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2. A company is producing toasters. Its production function is given by qf(L, K) KL2. The...
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. Wha...
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. What combination of labor and capital minimizes the cost of producing any output? To produce a given level of output q, how many units of L and K are needed? Express the optimal inputs choices L(q) and K(q) as functions of the level of output q
Suppose the firm's production function is given by q= F(K, L)= K2L with MPL=K2, MPK=2KL The...
Suppose the firm's production function is given by q= F(K, L)= K2L with MPL=K2, MPK=2KL The price per unit of capital is 10 and the price per unit of labor is 5. Find the cost minimizing quantity of labor to produce 500,000 units of output. Please round to the closest integer.
On short notice, Dr. Ford creates automatons according to the following production function: Q(L,K)=10L1/2. The wage...
On short notice, Dr. Ford creates automatons according to the following production function: Q(L,K)=10L1/2. The wage of a programmer such as Elsie is $100 per hour and the price of each automaton is $2000. His capital costs $10000 per hour total. A. Find the profit function. B. How many hours will Dr. Ford employ Elsie, if he is maximizing profits. C. Now consider the long run in which Dr. Ford can choose how much capital to employ according to the...
Afir's production engineers have estimated its production function as Q(KL) = 2K2/1/2 = 2-K L=2KL where...
Afir's production engineers have estimated its production function as Q(KL) = 2K2/1/2 = 2-K L=2KL where ' and 'L' represent the amounts of capital and labour, respectively, used in production each period, and 'Q' represents the amount of output produced each period. The firm pays a wage, w, for each person-hour of labour of $16. The rental rate of a machine-hour of capital, wk, is $100. What will be the firm's minimum cost of producing 10 units of output? What...
1-Home produces 2 goods X and Y . Home country has two factors of production, Labor...
1-Home produces 2 goods X and Y . Home country has two factors of production, Labor and Capital. All consumers at Home have preferences over two goods that can be represented by the utility function U(X,) =XY . The factor requirements per unit of output of the two goods are also fixed and they are shown in the following table: Good X Good Y Labour 1/3 2/3 Capital 2/3 1/3 Home country has 360 units of Labour and 600 units...
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and bo...
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and both wage and interest rates are equal to one, so that war- a) Given that the wage increases to 4. determine the elasticity of demand for labour at the new wage. Indicate whether the wage bill will increase or decrease as wage increases to 6. b) Find the linear demand function for labour...
A hamburger company produces hamburgers according to the production function Q = F(K,L) = 4K +...
A hamburger company produces hamburgers according to the production function Q = F(K,L) = 4K + 8L. 2 a. How many hamburgers are produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of hamburgers? c. How does your answer to part b change if the wage rate decreases to $20 per...
[Short-Run Production] Suppose that a firm is producing in the short run with output given by:...
[Short-Run Production] Suppose that a firm is producing in the short run with output given by: Q = 200.5L – 2.5L2, The firm hires labor at a wage of $25 per hour and sells the good in a competitive market at P = $50 per unit. Find the firm’s optimal use of labor and associated level of output. (For extra practice, what is the firm’s associated profit?) I have already finished and went to check my work on Chegg and...
1. Sketch the production isoquant for a production function that takes two inputs (e.g. y = f[l,k]). Show the cost minim...
1. Sketch the production isoquant for a production function that takes two inputs (e.g. y = f[l,k]). Show the cost minimizing combination of inputs by adding an isocost line to your sketch. (a) What is the relationship between the trs and the relative price of one input compared to the other at the cost minimizing combination of inputs? (b) What does the assumption of a diminishing technical rate of substitution (trs) mean? (What does a diminishing trs mean imply for...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Afir's production engineers have estimated its production function as Q(KL) = 2K2/1/2 = 2-K L=2KL where ' and 'L' represent the amounts of capital and labour, respectively, used in production each period, and 'Q' represents the amount of output produced each period. The firm pays a wage, w, for each person-hour of labour of $16. The rental rate of a machine-hour of capital, wk, is $100. What will be the firm's minimum cost of producing 10 units of output? What...
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and both wage and interest rates are equal to one, so that war- a) Given that the wage increases to 4. determine the elasticity of demand for labour at the new wage. Indicate whether the wage bill will increase or decrease as wage increases to 6. b) Find the linear demand function for labour...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
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