๐Ÿท๏ธ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION โ†’
Log in
Economics
1
answer
0
watching
52
views

Consider an economy that uses two factors of production, capital (K) and labor (L), to produce two goods, good X and good Y. In the good X sector, the production function is X = 4KX0.5 + 6LX0.5, so that in this sector the marginal productivity of capital is MPKX = 2KX-0.5 and the marginal productivity of labor is MPLX = 3LX-0.5. In the good Y sector, the production function is Y = 2KY0.5 + 4LY0.5, so that in this sector the marginal productivity of capital is MPK = KY-0.5 and the marginal productivity of labor is MPLY = 2LY-0.5. Finally, let the total endowment of capital in this economy be K = 800, the total endowment of labor be L = 1200, the price of good X be PX = 3, and the price of good Y be PY = 6.

What is the equilibrium rental rate of capital and the equilibrium wage rate?

Watch
1
answer
0
watching
52
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Joshua Stredder
Joshua StredderLv10
28 Sep 2019

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share

Related textbook solutions

Principles of Economics
2nd Edition, 2017
Openstax
ISBN: 9781947172364
Principles of Macroeconomics
2 Edition,
Openstax
ISBN: 9781947172388
Principles of Microeconomics
2 Edition,
Openstax
ISBN: 9781947172340

Related questions

Consider an economy that uses two factors of production, capital (K) and labor (L), to produce two goods, good X and good Y. In the good X sector, the production function is X = 4KX0.5 + 6LX0.5, so that in this sector the marginal productivity of capital is MPKX = 2KX-0.5 and the marginal productivity of labor is MPLX = 3LX-0.5. In the good Y sector, the production function is Y = 2KY0.5 + 4LY0.5, so that in this sector the marginal productivity of capital is MPK = KY-0.5 and the marginal productivity of labor is MPLY = 2LY-0.5. Finally, let the total endowment of capital in this economy be K = 800, the total endowment of labor be L = 1200, the price of good X be PX = 3 and the price of good Y be PY = 6.

Suppose now that the price of good X relative to the price of good Y increases. What will happen to the quantities produced? Are workers better off or are capital owners better off? Explain.

Consider an economy with the following production function:

Y = AK.5L.5
The labor force is constant. The rate of depreciation is รŽยด = .1, the savings rate is s = .3.

a. Has this production function constant returns to scale? Why?

b. Write the production function in per worker variables.

c. Does the per worker production function have diminishing marginal returns to capital? Why?

d. Write the fundamental Solow equation in per worker variables.

e. Depict the steady state of this economy.

f. What are the growth rates of per worker output and capital in steady state?

g. Calculate the steady state level of capital, output, consumption and savings.

h. Redraw the initial equilibrium and show what happens when the savings rate increases. Do the growth

rates change?

i. Redraw the initial equilibrium and show what happens when there is a one time increase in population.

. Do the growth rates change?

j. Redraw the initial equilibrium and show what happens when there is a one time innovation that increases

productivity. Do the growth rates change?

k. Redraw the initial equilibrium and show what happens when there is constant productivity growth. Do

the growth rates change?

Consider an economy with the following production function:

Y = AK0.5 L0.5

The labor force is constant. The rate of depreciation is รŽยด=0.1, the savings rate is s=0.3

a) Has this production function constant returns to scale? Why?

b) Write the production function in per worker variables.

c) Does the per worker production function have diminishing marginal returns to capital? Why?

d)Write the fundamental Solow equation in per worker variables.

e) Depict the steady state of this economy.

f) What are the growth rates of per worker output and capital in steady state?

g) Calculate the steady state level of capital, output, consumption, and savings.

h) Redraw the initial equilibrium and show what happens when the savings rate increases. Do the growth rates change?

i) Redraw the initial equilibrium and show what happens when there is a one time increase in populatikon. Do the growth rates change?

j) Redraw the initial equilibrium and show what happens when there is a one time innovation that increases productivity. Do the growth rates change?

k) Redraw the initial equilibrium and show what happens when there is constant productivity growth. Do the growth rates change?

Weekly leaderboard

Home
Homework Help 3,900,000
Economics 400,000
Start filling in the gaps now
Log in