Explain th.e question given below.

translates into a greater increase in the capital stock. (Note: another way to interpret q, is as the inverse of the relative price between machinery and output: when q, is high, machinery is relatively cheaper). (a) Transform the model (the production function, the equations for consumption and investment, and the capital accumulation equation) in per-worker form. Be careful, this is the model with population growth, so your per-worker capital accumulation equation will have terms involving both k, and kit on the right-hand side. (b) Use your capital accumulation equation from part (a) to explain why there is no steady-state in this model. (Hint:draw a graph with the typical investment and depreciation curves). (c) Suppose that capital per worker k, grows at a constant rate (we do not know that yet, but we will make a guess). Divide the capital accumulation equation by , and use this assumption to prove that q,k, has to be constant over time. (d) Use the fact that the growth rate of be equals (o - 1)4% together with the result from part (c) to derive an expression for the growth rate of capital k It as a function of y and o only. How does the growth rate of investment-specific technology y affect the accumulation of capital? (e) Use the growth accounting equation: 2M =04* to derive the growth rate of output per worker How about the growth rates of consumption and investment per worker? Is there balanced growth in this economy? (f) In class we noted that in the data the ratio ~ is constant over time. Show that this fact is violated in this model. Is this a problem? (Hint: In the real world we measure capital and output in the same units (dollar values). The value of capital in terms of output in this model is : - show that this value grows at the same rate as output Y?).19:35 Gal pal 100% June_BM_A_II.pdf Q.2. (A) Madam Dora purchased a TV set for $550 and later decided to sell for $600. She sold it under the following hire purchase terms. An initial payment of 30% of the price and the balance paid in monthly equal installment at 10% simple interest per annum for 2 year. i. Calculate the amount paid every month ii Calculate the amount the buyer paid for the TV set. [3] ifi. Calculate the percentage profit Madam Dora made on the cost price of the TV set. (B) An investment requires an initial payment of 10,000 cedis and annual payments of 1000 [7] cedis at the end of each year of the years. Starting at the end of the eleventh year, the investment returns five equal annual payments of X. Determine the value of X to yield an annual effective rate interest over the 15-year period. (C) Let R denote a fixed regular payment made at the beginning of each year for a years. If R is invested at annual effective interest rate of i,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 a(Production function) Condsider a representitive rm with a. production function which is ( i) twice continuously dierentiable; (ii) exhibits positive and diminishing marginal product and (iii) has constant return to scale: Y = F(K, L) (1) Given the capital rental price R and the wage to, and the good price P is normalized to 1, the rm can choose K and L to maximize its prot: 1}1{acF(K, L) RK 10L (2)