a)
To describe: The steady state values of capital-labor ratio, output per worker and consumption per worker is to be calculated.
a)
Answer to Problem 5NP
The steady-state values are −
Capital-labor ratio =
Output per worker =
Consumption per worker =
Explanation of Solution
Given that −
Output per worker =
Consumption per worker =
Capital stock per worker =
When the all above values of economy is constant then it is known as steady state condition.
The following equation will be used to represent the steady state value of the capital-labor ratio −
Given values −
s = 0.3
n = 0.05
d = 0.1
Put the above values in Equ (1) −
Divide the above equation by
Square on both sides −
Now, the capital-labor ratio = 36
The output per worker is calculated by using the following equation −
Now, put the calculated value in above equation −
Now, the steady state value for the output per worker = 18
The following equation will be use to represent the consumption per worker −
Also given that −
Population growth rate, n = 0.05
Depreciation rate, d = 0.1,
Now, put the given and calculated values in Equ (2) −
The consumption per worker,
Introduction:
The ratio between capital and labor is known as capital-labor ratio and the ratio between the output and labor is known as output per worker.
b)
To describe: The steady state values of capital-labor ratio, output per worker and consumption per worker is to be calculated with saving rate 0.4 instead of 0.3.
b)
Answer to Problem 5NP
The steady-state values are −
Capital-labor ratio =
Output per worker =
Consumption per worker =
Explanation of Solution
Given values −
s = 0.4
n = 0.05
d = 0.1
The following equation will be used to represent the steady state value of the capital-labor ratio −
Now, put the given values in above Equ (1) −
Divide the both side of above Equ by
Square both sides −
The capital − labor ratio =
The output per worker is calculated by using the following equation −
Now, put the calculated value in above equation −
Now, the steady state value for the output per worker = 24
The following equation will be use to represent the consumption per worker −
Also given that −
Population growth rate, n = 0.05
Depreciation rate, d = 0.1,
Now, put the given and calculated values in Equ (2) −
The consumption per worker,
Introduction: The ratio between capital and labor is known as capital-labor ratio and the ratio between the output and labor is known as output per worker.
c)
To describe: The steady state values of capital-labor ratio, output per worker and consumption per worker is to be calculated with 0.8 population growth rate.
c)
Answer to Problem 5NP
The steady-state values are −
Capital-labor ratio =
Output per worker =
Consumption per worker =
Explanation of Solution
Given values −
s = 0.4
n = 0.08
d = 0.1
The following equation will be used to represent the steady state value of the capital-labor ratio −
Now, put the given values in above Equ (1) −
Divide the both side of above Equ by
Square both sides −
The capital − labor ratio =
The output per worker is calculated by using the following equation −
Now, put the calculated value in above equation −
Now, the steady state value for the output per worker = 15
The following equation will be use to represent the consumption per worker −
Also given that −
Population growth rate, n = 0.08
Depreciation rate, d = 0.1,
Now, put the given and calculated values in Equ (2) −
The consumption per worker,
Introduction:
The ratio between capital and labor is known as capital-labor ratio and the ratio between the output and labor is known as output per worker.
d)
To describe: The steady state values of capital-labor ratio, output per worker and consumption per worker is to be calculated with following production function −
d)
Answer to Problem 5NP
The steady-state values are −
Capital-labor ratio =
Output per worker =
Consumption per worker =
Explanation of Solution
Given values −
s = 0.3
n = 0.05
d = 0.1
The following equation will be used to represent the steady state value of the capital-labor ratio −
Now, put the given values in above Equ (1) −
Divide the both side of above Equ by
Square both sides −
The capital-labor ratio =
The output per worker is calculated by using the following equation −
Now, put the calculated value in above equation −
Now, the steady state value for the output per worker = 32
The following equation will be use to represent the consumption per worker −
Also given that −
Population growth rate, n = 0.05
Depreciation rate, d = 0.1,
Now, put the given and calculated values in Equ (2) −
The consumption per worker,
Introduction: The ratio between capital and labor is known as capital-labor ratio and the ratio between the output and labor is known as output per worker.
Want to see more full solutions like this?
- 1. A country has the per-worker production function: Yt = 6k/3 where y, is output per worker and k, is the capital-labor ratio. The depreciation rate is 0.1 and the population growth rate is 0.1. The saving function is S; = 0.1Y, where S, is total national saving and Y, is total output. a) What is the steady-state value of capital-labor ratio? b) What is the steady-state value of output per worker? c) What is the steady-state value of consumption per worker? Answer: 2. What happens in the steady state to the capital-labor ratio, output per worker, and consumption per worker when each of the following events occur? You should assume that the steady-state capital-labor ratio is below the Golden Rule level. k y a) Productivity falls b) Population growth falls c) The saving rate falls d) The depreciation rate fallsarrow_forwardSuppose that the per-worker production function for an economy is given by y = 10k°3. The depreciation rate is 14%, the savings rate is 23%, and the growth rate of labour hours is 8%. a. The steady-state capital stock per worker for this economy is (Round to two decimal places as needed.)arrow_forwardPopulation Growth and Technological Progress – Work It Out PLEASE WRITE ANSWERS CLEARLY An economy has a Cobb-Douglas production function: Y = K“(LE)'-a The economy has a capital share of 0.30, a saving rate of 42 percent, a depreciation rate of 4.00 percent, a rate of population growth of 5.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = y* = marginal product of capital =arrow_forward
- Question 2 A country has the following per-worker production function Yt = 5k0.5 Where yt is output per worker and kɩ is the capital-labor ratio. The depreciation rate is 0.2 and the population growth rate is 0.05. The saving function is St = 0.2Yt Where S, it the total national saving and Y, is total output. 1.1 Derive the steady-state values of the capital-labor ratio, output per worker, consumption per worker, and investment per worker? 1.2 Show your results on the Solow diagram. 1.3 What is the long-run balanced growth in total output and capital? 1.4 What is the long-run balanced growth in output per worker and capital per worker? 1.5 Explain the difference between capital deepening and capital widening. 1.6 Suppose the economy begins with a level of k less than k*. As k moves toward k*, is w (a wage for each unit of labor) growing at a rate greater than, less than, or equal to its growth rate on the balanced growth path? 1.7 Can this model generate sustained economic growth in…arrow_forward4.If population growth rate is 0.03, and the depreciation rate is 0.2, then in order to maintain the steady state capital-labor ratio equal to the amount found in Qs. 2, what would be the investment per worker?arrow_forwardIf the share of GDP used for capital goods is 0.08, the growth rate of productivity is 0.09, the growth rate of population is 0.02, the depreciation rate is 0.02, the initial capital/output ratio is 3.75, and the elasticity of GDP with respect to capital is 0.1, then what is the growth rate of the GDP per capita? Use three decimal places.arrow_forward
- Why do large differences in capital per worker lead to relatively small differences in predicted GDP across countries? Workers exert more effort when they have less capital Capital has a high depreciation rate 4 O The exponent on capital in the production function is much lower than one O Capital is not an input in productionarrow_forwardIn Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been in a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of…arrow_forwardIn Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been in a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of…arrow_forward
- Assume that a country's per-worker production is y = k1/2, where y is output per worker and kis capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10) 2 andthere is no population growth or technological change.a. If the saving rate (s) is 0.4, what are capital per worker, production per worker, andconsumption per worker in the steady state?b. Solve for steady-state capital per worker, production per worker, and consumption perworker with s = 0.6.c. Solve for steady-state capital per worker, production per worker, and consumption perworker with s = 0.8.d. Is it possible to save too much? Why?arrow_forwardWhy Capital does not Flow from Rich to Emerging Countries? We assume that the production function in country i is 1 1 2 Yi = A ² k², (1) where y, and ki are output and capital per capita, respectively, in country i, and A is a measure of technology in country i. (a) Calculate the marginal product of capital (MPK) denoted by Ri in country i. (b) Express the MPK in terms of output per capita, yi, i.e., eliminate ki from Ri by using the production function (1). (c) We consider two countries, indexed by i 1 and i 2, whose production function is described by (1). Both are assumed to have the same level of productivity, i.e., A₁ A2. We assume y2 50y₁. Calculate the ratio R₁/R₂. (d) We keep assuming that y2 50y1, but now we assume that A2 educational attainment is higher in country 2. Calculate the ratio R₁/R₂ under 10A₁ because these assumptions. FX = - (e) We keep assuming y2 50y₁ but now we consider that technology in country 1 is a function of technology of the more advanced country 2,…arrow_forwardda qaoudon Suppose that the production function is given by Y=05/K √N, where Y is output, K is capital, and N is the number of workers. The steady-state level of capital per worker in terms of the saving rate, s, and the depreciation rate, 6, is KIN= (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g. a superscript can be created with the character.) The steady-state level of output per worker in terms of the saving rate, s, and the depreciation rate, 6, is VIN= (Property format your expression using the tools in the palette.) The equation for steady-state consumption per worker in terms of the saving rate, s, and the depreciation rate, 6, is CIN=(Property format your expression using the tools in the palette.)arrow_forward
- Exploring EconomicsEconomicsISBN:9781544336329Author:Robert L. SextonPublisher:SAGE Publications, Inc