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, which is a nonlinear function?
b) Based on your regression model, how to interpret ?, ?1, ?2, and
?3? Suppose that
you believe that the marginal return of labor is not a constant but
rather increases
when K increases. How could you modify your model to capture this
effect?
A “Cobb–Douglas” production function relates production (Q) to factors of production, capital (K), labor (L), and...
8.5. Consider the Cobb-Douglas production function Y = BILB2 KB where Y= output, L = labor input, and K = capital input. Dividing (1) through by K, we get (Y/K) = B.(L/KB2 KB2+B3-1 Taking the natural log of (2) and adding the error term, we obtain In (Y/K) = Bo + B2 In (L/K) + (B2+ B3 - 1) In K+u; (3) where Bo = In BI. a. Suppose you had data to run the regression (3). How would you...
Suppose you have data on output quantity, labor input, and capital input for all the firms (N-50) in a given industry. Suppose we believe that the production function is Cobb-Douglas: (a) Transform this equation into a linear model so that the parameters can be (b) What is the null-hypothesis for testing whether the production function is (c) Derive the 95% confidence interval for testing the null-hypothesis against estimated by OLS. Give an interpretation of Bi constant returns to scale? the...
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production technology exhibit increasing, constant, or decreasing returns to scale? (b) Suppose that the rental rate of capital is r = 1, the wage rate is w = 1, and the ?rm wants to produce Q = 3. In the long-run, what combination of L and K should they use? (It would be good to practice doing this with the Lagrangian, even if you can...
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) Determine the labor, capital and energy production elasticities. Suppose that worker hours are increased by 2 percent holding other inputs constant. What would be the resulting percentage change in output? Suppose that capital is decreased by 3 percent holding other inputs constant. What would be the resulting percentage change in output? What type of returns to scale appears...
1. The Cobb-Douglas production function Y = K51L2U is nonlinear. How would you estimate it using OLS?
The Labor Share and Data The production function is Cobb-Douglas, Y = F (K, L) = ĀKαL1−α with Ā = 1, depreciation of δ = 0.07 savings rate of 20% and population growth of 1%. 1. Suppose you have data on the total payments to labor and GDP, take the ratio of labor payments over GDP, (wL)/Y, and show the parameter in the model this corresponds to. To answer this, you will have to use the perfect competition assumption that...
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...
In a Cobb Douglas production function the marginal product of labor will increase if: a. the quantity of labor increases. b. the quantity of capital increases. c. capital's share of output increases. d. average labor productivity decreases.
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...
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...