A firm uses inputs L and K to produce output Q and the production function is Q = 5LK. The firm is currently using inputs L = 6 and K = 8. If the firm reduces its capital purchase to only 2 units, how much additional K must it purchase to keep output constant? Group of answer choices 12 14 16 18
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A firm uses inputs L and K to produce output Q and the production function is Q = 5LK. The firm is currently using inputs L = 6 and K = 8. If the firm reduces its capital purchase to only 2 units, how much additional K must it purchase to keep output constant? Group of answer choices 12 14 16 18
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- 10)Given the production function f (L K) = L2 / 3. K1 / 3, where L is the working hours and K is the capital. assuming that the capital price is r = 4 euros and the price per hour of work is w = 27 euros and that all the factors of production are variable, what is the minimum cost of producing 10 units of product? Choose one: A) 260e B) 230e C) 240e D) 250e E) 270eYour automobile assembly plant has a Cobb-Douglas production function given byq=x0.4y0.6, where q is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Annual operating costs amount to an average of $28,000 per employee plus the operating budget of $365y. Assume that you wish to produce 3,000 automobiles per year at a minimum cost. How many employees should you hire? (Round your answer to the nearest employee.)x = Incorrect: Your answer is incorrect. employeesConsider a firm with a production function given by y = min{yax,, bx2}. This firm can sell its product for price p and buy its inputs at input costs w1 and w2. In this situation, the conditional input demand functions are given by: 2.2 y? x,(y,W1, W2) = а %3D x2(y, W1, W2) : %3D Find the following components of the solutions to the cost minimization and profit maximization problems, and show that the required feature holds. The sequence in which the features are listed is not related to the sequence in which they need to be found. 2.2.1 The minimum cost function 2.2.2 The supply function 2.2.3 The input demand functions 2.2.4 The maximum profit function 2.2.5 Show that the maximum profit function is convex in prices
- .(a) A firm has production function q(k,l) = k'/³1²/3, where k denotes the capital used and I denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and I that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, X*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that d* =Coca cola uses labour(L) and capital (k) in its production process. It estimates that the production function facing it is given by Q= K0.5 L0.5. The company can sell a bottle of coke at GH4. The cost of a machine is GH3 and that of Man- hour is GH5. The firm's total cost if production at the end of production is expected to be GH 3000. Required: Determine The optimal level of capital and labour usage The firm’s firm’s profit at the optimal levels of capital and labour usage The firm’s elasticity of output with respect to labour and capital and interpret itA Cobb-Douglas production function for new company is given by ?(?, ?) =?³/⁵ ?²/⁵ where K represents the units of capital and L represents the units of labor. Suppose units of labor and capital cost $200 and $100 each respectively. If the budget constraint is $30,000, find the maximum production level for this company.
- a) Given that a firm has a production technology, y= (X² + X²)², derive the MRTS12Question 1 Suppose that a certain factory output is given by the Cobb-Douglas production function Q(K, L) = 60K¹/³12/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory's output. If a unit of labour costs $100, unit of capital $200, and $200,000 is budgeted for production (e) Determine how many units should be expended on labour and how many units should be expended on capital in order to maximize production. (f) What is the maximum production level? (g) Use the bordered Hessian to prove that the level of production is indeed maximized.A firm is able to adjust both L and K and has a production function q = KL, where K is the amount of capital and L is the amount of labor it uses as inputs. The cost per unit of capital is r and the cost per unit of labor is w. The (conditional) demand for capital (also known as the optimal level of capital) is given by: O qwr O the square root of qr/w O qw/r O q/wr O the square root of qw/r
- Coca cola uses labour(L) and capital (k) in its production process. It estimates that the production function facing it is given by Q= K0.5 L0.5. The company can sell a bottle of coke at GH4. The cost of a machine is GH3 and that of Man- hour is GH5. The firm's total cost if production at the end of production is expected to be GH 3000. Required: Determine The expression for the firm's marginal product of capital The expression for the firm's marginal product of labour The nature of the returns of the poductionCoca cola uses labour(L) and capital (k) in its production process. It estimates that the production function facing it is given by Q= K0.5 L0.5. The company can sell a bottle of coke at GH4. The cost of a machine is GH3 and that of Man- hour is GH5. The firm's total cost if production at the end of production is expected to be GH 3000. Required: Determine The expression for the firm's marginal product of capital The expression for the firm's marginal product of labour The nature of the returns of the poduction The optimal level of capital and labour usage The firm’s firm’s profit at the optimal levels of capital and labour usage The firm’s elasticity of output with respect to labour and capital and interpret itA U.S. electronics firm is considering moving its production abroad. Its production function is: q=L = L 0.50 0.50 (based on Hsieh, 1995), so MPL = 0.5q/L and MPK = 0.5q/K. In the United States, w=$10=r. At its Asian plant, the firm will pay a 10% lower wage and a 10% higher cost of capital: w* = $9.09 and r* = $11.00. What are L and K and what is the cost of producing q= 100 units in both countries? (for all responses, enter a real number rounded to two decimal places) In the U.S., L is 100, K is 100, and the cost of production is $ 2000 In Asia, Lis