Macroeconomics (Fourth Edition)
4th Edition
ISBN: 9780393603767
Author: Charles I. Jones
Publisher: W. W. Norton & Company
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Chapter 5, Problem 3RQ
To determine
The economic meaning of the vertical gap between the investment curve and
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What is the economic meaning of the vertical gap between the investmentcurve and the depreciation curve in the Solow diagram?
Explain in detail the difference between endogenous variables and Exogenous variables. Use an example for each from the Solow mode
Consider a basic Solow-Swan model. Suppose the aggregate production function is Y - AKL
and that A=1, the depreciation rate is = 0.06 and the saving rate is s = 0.12. In steady state,
d
which of the following is TRUE?
O Output per worker is 2.00 and consumption per worker is 0.24
O Output per worker is 2.00 and consumption per worker is 1.76
O Output per worker is 1.68 and consumption per worker is 1.48
O Qutput per worker is 1.68 and consumption per worker is 1.12
Chapter 5 Solutions
Macroeconomics (Fourth Edition)
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- Suppose a Solow economy is initially at its steady state k∗, and suddenly is hit by a decrease in the depreciation rate δ, from δ to δ1. This change does not alter any of the other exogenous parameters in the model Depict this situation in a graph What happens to steady state level of capital per capita in this situation? What happens to the level of capital per capita over time? Depict this in a graph and explain intuitively.arrow_forwardIn the Solow model with technological progress, suppose that the rate of depreciation is 10% per year, the population growth rate is 2% per year, and the growth rate of technology is 3% per year. Which of the following represents the level of investment needed to maintain a constant capital stock (K) in this economy? 0.02K 0.03K 0.05K 0.10Karrow_forwardAssume that in the Solow model the aggregate production function takes the Cobb-Douglas form: Y = 8K“ (AL)'-a where Y is output, K is capital input, L is labour input, and A is the level of labour- augmenting technical progress. Capital grows through investment but also decays due to wear and tear at a constant rate per period. Assume that A is growing at the exogenous rate g, that L is growing at the exogenous raten, and that households save a constant proportion s of their income. There is perfect competition in the markets for output and the inputs. a. Find the steady-state level of output per unit of labour in terms of A and the parameters of the model. What is the growth rate of total factor productivity (TFP) in terms of the parameters of the model? b. Find the steady state level of the capital-output ratio (k/y) in terms of the parameters of the model. c. Write down an expression for consumption per effective labour (c*) in the long run and show how it is affected by an increase…arrow_forward
- Consider an economy described by the textbook Solow model with the following Cobb-Douglas production function: Y = ÅK°L*. %3D where a The economy is producing 100 units of output and the productivity parameter is equal to 1. the depreciation rate is 6%, the investment rate is 24%, and there are 64 workers, the growth rate of total output Y, is positive and the economy is converging to to its steady-state output per capita of 100 units. Question 6 total depreciation exceeds gross investment, the economy is below its steady state and outout per person is growing at a positve rate Question 7 Starting from steady state a permanent decrease in the rate of depreciation in the Solow model causes output per capita to Select) in the short nun in the long run the growth rate of the economy Sekectarrow_forward10. In the steady state in a Solow model including effective/productive workers, the growth of output per effective worker is: G 0 N+G Depreciation rate Savings ratearrow_forwardUse 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.arrow_forward
- Problem 1. Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, 8, and a population growth rate, n. The production function is given by Y = AK + BK³3/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb- Douglas production function. • (i) Does this production function exhibit constant returns to scale? Explain why. (ii) Does it exhibit diminishing returns to physical capital? Explain why. • (ii) Express output per person, y =- -, as a function of capital per person, k =. • (iv) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (v) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. • (vi) Suppose first that sA 8 + n. Draw the savings and depreciation curves, making sure to label the steady state level of capital(if it exists). Under these…arrow_forwardProblem 1. Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, 8, and a population growth rate, n. The production function is given by Y = AK + BK³3/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb- Douglas production function. • (i) Does this production function exhibit constant returns to scale? Explain why. (ii) Does it exhibit diminishing returns to physical capital? Explain why. • (ii) Express output per person, y =- as a function of capital per person, k =. • (iv) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (v) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. • (vi) Suppose first that sA 8 + n. Draw the savings and depreciation curves, making sure to label the steady state level of capital(if it exists). Under these circumstances,…arrow_forwardProblem 1. Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, 8, and a population growth rate, n. The production function is given by Y = AK + BK³3/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb- Douglas production function. • (i) Does this production function exhibit constant returns to scale? Explain why. • (ii) Does it exhibit diminishing returns to physical capital? Explain why. (iii) Express output per person, y =, as a function of capital per person, k =. • (iv) Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?) (v) Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model. • (vi) Suppose first that sA 8 + n. Draw the savings and depreciation curves, making sure to label the steady state level of capital(if it exists). Under these…arrow_forward
- Use the Solow model below to answer the question. Y Y3 Y₂ Y₁ K₁₁ K₂ K3 Y = Af(K,H) dk SY K Suppose that Y₁ is 1,475, Y₂ is 6,184, and Y3 is 10,992. The savings rate for this economy is 30% and the depreciation rate is 8.2%. If this economy is currently at a GDP of 1,475, what is the smallest amount of foreign aid which would move the economy up to a GDP of 10,992? Assume that all foreign aid becomes investment. Round your final answer to two decimal places.arrow_forwardConsider an economy as per solow model, with a Cobb-Douglas production function with constant returns to scale with respect to K and L. Moreover, you know that the economy is producing 80 units of total output and the productivity parameter is equal to 1. If the depreciation rate is 10%, the investment rate is 10%, and there are 75 workers, the growth rate of GDP per person ____________. a) is equal to zero because the economy is at its steady state b) is negative because the economy is above its steady state c) is positive because the economy is below its steady state d)cannot be determinedarrow_forwardExplain the Solow Model when there is an improvement of technologyarrow_forward
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