the economy is in the steady state of Question 2, compute the percentage change in = that is needed to increase the long run per capita capital by 5%. [06 marks] 4. Assume the economy is in the steady state of Question 2 and suddenly, = decreases by 10%, calculate the percentage change in s that is needed to keep the long run per capita output unchanged. [06 marks] 5. Assume the economy is in the steady state of Question 2 and n goes down by 5% while z increases by 5% and s increases by 5%. Using the Taylor approximation, evaluate the contribution of each variable to the total change in the steady state consumption c". [08 marks]There are no indices used, as there is in the math formula, because we reassign x to the new value. Otherwise, this line looks just like the math formula as we utilize the automatic derivative notation defined in the HTH229 package, (For any given problem we could of course compute f'(x) by hand and use that) In the above, we soo after 1 step, f(x) is close to 0, but with a few more steps can be as accurate as possible in 64-bit floating point. (a) Applying Newton's Method to the function /(x) = sin(x) with an initial guess 3, what is the answer after 2 iterations? (b) The value of a in after these 2 iterations is 2.89...e-NN. NN is one of 1,2, ..., 16. What is NN? (c) After 3 iterations, f(x) is 1.2246467991473532e-16, essentially zero in floating point, and no more updates will improve this (the 1 (x)/f\\(x) term is basically O). The value of x is mathematically an approximate zero, as f(x) is not 0 and moreover x is a floating point number, hence can not be the irrational . On the computer we have: x - pi is exactly 0 in floating point math x - p1 is 2.220446049250313e-16 By hand, as above, use Newton's method to find a zero for the function / (x) = x) - x - 1. Start at x = 1.6. (d) What is the approximate zero after 5 iterations, or steps? (e) The value of /(x) after 5 steps is 1.21...- NN. NN is one of 1.2, .... 16. What is NN7 (f After 7 steps, Newton's method will no longer increase accuracy of the approximate zero. The value of f(x) aftere 7 steps is 6.56...-NN. What is NN?It is estimated that 13% of the cost of goods sold represents fixed factory overhead costs and that 22% of the operating expenses are fixed. Since Royal Cola is only one of many products, the fixed costs will not be materially affected if the product is discontinued, a. Prepare a differential analysis, dated March 3, to determine whether Royal Cola should be continued (Alternative 1) or discontinued (Alternative 2). If an amount is zero, enter zero "0". Use a minus sign to indicate a loss. Differential Analysis Continue Royal Cola (Alt. 1) or Discontinue Royal Cola (Alt. 2) January 21 Differential Effect Continue Royal Discontinue Royal Cola (Alternative 1) Cola (Alternative 2) on Income (Alternative 2) Revenues Costs: Variable cost of goods sold Variable operating expenses Fixed costs Income (Loss) b. Should Star Cola be retained? Explain. As indicated by the differential analysis in part (A), the income would by $ if the product is discontinued