Assist ,in in solving the attached questions.

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 (TEP). 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*15. 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 (TP). 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 3: Fact II. Assume the endogenous growth model (from Chapter 8) perfectly explain the growth situation in the country Econland, where a representative consumer starts the current period with H. units of human capital and does not use time for leisure. In each period, the consumer has one unit of time, which can be allocated between work and accumulating human capital. Let u denote the fraction of time devoted to working in each period. The consumer's quantity of human capital is the measure of the productivity of the consumer's time when he or she is working. For each efficiency unit of labour supplied, the consumer receives the current real wage w. The consumer cannot save, but they can trade off current consumption for future consumption by accumulating human capital. b is a parameter that captures the efficiency of the human capital accumulation technology, with b > 0. The representative firm produces output using only efficiency units of labour. The production function is given by Y -zuHe where He is the units of labour in production. Sunnose the economy of Ecoaland was initially in a steady state with H.= Has He In the bane of giving the economy aconsumption and investment in that steady state? [Note: No matter how many periods we compute, for enough decimal places, there will always be tiny increments. Do not worry about that. If you see that the numbers stabilize over time, converging to a constant level, just consider the numbers in period 450 to be the final, steady-state numbers.] (e) Calculate the growth rate of GDP every period. How does this growth rate change over time? According to this model, do poor countries (i.e., countries with low GDP) grow faster, slower, or at the same rate as rich (i.e., high-GDP) countries? (f) Is it possible to obtain long run growth by increasing the savings rate? To answer this. replicate your above calculations devoting, every period, 85% of GDP to investment and only 15% to consumption. Is there sustained growth, or another steady state? If there is a steady state, how much is capital, output, consumption and investment in that steady state? (g) What savings rate maximizes the steady-state level of output? What savings rate maximizes the steady-state level of consumption? To answer this, try different values of the savings rate. say in increments of 0.01. That is, see what happens when $=0%, 1%, 2%, ..., 99%, 100%. After completing parts (a)-(g). leave your computer and get some old-fashioned pen and paper for parts (h) and (i). Part (h) requires solving a system of equations and (i) requires using calculus to solve a maximization problem. (h) For general parameter values ( A, a, s, 6, X,,N) derive the steady-state capital stock, output, consumption and investment. Hint: You can find the solution using My = K, = Ass, the law of motion of capital , = (1-5)X, + 1,, the savings/investment condition /, = s, and the production function Y, = AX," N,"". Verify that the results obtained by this method are the same as the computational results from parts (d) and (f). (i) Use your results from part (h) to analytically find the golden-rule savings rate s*, which maximizes steady-state consumption. Verify that the results obtained by this method are the same as the computational results from part (2).1. The Large Open Economy. Consider the US neoonomg,r which has desired mnsumption and investment functions: (3\"3 = 1m + 0.751\" sins" and IUS = 2m mar\" Furthermore1 government spending and the full employment level of output are given by: G\" = 4m and if\" = 2,000 The rest of the mrld has a desired oonsnrnption and investment as follows: Cm\" = 1m + 0.5+me sins\" and 130W = 2m - r\" Likewise, gowernIn-t spending and full employment output are: Gmw = 2m and em = 1,5131] a} Suppose that the US end the Rat of the World are large open eeonomies. That is1 the sum of net exports in the US and the Rest of the World must be equal to zero. Solve for the equilibrium world interest rate. Note that I have assumed that net factor payments are equal to zero, meaning that CA = NX. h} Fill in the table with the correct equilibrium values. Be sure to show your -- work. Three different drugs are being compared for their effectiveness in treating a certain illness. The mean number of days before the patient is discharged from hospital under each treatment is summarised below, together with the sample size and the sum of squares of the observations: Treatment Sample size Sample mean Sum of squares A 10 264 B 6 310 84 (i) For these three treatments, calculate estimates for the: (a) overall mean (b) common underlying variance. [4] (ii) Perform an analysis of variance to show that real differences exist among the three treatments at the 1% level. [3] (iii) Show that the mean number of days before discharge under treatment A is significantly better than under treatment B. [3] (iv) The cost per day for treatments A. B and C are f7.50, f5.85 and f14.95 respectively. Given that it can also be shown that there are significant differences between each pair of treatments, briefly advise the hospital on which treatment it should use. [2] [Total 12]Three different drugs are being compared for their effectiveness in treating a certain illness. The mean number of days before the patient is discharged from hospital under each treatment is summarised below, together with the sample size and the sum of squares of the observations: Treatment Sample size Sample mean Sum of squares A 10 264 B 6 310 84 (i) For these three treatments, calculate estimates for the: (a) overall mean (b) common underlying variance. [4] (ii) Perform an analysis of variance to show that real differences exist among the three treatments at the 1% level. [3] (iii) Show that the mean number of days before discharge under treatment A is significantly better than under treatment B. [3] (iv) The cost per day for treatments A. B and C are f7.50, f5.85 and f14.95 respectively. Given that it can also be shown that there are significant differences between each pair of treatments, briefly advise the hospital on which treatment it should use. [2] [Total 12]