Assume the production of a good, X, follows the Cobb-Douglas function Q=40K0.3 L0.7. If w= $10 and r= $4, use Excel's optimizer to minimize costs if Q=500. In Solver, select the “Evolutionary” method.
The Cob Douglas production function
is of the form,
Q = c.K^a*L^b
Where c is total factor productivity, k is capital, a is output
elasticity of capital, L is labor and b is output elasticity of
labor
TC = K*4+L*10
By minimizing TC and setting Q = 500, running the solver using
Evolutionary solver method we get, L=12.48 and K =12.49 units
Assume the production of a good, X, follows the Cobb-Douglas function Q=40K0.3 L0.7. If w= $10...
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...
A firm production is represented by the following Cobb-Douglas function: Q=K1/4L3/4 The rental rate, r, of capital is given by $100 and the price of labor w is $200. a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs? b. How much capital and labor should be used to produce 300 units? c. What is the minimum cost of producing 300 units? d. What is the additional cost of...
Assume the following Cobb-Douglas production function:
Assume the following Cobb-Douglas production function: Y = AK 0.4 20.6 If Y=12; K=8; and L=95, answer the following questions (SHOW ALL YOUR WORK): - 1. What is total factor productivity? 2. With your answer in (1), assume L=95 and estimate the production function with respect to K 3. Estimate the marginal product of capital and demonstrate diminishing marginal product of capital 4. Estimate real capital income 5. Estimate the share of capital income...
3. Suppose a company's production is given by the Cobb-Douglas function: Q = 60L3K3 Where L & K represent quantities of labor and capital. Suppose each unit of labor costs $25, each unit of capital costs $100, and the company wants to produce exactly Q=1920. a. Use the method of Lagrangian Multipliers to find the quantity of Land K that meet production requirements at the lowest cost. (5 pts) b. Show that the values found in part (a) satisfy the...
Assume a Cobb-Douglas production function F(KL) = Kal1-a with 0 < x < 1, which means f(k) = k«. (f) [4 marks] Does the saving rate SGR needed for the Golden rule rise, remain the same, or fall when climate change increases 8? Explain your argument.
The Cobb-Douglas production function is given as: Q = AK1-aLa Where 0<a<1, a = .8, K =4 is the amount of capital, and L=16 is the number of unit of labor, and A = 12 is the measure of TECHNOLOGY INDEX a) Find the real wage of labor (marginal product of labor), W/P, (b) Find rate of return of capital (marginal product of capital), and (c) Discuss the insights of your findings. (d) Why is there not a large amount...
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,...
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...
4. Given a Cobb-Douglas production function Q = 25020602. 1) Derive expressions for the average and marginal products of labour and capital; 2) Derive the partial elasticity w.t.r (with respect to) labour and capital.
Suppose a firm producing masks has a Cobb-Douglas production function Q = 3KL. Which of the following curves represent the firm's isoquant of producing 120 masks? 70 60 QA 50 QB 40 K Qc 30 QD 20 10 o 10 11 9 2 3 5 4 6 OQA OQв ООс OQD