Macroeconomics
13th Edition
ISBN: 9781337617390
Author: Roger A. Arnold
Publisher: Cengage Learning
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Question
Chapter 17, Problem 6WNG
To determine
Change in production function and thereby change in the Long Run
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A country has a Cobb-Douglas production function given by: Y = AK0.5H0.1
If total factor productivity is 46, human capital is 1,828, and the capital stock is 2,736, what will
this country's GDP be?
Do not round until your final answer, when you may round to two decimal places.
Country A produces GDP according to the following equation: GDP
5K and has a capital
=
stock of 13,399. If the country devotes 13% of its GDP to producing or repairing investment goods,
how much is this country currently investing?
Rounds your answer to two decimal places.
The following graph shows a variety of possible production functions (PFs) in an imaginary economy, assuming constant levels of human capital and technology.
Because human capital and technology remain unchanged, each of these production functions represents a different level of the capital stock.
Fill in the table with the curve that corresponds to each of the capital stock levels described.
Levels of Capital Stock
This corresponds to which curve? (PF1, PF2, PF3)
Highest
Middle
Lowest
Fill in the blank:
The slope of the line connecting the origin to point B is __________ (options: flatter, steeper) than the slope of the line connecting the origin to point A, because the slope of such a line is equivalent to ___________ (options: productivity, the marginal physical product of labor, marginal cost).
Please answer the following question as soon as possible.
Thanks a lot!
Imagine we live in a classical world. Suppose that the production function is ? = ?^(1/2)?^(1/2), where L is the amount of labor and K is the amount of capital. The economy has 100 units of labor and 100 units of capital.
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- Do not use chatgpt.arrow_forward0.5 0.5 Given a production function: Y = AK N If output grows at 5%, capital grows at 2% and the number of workers grows at 4%, then technology (or total factor productivity) grows at % ? (Answer in integer only, no decimal place.) Your Answer: Answer Given a production function: Y = AK0.5 N0.5. If output grows at 5%, capital grows at 2% and the number of workers grows at 4%, then technology (or total factor productivity) grows at %? (Answer in integer only, no decimal place.) Your Answer: Answerarrow_forwardAssume that production in an agricultural economy takes place according to Y = AT0.5 L0.5 where Y is output, A is technology, T is the amount of land and L is the labour force. This means that growth in this economy can be decomposed as follows. gy = ga +0.5g7 + 0.5gL, where gy is the growth rate of output, ga is the growth rate of technology, gT is the growth rate of land and gr, is the growth rate of the labour force. Assume that everyone in this economy works and so the labour force is equal to the population, which grows at a rate n > 0. Assume that the quantity of land is fixed. Answer all parts below: (a) Find an expression for the growth rate of per-capita income. (b) Using this equation, explain why the Malthusian Trap could be present in this economy. (c) Why might the Malthusian Trap not apply in this economy? Carefully explain under what conditions the Malthusian Trap will and will not apply in this economy.arrow_forward
- The graphs show the productivity curve for an economy. In the left graph show the effect of an increase in physical capital. Draw either a new productivity curve or an arrow along the curve showing the direction of change. In the right graph, show the effect of an increase in human capital. Draw either a new productivity curve labeled PC, or an arrow along the curve showing the direction of change. >>> Draw only the objects specified in the question. Real GDP per hour of labor (2009 dollars) O 32- Real GDP per hour of labor (2009 dollars) o 32- 28- PCo 28- PCo 24- 24- 20- 20- 16- 16- 12- 12- 8- 8- 4- Nextarrow_forwardThe following graph shows a variety of possible production functions (PFs) in an imaginary economy, assuming constant levels of human capital and technology. Because human capital and technology remain unchanged, each of these production functions represents a different level of the capital stock. Fill in the blank: The slope of the line connecting the origin to point C is __________ (options: flatter, steeper) than the slope of the line connecting the origin to point B, because the slope of such a line is equivalent to ___________ (options: productivity, the marginal physical product of labor, marginal cost).arrow_forwardBy choosing a point along the total physical product curve, physical output is Quantity Outputs y O Output= A f {Land, Labor, Capital, Technology, Entrepreneurship) where A represents the productivity of resources. Quantity Inputs 2.3 2.4 T.arrow_forward
- Suppose a country has a population of 120 people, a working-age population of 100 people, its labor force participation rate is 0.5 (50%), and the quantity of output is 60 units. Suppose that the production function of the economy is given by Y=2N, where Y represents the quantity of output and N represents the number of workers needed to produce the output. I know the answer is 0.4 but I don't understand how to get it. Thank you!arrow_forward10. As an alternative to the story of Robinson Crusoe, macroeconomists use the "aggregate production function," written as Y = AF(L,K,H,N), to link economy-wide output Y to the number of workers L, the stock of physical capital K, the stock of human capital H, the stock of natural resources N, and stock of technological knowledge A. With reference to this aggregate production function, please indicate whether each of the following statements is true or false. (a) The aggregate production function exhibits "constant returns to scale" if doubling the four inputs - workers L, physical capital K, human capital H, and natural resources N – while holding the stock of technological knowledge A fixed leads to a doubling of output. (b) The aggregate production function exhibits "constant returns to scale" if tripling the four inputs - workers L, physical capital K, human capital H, and natural resources N – while holding the stock of technological knowledge A fixed leads to a tripling of…arrow_forwardSuppose China has a production function of the form: GDP per worker = Tx (physical capital per worker)0.4 x (human capital per worker)0.6 Using this production function, which of the following statements are true? (Select all that apply) Unlike physical and human capital, technology (T) is not directly measured GDP per worker will increase if the labor force grows Output per worker will grow more if human capital increases by 1% than if physical capital increases by 1% None of the abovearrow_forward
- 11. In 2022 a country has the following data: GDP TFP Capital Labor Y A K L 400 1,100 20 The production function is Y = A¿KQ4 LQ.6 and the capital stock evolves according to Kt+1 growth rate of labor is 0.6% and TFP growth is 2%. Assume that population is equal to labor. Use the Solow model to calculate per-capita GDP in 2024 (two years later). (1 – d)Kt + It. The saving rate 22%, the depreciation rate is 10%, the (а) 498.32 (b) 504.42 (c) 516.96 (Right answer) (d) 548.87arrow_forwardUsing the production function Real GDP = T (L, K), define the term production function and describe what each of the variables (T, L, and K) represents. When graphed with Real GDP on the vertical axis and labor on the horizontal axis, which variable(s) can shift the production function and which variable(s) can cause a movement along the production function?arrow_forwardTrue or False A production function in "economics" summarizes the technological relationship between inputs and outputs.arrow_forward
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