Consider the following Cobb-Douglas production function for a firm that uses labor hours (L), capital (K), and energy (E) as inputs:
Q = (0.0012L^0.45)(K^0.3)(E^0.2)
Consider the following Cobb-Douglas production function for a firm that uses labor hours (L), capital (K),...
A “Cobb–Douglas” production function relates production (Q) to factors of production, capital (K), labor (L), and raw materials (M), and an error term u using the equation: ? = ???1??2M?3? ?, where ?, ?1, ?2, and ?3 are production parameters. a) Suppose that you have data on production and the factors of production from a random sample of firms with the same Cobb–Douglas production function. How would you propose to use OLS regression analysis to estimate the above production parameters,...
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.
An economy has a Cobb-Douglas production function: Y = K°(LE)1-a The economy has a capital share of 0.25, a saving rate of 43 percent, a depreciation rate of 3.00 percent, a rate of population growth of 4.25 percent, and a rate of labor-augmenting technological change of 3.5 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. k* = 2.83 y* * = 1.30 =...
A firm has a Cobb-Douglas production function q = AKL, where K denotes capital, L is labor, and A, a, b, are constants. ginal returns to labor in the short run if its production function is 1. Sketch an isoquant line, write a mathematical formula for its slope, and provide an interpretation for its meaning. 2. On a separate graph, draw an isocost line, write a mathematical formula for its slope, and provide an interpretation for its meaning. 3. On...
Economic Growth II — Work It Out Question 1 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 47 percent, a depreciation rate of 4.00 percent, a rate of population growth of 2.25 percent, and a rate of labor-augmenting technological change of 2.5 percent. It is in steady state. a. At what rates do total output and output per worker grow? Total output growth rate: %...
Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $300 and each unit of capital costs $1,200. Further suppose a total of $120,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject...
Athens is an agricultural economy with the following Cobb-Douglas production function that uses land (x) and labor (L) as factor inputs to produce grain (V) as the real output. Y = 2x0.5 70.5 = 2/XVI Land stock is 25 units. Labor supply is 16 workers. Find real output per worker.
The Cobb-Douglas model of production in an economy is P(L, K) = b["Kl-a where • Pis the total production (the monetary value of all goods produced in a year) • L is the amount of labor (the total number of person-hours worked in a year) • K is the amount of capital invested (the monetary worth of all machinery, equipment, and buildings) • band a are constants which characterize the particular economy. Suppose that a manufacturer uses the Cobb-Douglas model...
Consider the Cobb-Douglas production function Q = 6 L^½ K^½ and cost function C = 3L + 12K. a. Optimize labor usage in the short run if the firm has 9 units of capital and the product price is $3. b. Show how you can calculate the short run average total cost for this level of labor usage? c. Determine “MP per dollar” for each input and explain what the comparative numbers tell in terms of the amount of labor...
7. Suppose a country's economy can be represented by the following Cobb-Douglas production function for per capita output: y -k where a -1/3. The depreciation and investment rates are respectively δ-5% and γ-26.21%. Suppose that capital per worker at period 0 is ko-12 What is the percent change in the level of income per worker between period 0 and period 1? (b) Increases by 5.4% (c) Decreases by 2.4% (d) Increases by 7.4% (e) Increases by 1.7%