Please help me with my macroeconomics question

Chapter 6 - Problem 2 Consider an economy described by the following equations: Y = C+I+G+NX, Y = 5000, G = 1000, 7 = 1000, C = 250 + 0.75(Y - T). / = 1000 - 50r, NX = 500 -5006, r=r = 5 a. In this economy, solve for national saving, investment, the trade balance, and teh equilibrium exchange rate. b. Suppose now that G rises to 1250. Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find. c. Now suppose that the world interest rate rises from 5 to 10 percent, (G is again 1000). Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find. Chapter 6 - Problem 11 A Case Study in this chapter concludes that if poor nations offered better production efficiency and legal protections, the trade balance in rich nations such as the United States would move toward surplus. Let's consider why this might be the case. a. If the world's poor nations offer better production efficiency and legal protection, what would happen to the investment demand function in those countries? b. How would the change you describe in part (a) affect the demand for loanable funds in world financial markets? c. How would the change you describe in part (b) affect the world interest rate? d. How would the change you describe in part (c) affect the trade balance in rich nations?Chapter 8 - Problem 1 Country A and country B both have the production function Y = 10.5105. a. Does this production function have constant returns to scale? b. What is the per-worker production function, y=f(k)? C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and 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. 1. Suppose that both countries start off with a capital 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 or computer spreadsheet to show how the capital stock per worker will evolve over time in both countries. For each year, calculate income per worker and consumption per worker. How many years will it be before the consumption in country B is higher than the consumption in country A. Chapter 8 - Problem 5 Draw a well-labeled graph that illustrates the steady state of the Solow model with population growth. Use the graph to find what happens to steady-state capital per worker and income per- worker in response to each of the following exogenous changes. a. A change in consumer preferences increases the saving rate. b. A change in weather patterns increases the depreciation rate. C. Better birth-control methods reduce the rate of population growth. . A one-time, permanent improvement in technology increases the amount of output that can be produced from any given amount of capital and labor. Chapter 8 - Problem 6 Many demographers predict that the United States will have zero population growth in the twenty-first century, in contrast to average population growth of about one percent per year in the twentieth century. Use the Solow model to forecast the effect of this slowdown in population growth on the growth of total output and the growth on output per person. Consider the effects both in the steady state and in the transition between the steady states. Chapter 9 - Problem 3 Proof each of the following statements about the steady state of the Solow model with population growth and technological progress. a. The capital-output ratio is constant. b. Capital and Labor each earn a constant share of an economy's income. (Hint: Recall the definition MPK=f(k+1)-f(k)). c. Total capital income and total labor income both grow at the rate of population growth plus the rate of technological progress, n+g. d. The real rental price of capital is constant and the real wage grows at the rate of technological progress g (Hint: the real rental price of capital equals total capital income divided by the capital stock and the real wage equals total labor income divided by the labor force) Chapter 9 - Problem 5 The amount of education the typical person receives varies substantially among countries. Suppose you were to compare a country with a highly educated labor force and a country with a less educated labor force. Assume that education affects only the level of efficiency of labor. Also assume that the countries are otherwise the same: They have the same saving rate, the same depreciation rate, the same population growth rate, and the same of technological progress. Both countries are described by the Solow model and are in their steady states. What would you predict for the following variables? a. The rate of growth of total income. b. The level of income per worker. c. The real rental price of capital. d. The real wage.3. The chapter analyzes Fisher's model for the case in which the consumer can save or borrow at an interest rate of r and for the case in which the consumer can save at this rate but cannot borrow at all. Consider now the intermediate case in which the consumer can save at rate rs and borrow at rate 7, where rs