ECO 2143 Chapter Notes - Chapter 16: Capital Accumulation, Production Function, Pus

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lavenderoyster641

23 Feb 2020

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Labour force (l) = population x participation rate. Employment (n) = labour force (l) x (1 - unemployment rate (u)) Output per capita = employment /population x output per worker. The amount of capital determines the amount of being produced. The amount of output determines the amount of saving and investment, and thus the amount of capital being accumulated. Relationship between output and capital per worker y/n = f(k/n, 1) The function f represents the same relation between output and capital per worker as a function of f: f(k/n)= f(k/n,1) Constant population and constant participation rate imply that the labour force is constant. Constant labour force and constant employment imply that the level of employment n is constant. Output per worker (y/n) is an increasing function of capital worker (k/n) Where the function f represents the same relation between output and capital per worker as the function f:

Related Questions

Consider an economy described by the production function: Y = F(K,L) = K^0.4 L^0.6

a. What is the per-worker production function?

b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.

c. Assuming that the depreciation rate is 15% per year, make a table showing steady state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent, and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?

d. Use information from Chapter 3 to find the marginal product of capital. Add to your table, from part (c) the marginal product of capital net of depreciation for each of the saving rates. What does your table show about the relationship between the net marginal product of capita and steady-state consumption?

cyanbee395

Suppose the output per effective worker is production function is y=10k^1/2, where k equals the amount of capital per effective worker and the capital lasts an average of 10 years. Assume that the saving rate is 32 percent, the rate of growth of population is 4 percent and the rate of technological growth is 2 percent.

a) Solve for the steady state levels of capital per effective worker, output per effective worker, investment per effective worker and consumption per effective worker.

b) Calculate the growth rate of total capital income and the growth rate of total labor income at the steady state.(Hint: Capital and labor each earn a constant share of the economy's income ).

c) Prove, at the steady state, (i) the capital-output ratio is constant;(ii) the real wage grows at the rate of 2 percent.

d) Calculate all of the following at their Golden Rule levels: Capital per effective worker, output per effective worker, saving and investment per effective worker, and the consumption per effective worker.

e) Whether the saving rate is too high or too low?

crimsonhound401

Country A has the production function: Y = F (K, L) = K^0.5L^0.5

a. Express the production function in per worker terms. Thus, y = f (k) where y = Y/L and k=K/L

b. Suppose that both countries start off with a capital stock per worker of 2 (i.e. k = 2). What are the levels of income per worker and consumption per worker? Illustrate this on a graph

c. Assume that neither country experiences population growth or technological progress. Assume further that country A saves 10 percent of its output and the stock of capital depreciate by 5 percent each year. Using your answer from part (a) and the steady-state condition that investment equals depreciation

i. Find the steady-state level of capital per worker for each country.

ii. Find the steady-state levels of income (output) per worker and consumption per worker for each country

iii. Show on a graph the steady-state capital stock per worker, output per worker and consumption per worker for each country

d. State the condition for the Golden Rule and find the Golden Rule level of capital.

silverbeetle747

ECO 2143 Chapter Notes - Chapter 16: Capital Accumulation, Production Function, Pus

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