4. Suppose an economy has capital share of half, a savings rate of 12%, depreciation rate...
4. Suppose an economy has capital share of half, a savings rate of 12%, depreciation rate of 2%, population growing at 2% and labor-augmenting technological change of 2% yearly.
a) What is the steady-state level of capital per efficiency unit of labor?
b) Is this economy at the golden rule level of savings/investment? Fully detail your reasoning.
c) If the economy decides to transition to Golden Rule, what will happen to consumption, capital per efficiency unit of labor and output per efficiency unit of labor in the short run and the long run?
d) Is it always better for an economy to have more rather than less output per efficiency unit of labor? Explain.
Homework Answers
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4. Suppose an economy has capital share of half, a savings rate
of 12%, depreciation rate...
2. Suppose that the US is initially at the golden-rule level of steady-state capital accumulation given...
2. Suppose that the US is initially at the golden-rule level of steady-state capital accumulation given the current rates of depreciation, technological progress, and population growth a. What does “the golden-rule level of steady-state capital accumulation” mean? b. When there are positive rates of depreciation, technological progress, and population growth, explain how each of the following variables is changing over time when the economy is at the golden-rule level of capital: i. Labor ii. Labor efficiency units iii. Total capital...
1. Assume that an economy described by a Solow model has a per-worker production function given...
1. Assume that an economy described by a Solow model has a per-worker production function given by y- k05, where y is output per worker and k is capital stock per worker (capital-labor ratio). Assume also that the depreciation rate δ is 5%. This economy has no technological progress and no population growth (n 0). Both capital and labor are paid for their marginal products and the economy has been in a steady state with capital stock per worker at...
An economy has a Cobb-Douglas production function: Y = Ka(LE)(1-a). The economy has a capital share...
An economy has a Cobb-Douglas production function: Y = Ka(LE)(1-a). The economy has a capital share of a third (means a= 1/3), a saving rate of 24 percent, a depreciation rate of 3 percent, and a rate of labor-augmenting technological change of 1 percent. It is in steady state. a. At what rate does total output, output per worker, and output per effective worker grow? b. Solve for steady state capital per effective worker, output per effective worker, consumption per...
Consider an economy in a steady state with population growth rate η, a rate of capital depreciati...
Consider an economy in a steady state with population growth rate η, a rate of capital depreciation δ , and a rate of technological progress g. a) At the steady state Δk = 0, where k equals capital per effective worker. What condition must be met for this to hold? Describe the condition in words as well as mathematical expressions. b) Describe in words what is maximized at the Golden Rule level of k. c) What mathematical condition must be...
1) Consider an economy having a Cobb Douglas production function, where the share of capital income...
1) Consider an economy having a Cobb Douglas production
function, where the share of capital income in total income is 1/2.
The depreciation rate is
, population growth rate is n = 0.02
2) Assume a general savings rate
, depreciation rate
and a production per worker
, where 0< <1.
Suppose the savings rate increases. What happens to the golden rule
level of capital?
3) Consider an economy that is described by the production
function
. The depreciation rate...
1. Solow growth model: a. Draw the steady-state equilibrium by drawing the savings line and the...
1. Solow growth model: a. Draw the steady-state equilibrium by drawing the savings line and the investment line. Show the steady-state values of savings, investment and capital per worker. b. On the same graph, also draw the output per worker (or per-worker production function) line. At the steady-state, mark the level of consumption per worker and savings per worker. c. What is the growth rate of yt, Ct, kt (per-worker variables, represented with an "upperbar" in class) in the steady-state?...
Solow growth model: 1. a. Draw the steady-state equilibrium by drawing the savings line and the...
Solow growth model: 1. a. Draw the steady-state equilibrium by drawing the savings line and the investment line. Show the steady-state values of savings, investment and capital per worker. b. On the same graph, also draw the output per worker (or per-worker production function) line. At the steady-state, mark the level of consumption per worker and savings per worker. c. What is the growth rate of yYt, Ct, kt (per-worker variables, represented with an "upperbar" in class) in the steady-state?...
Consider an economy described by the following production function: Y=K0.2L0.8 Suppose the depreciation rate is 10%....
Consider an economy described by the following production function: Y=K0.2L0.8 Suppose the depreciation rate is 10%. Explain what the golden rule level of capital is. For this economy, calculate the golden rule level of capital per worker, output per worker, depreciation per worker and consumption per worker. Plot the results obtained in (b) above. Calculate the saving rate that would give the golden rule level. Explain what happens to the consumption level if the saving rate departs from the one...
An economy has a Cobb-Douglas production function: Y = K"(LE)!-a The economy has a capital share...
An economy has a Cobb-Douglas production function: Y = K"(LE)!-a The economy has a capital share of 0.25, a saving rate of 40 percent, a depreciation rate of 3.00 percent, a rate of population growth of 0.75 percent, and a rate of labor- augmenting technological change of 2.0 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.
Consider an economy with the following production function zf(k ∗ ) = z (k ∗ )^0.5...
Consider an economy with the following production function zf(k ∗ ) = z (k ∗ )^0.5 1. Solve for golden rule capital per worker and optimal savings rate using the equation characterizing the best steady state. Then, you can back out optimal saving rate given that the best capital per worker. 2. Assume that we are at the steady state with a saving rate s1 < sgold. If the government increases the saving rate up to sgold through policies, what...
1. Assume that an economy described by a Solow model has a per-worker production function given by y- k05, where y is output per worker and k is capital stock per worker (capital-labor ratio). Assume also that the depreciation rate δ is 5%. This economy has no technological progress and no population growth (n 0). Both capital and labor are paid for their marginal products and the economy has been in a steady state with capital stock per worker at...
1) Consider an economy having a Cobb Douglas production
function, where the share of capital income in total income is 1/2.
The depreciation rate is
, population growth rate is n = 0.02
2) Assume a general savings rate
, depreciation rate
and a production per worker
, where 0< <1.
Suppose the savings rate increases. What happens to the golden rule
level of capital?
3) Consider an economy that is described by the production
function
. The depreciation rate...
1. Solow growth model: a. Draw the steady-state equilibrium by drawing the savings line and the investment line. Show the steady-state values of savings, investment and capital per worker. b. On the same graph, also draw the output per worker (or per-worker production function) line. At the steady-state, mark the level of consumption per worker and savings per worker. c. What is the growth rate of yt, Ct, kt (per-worker variables, represented with an "upperbar" in class) in the steady-state?...
Solow growth model: 1. a. Draw the steady-state equilibrium by drawing the savings line and the investment line. Show the steady-state values of savings, investment and capital per worker. b. On the same graph, also draw the output per worker (or per-worker production function) line. At the steady-state, mark the level of consumption per worker and savings per worker. c. What is the growth rate of yYt, Ct, kt (per-worker variables, represented with an "upperbar" in class) in the steady-state?...
An economy has a Cobb-Douglas production function: Y = K"(LE)!-a The economy has a capital share of 0.25, a saving rate of 40 percent, a depreciation rate of 3.00 percent, a rate of population growth of 0.75 percent, and a rate of labor- augmenting technological change of 2.0 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.
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