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Consider the following small open economy model with production. At dates 1 and 2, the home country receives exogenous fixed endowments y1 and y2 respectively. The home country has access to the international capital market at a fixed interest rate r* at which it can save or borrow. Let the net saving of the home country be s1 and its consumption stream in two periods be given by
c1 and c2 respectively.the following maximization problem:
Max ln c1 + ln c2
s.t. C1 + S1 = Y1
C2 = C1(1+r*) + Y2
Derive optimal consumption and current account functions and carefully interpret it in terms of a two-period Fisherian graph.
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- Consider the following small open economy model with production. At dates 1 and 2, the home country receives exogenous fixed endowments y1 and y2 respectively. The home country has access to the international capital market at a fixed interest rate r* at which it can save or borrow. Let the net saving of the home country be s1 and its consumption stream in two periods be given by c1 and c2 respectively.the following maximization problem: Max ln c1 + ln c2 s.t. C1 + S1 = Y1 C2 = C1(1+r*) + Y2 Derive optimal consumption and current account functions and carefully interpret it in terms of a two-period Fisherian graph. Refer to (a). Suppose the home country also has an access to an investment technology which means that if it invests k units at date 1, it produces y2 = Aka units of output in the next period where A >0 and 0 < a< 1 . Modify budget constraints for (a)Derive the optimal investment and saving rules for this economy assuming the same logarithmic utility function…Consider the following small open economy model with production. At dates 1 and 2, the home country receives exogenous fixed endowments y1 and y2 respectively. The home country has access to the international capital market at a fixed interest rate r* at which it can save or borrow. Let the net saving of the home country be s1 and its consumption stream in two periods be given by c1 and c2 respectively.the following maximization problem: Max ln c1 + ln c2 s.t. C1 + S1 = Y1 C2 = C1(1+r*) + Y2 (a)Derive optimal consumption and current account functions and carefully interpret it in terms of a two-period Fisherian graph. Refer to (a). Suppose the home country also has an access to an investment technology which means that if it invests k units at date 1, it produces y2 = Aka units of output in the next period where A >0 and 0 < a< 1 . Modify budget constraints for (b)Derive the optimal investment and saving rules for this economy assuming the same logarithmic utility…Assume that the production function for a country is given by Y = √K and annual investment is given by the function I = √ × Y where 0.320, and that the yearly depreciation rate is 5.33%. Suppose that this year, the output in the country is 1, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking. years
- Do not type in dollar signs or round any of your answers. Suppose a country's production function is Y = K1/2L1/2. If capital depreciates at the rate of 5 percent each year and the population grows at the rate of 1 percent each year, calculate the savings rate that would lead to a steady-state equilibrium value for capital per worker of 100 machines: savings rate = percent In this steady-state equilibrium, output per worker is and consumption per worker isThe 2020 Economic Report of the President on your country contained the following statements: "Devoting a large share of national output to investment would help restore rapid productivity growth and rising living standards in this period of COVID-19." Do you agree with this claim? Explain.Use the Solow model below to answer the question. Y 3 Y ₂ 2 Y₁ K₁ K₂ K3 Y = Af (K, H) dk SY K Suppose that Y₁ is 1,436, Y₂ is 6,076, and Y3 is 11,238. The savings rate for this economy is 11% and the depreciation rate is 5.1%. If this economy is currently at a GDP of 1,436, what is the smallest amount of foreign aid which would move the economy up to a GDP of 11,238? Assume that all foreign aid becomes investment. Round your final answer to two decimal places.
- The Harrod - Domar growth model is a simple macroeconomic growth model that states that investment is proportional to change in income:/= 3.5(Y, -Y.,), where I, is the investment at the time - period (in $ million) Y, and Y., are the income at the time - period and -1, respectively (in $ million) 3.5 is the capital - output ratio (constant). The savings at the time-period / depends on the proportional share of income: S = 0.25Y, where S, is the saving at the time - period / ( in $ million) 0.25 is the average saving rate (constant). Investment and savings must be equal in any period so that the equilibrium condition can be written as I = S, Using the assumptions above answer the following questions: (a) Write the equilibrium equation as a difference equation in Y, using the equilibrium condition provided above. (b) Solve the difference equation that you derived in (a), assume that given Y = $9.5 million. (c) Comment on the stability of the system. 0In Wonderland production per worker (y) depends on capital per worker() such the y=10vk. Every year 15% of the capital stock depreciates, while workers in Wonderland save 10% of their income. Every year the population grows ratas te of 3% (c) The country of Neverland is identical to Wonderland in terms of output per worker, the savings rate, the depreciation rate and population growth. They differ in one respect: Wonderland has capital per worker of 10, whereas Neverland has capital per worker of 20. Which country experiences a higher growth rate of output per worker and how will their growth rates evolve over time?Consider the Production Function: Y=√K√N a) Derive the steady-state levels of output per worker and capital per worker in terms of the saving rate (s) and the depreciation rate.b) Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of the saving rate (s) and the depreciation rate.c) Suppose depreciation is 5% and savings rate is 10%. Calculate the steady-state output per worker.d) Now suppose the savings rate increases to 20%. What is the new steady-state output per worker?
- Assume a two-period small open economy model, where the national product is 50 in the current period, and 88 in the future period. The world real interest rate is 10% per period. The representative consumer has the following utility function: U(c,G,c’,G’) = ln(c+G) + ln(c’+G’). a) What are the optimal consumption plus government spending in the current and in the future period? What is the current account surplus? Show this in a diagram. b) Now, suppose that governments in the rest of the world impose a tax on lending to foreigners of 5%. Determine how this affects consumption plus government spending in the present and the future, and the current account surplus. Explain your results. c) Suppose that governments in the rest of the world still impose a tax on lending to foreigners of 5%. However, the national country found a huge reserve of oil and the current period income increased to 100. The Determine how this affects consumption plus government spending in the present and the…Country A and country B both have the production function Y= F(K,L)= K 1/2 L 1/2 Assume that neither country experiences population growth nor technological progress and that 5% of capital depreciates each year. Assume further that country A saves 10% of output each year and country B saves 20% of output each year. Using your answer from part (a) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker. (b) Suppose that both countries start off with a capital per stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator to show how the capital stock per worker will evolve over time in both countries. For each year, calculate income per worker and…An economy has 20 million workers in research and development, where their productivity is 0.004, and the level of technology is 6.75. The depreciation rate is 0.15, and the saving rate is 0.2. The per worker production function is y = Akl/3(1-a), and there are 180 million production workers. Show that, in equilibrium, the ratio of capital to output is constant.