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EXERCISE 1 COST MINIMIZATION, PART I Consider a firm with a Cobb-Douglas production function defined by...
Consider the Cobb-Douglas production function Q = 6 L^½ K^½ and cost function C = 3L...
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...
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?
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?
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 production is represented by the following Cobb-Douglas function: Q=K1/4L3/4 The rental rate, r, of...
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...
A firm operates with the production function Q = 25K0.5L0.4 and buys input K at $20...
A firm operates with the production function Q = 25K0.5L0.4 and buys input K at $20 a unit and input L at $8 a unit. To minimize the cost of producing 400 units of Q, the firm buys ?? units of L and ?? units of K. The value of Lagrange multiplier when Q=400 is ??. In this cost minimization problem, the second principal minor of Bordered Hessian is ?? If the firm wants to increase production by 2 units...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The economy has 27,000 units of capital and a labour force of 1,000 workers. a. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock. b. If the real wage can adjust to equilibrate labour supply and labour de- mand, what is the real wage? In this equilibrium, what are employment, output, and the total...
Consider the following Cobb-Douglas production function for a firm that uses labor hours (L), capital (K),...
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...
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...
3. Suppose a company's production is given by the Cobb-Douglas function: Q = 60L3K3 Where L...
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...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The economy has 27,000 units of capital and a labour force of 1,000 workers. a. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock. b. If the real wage can adjust to equilibrate labour supply and labour de- mand, what is the real wage? In this equilibrium, what are employment, output, and the total...
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...
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...
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