Do not type in dollar signs or round any of your answers. Solow Model. Suppose a country's production function is Y = K1/2L1/2. If capital depreciates at the rate of 4 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 aggregate output (Y) equal to 900 assuming the labor force is equal to 150 workers: savings rate = percent Given the savings rate calculated above, steady-state capital per worker (k*) is equal to output per worker (y*) is equal to , and consumption per worker (c*) is equal to

Do not type in dollar signs or round any of your answers. Solow Model. Suppose a country's production function is Y = K1/2L1/2. If capital depreciates at the rate of 4 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 aggregate output (Y) equal to 900 assuming the labor force is equal to 150 workers: savings rate = percent Given the savings rate calculated above, steady-state capital per worker (k) is equal to output per worker (y) is equal to , and consumption per worker (c*) is equal to

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Is the following statement true, false, or uncertain? According to the Solow growth model, an increase in the saving rate should lead to a decline in consumption per person in the long run.
Recent data shows that the aging population in many Asian economies is getting larger in their demographic structure. According to the life-cycle theory of saving, people save during their working age and dissave when they are retired; consequently, given that the working population is shrinking, a researcher worries that the national saving rate in many Asian economies most likely would decrease in the foreseeable future. Discuss the implication of the above-mentioned issue to economic growth under the framework of the Solow growth model.
4. Consider a Solow growth model where the saving rate is 0.5 and the production function is given by Y; = K°(^'L)'-«, where a = 1/3 and y = 1.02. In addition assume that the depreciation rate of capital is 8 = 0.01. Finally, assume that the capital stock at time 0 is such that the economy is on the balanced growth path from the beginning of time. Calculate the interest rate and the capital-output ratio.
Consider an economy characterized by a Cobb-Douglas production function Y = Y = AK "L¹-a, with A = E¹-a, and E grows at a rate ge. The economy is in steady state, with sustained growth. Consider the following two statements: (1) The capital-output ratio is constant; (2) The contribution of capital to output growth in a growth accounting exercise is zero. a. (1) and (2) are both false. b. (1) is true, but (2) is false. c. (1) and (2) are both true. d. (1) is false, but (2) is true.
Consider the Solow growth model where Y = F(K, L). Y is output, K is capital stock and L is the work force. Derive the steady state equilibrium condition of this model if depreciation rate is zero, s is the savings rate, and n is the labour force growth rate, and draw the diagram showing the equilibrium.
The output of an economy is characterized by a Cobb-Douglas production function with constant return to scale and an output elasticity with respect to capital equal to 0.3. Also given are the following parameters: 30% saving rate, 5% depreciation rate, 2% population growth rate, and the technology factor is 2. a). Find the capital-labour ratio, and also the output, consumption and investment on a per capita basis in the steady state equilibrium. b). Is a government policy that raises the saving rate to 40% socially desirable? Explain your answer with reference to a comparison of this new steady state equilibrium and the initial steady state equilibrium in a) above. c). If the initial capital-labour ratio is 30, is the economy operating efficiently in the sense that welfare cannot be improved? Explain concisely. What if the initial capital-labour ratio is 15? Again explain concisely.
Exercise 4: Growth and capital over-accumulation = Suppose two countries, A and B, with the same production function Y KaL¹-a. The value of a is 0.30, the growth rate of population is 2% and the depreciation rate is 5%. a) Show that with price-taking firms the share of labor must be 1 a. b) Compute the stock of capital, output and consumption per unit of labor in the steady state if the savings rates were 25% for country A and 35% for country B. c) Compare both economies to the Golden Rule. d) Explain what would happen to both countries if suddenly their savings rate became the Golden Rule savings rate.
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Explain why consumption per worker grows at a different rate than in Solow model II (with population growth)
Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Explain how the economy goes from one steady state to another.
Consider the following version of the Solow model where the saving line s% has the following shape (d is the depreciation rate and population growth is zero): sy/k k°. k a. How many steady states does this model have? Which of them are stable? Explain. Where will be the long run steady state if the economy starts at kf? And if it starts at k? (Hint: an equilibrium is stable if a small perturbation does not lead the economy to a different equilibrium). b. Is there convergence in this model? If so, absolute or conditional? Explain. c. How would your answers to (a) and (b) change if the economy experiences a one-time improvement in technology?
Problem 3: Solow Growth Mode Use the Solow model to evaluate this question. The production function is given as K/3 (AL)2/3= K/32/32/3 Given this information, answer the following questions. Yt How does capital evolve in this model? Write out the capital accumulation equation and explain. Solve for the steady state level of capital, output, and consumption.