ECON 255 Lecture Notes - Production Function, Technological Unemployment, Capital Accumulation

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sapphirellama714

13 Mar 2014

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The growth theory states that, by increasing the capital, k, and keeping other factors such as labor and technology constant, the marginal return will diminish. What happens to the equation: y/l = a(k/l, l/l) y = a: f(k) If we increase the inputs by the same constant number, the output will increase by the same amount too. The equation is y = a: f(k) which means income per capita depends on technology and capital per capita. Remember the graph for a production function with decreasing returns. Gross investment = s: a, f(k) Net investment = [s: a, f(k)] - k k is capital depreciation. The graph is income, y, against capital, k. Increase in saving ,s, and capital, k will shift the saving function upward. According to solow"s model: when technology expands, capital accumulation expands too. The belief that a labor-saving technology will render human labor obsolete if this is true, many people in today"s world will be unemployed.

Related Questions

Country A and country B both have the production function:

Y = F(K,L) = K^(1/3)L^(2/3).

a) Does this production function have constant returns to scale? Explain.

b) What is the per-worker production function, y = f(k)

c) Assume that neither country experiences population growth nor technological progress and that 20-percent of capital depreciates each year. Assume further that country A saves 10% of output each year and country B saves 30% of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker.

d) Suppose that both countries start off with a capital stock per worker of 1. What are the levels of income per worker and consumption per worker?

marooncrab607

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

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

ECON 255 Lecture Notes - Production Function, Technological Unemployment, Capital Accumulation

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