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3. Suppose a company's production is given by the Cobb-Douglas function: Q = 60L3K3 Where L...
Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, ...
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...
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production...
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 has a Cobb-Douglas production function q = AKL, where K denotes capital, L is...
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...
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of...
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of workers and k is units of capital.mrtslk is k/l. the wage rate is $900 per week, and a unit of capital costs $400 per week. what is the least cost input combination for producing 675 units of output?
Problem 1. Suppose that production function for the corporate sector is well presented by the Cobb-Douglas...
Problem 1. Suppose that production function for the corporate sector is well presented by the Cobb-Douglas production function: Y = K0.3L0.7 With this production function: MPL(K, L)=0.7K0.3L0.3 and MPK(K, L)=0.3K0.7L0.7 a) Suppose the capital stock of the firm is K¯ =10. Show that the demand for labor is given by: b) Find the amount of labor demanded for W P = 0.1,W P = 0.3, W P = 0.5, W P = 0.7 and W P = 0.9. Plot the...
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of...
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of workers and k is units of capital.mrtslk is k/l. the wage rate is $900 per week, and a unit of capital costs $400 per week. assuming no fixed cost, what is the firm's total cost of production if it uses least-cost input combination to produce 675 units of output?
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
A “Cobb–Douglas” production function relates production (Q) to factors of production, capital (K), labor (L), and...
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,...
The Cobb-Douglas production function is given as: Q = AK1-aLa Where 0<a<1, a = .8, K...
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...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
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...
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...
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
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