ECON 2000 Lecture Notes - Lecture 7: Golden Rule, Production Function, Consumption Function

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amberchinchilla194

20 Aug 2016

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Ch 7 economic growth i: capital accumulation and population. Differences in income come from differences in capital, labor and technology. Solow growth model: theory of economic growth in per-capita income: shows how saving, population growth, and technological progress affect the level of an economy"s output and its growth over time. Supply & demand for goods determine the accumulation of capital: assumptions: labor force & technology is fixed. Supply of goods is based on the production function : y = f(k,l) Since the solow model assumes constant returns to scale: y/l = f(k/l, l/l, therefore, y = f(k) Shows that the amount of output per worker (y/l) is a function of the amount of capital per worker (k/l) Slope of the production function shows how much extra output a worker produces when given an extra unit of capital: mpk = f(k+1) f(k)

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

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

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

ECON 2000 Lecture Notes - Lecture 7: Golden Rule, Production Function, Consumption Function

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