6. Consider the Solow model discussed in class. Consider a population growth rate increase from n to n'. Show graphically what happens to capital per worker (k) and output per worker (y).
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- The Solow Growth Model is an exogenous model of economic growth that analyzes changes in the level of output in an economy over time as a result of changes in the population growth rate, the savings rate, and the rate of technological progress. Consider the Solow model. a) Explain using a graph why there is a poverty trap in this model b)Describe how an economy such as one characterized by this model may break out of a poverty trap.B. The rate of technological progress rises. 2. Describe how, if at all, each of the following developments affects the break-even and actual investment lines in our basic diagram for the Solow model: a. The rate of population growth falls. B. The rate of technological progress rises. C. The production function is Cobb-Douglas, F(K,AL) = K" (AL)1-" , and capital"s share, ", rises. D. Workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before.If half of the capital decreased,what will be the new steady state level of capital per capita? Draw a picture.(Solow Model)
- 5. Use the simple Solow model, with no population growth. The formula for steady-state consumption per worker (c*) as a function of output per worker and investment per worker is: c * = f(k*) - δk* c * = f(k*) + δk * c * = f(k*) ÷ nk* c * = k* - f(k)*Q1) Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of population growth falls.(a) What happens to the balanced-growth-path values of capital per worker, output per worker, and consumption per worker? Sketch the paths of these variables as the economy moves to its new balanced growth path.(b) Describe the effect of the fall in population growth on the path of output (that is, total output, not output per worker).Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience and that there is labor-augmenting technological progress, with a production function Y =F(K,bN) where b denotes the number of units of "human capital" per worker, and bN is "efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1 + f ) b, where f is the growth rate in human capital. (c) In the real world, we usually consider education level as a proxy to human capital. To examine the theory, what suggestions can you make to growth economists? What are factors other than education can you think of that contribute to human capital?
- Suppose an economy described by the Solow model is in a steady state with population growth n of 1.8 percent per year and technological progress g of 1.8 percent per year. Total output and total capital grow at 3.6 percent per year. Suppose further that the capital share of output is 1/3. If you used the growth-accounting equation to divide output growth into three sources—capital, labor, and total factor productivity—how much would you attribute to each source?2b. “The Solow model shows that the higher the rate of population growth, the higher the steady-state levels of capital per worker and output per worker because more population means more worker so more output”. Do you agree with the statement? Graphically explainConsider the Solow model. Using suitable diagrams, compare the different dynamics for the levels and growth rates of capital per capita and output per capita following: (a) a new wave of immigration, (b) an increase in the saving rate, (c) a one-shot foreign investment which increase the size of the available stock of capital, (d) an important technological advance.
- 8 Suppose we are considering a Solow Model without technology progress. Population growth rate=0.03 The capital accumulation is sY-dK s=0.1, d=0.02 Please calculate the capital per capita under the steady state. A. 2 B. 4 C. 6 D. 8 E. 16 F. None of the above1. 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.Assume that the economy’s production function is Cobb Douglas so per-capita output is ? = k^α, where k is per-capita capital. Using the Solow growth model, explain the impact of the loss of capital on the growth rate of per-capita output in the years following the disaster.