3. Suppose a firm competing in a perfectly competitve market uses machines (K) and workers (L)...
3. Suppose a firm competing in a perfectly competitve market uses machines (K) and workers (L) to produce containers of nails. Their production technology is given by q = (K)3 (L)3 . Suppose the firm already has 27 machines, the cost of people is w = $12 and each container of nails sell for P = $12.
(a) Set up the firm’s problem. What time frame is being examined here? How many workers does the firm hire? How much does the firm produce? (All the numbers here are whole numbers)
(b) Suppose the firm has profits equal to zero, what else can you say about the time frame? What value would r take for this to be true?
(c) Suppose a new method of producing machines makes the rental rate of capital r = 24, how many machines (K) and workers (L) will the company want when able to adjust both if they do not want to adjust their quantity? Make sure to set up the firms problem correctly. Sketch the solution using the isoquant and isocosts.
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3. Suppose a firm competing in a perfectly competitve market
uses machines (K) and workers (L)...
1. A firm uses labor and machines to produce output according to the production function f(L,...
1. A firm uses labor and machines to produce output according to the production function f(L, M) 2L2 M , where L is the number of units of labor used and M is the number of machines. The cost of labor is $20 per unit and the cost of using a machine is $5. a. Suppose that the firm wants to produce its output in the cheapest possible way. Find the input demand functions for machines and workers. Please show...
1. A firm uses labor (L) and machine (K) to assemble garden benches. The firm has...
1. A firm uses labor (L) and machine (K) to assemble garden benches. The firm has the pro- duction function Q = F(L,K) = 207LVK, where L is the number of full-time workers the firm hires per day and K is the number of machines the firm uses per day. Both L and K can be non-integers (for example, a worker can work for half a day). Each worker costs $100 a day and each machine costs $200 a day....
Suppose that the production function for your firm is given by: F(L,K)=L12K1/2 w=$1 and r=$1. In...
Suppose that the production function for your firm is given by: F(L,K)=L12K1/2 w=$1 and r=$1. In the long-run, how many workers and capital should you hire in order to produce Q units of output? Select one: a. L=2Q; K=Q b. L=Q; K=Q2 c. L=0.5Q; K=0.5Q d. L=Q; K=Q e. None of the above
Consider a representative firm that produces using capital (K) and labor (N). The firm hires workers...
Consider a representative firm that produces using capital (K) and labor (N). The firm hires workers at wage w and rent capital at rental rate r. Suppose the firm has the production function: F(K, N) = K™NB with a + ß < 1 and a, ß E (0,1) ii) Set up the firm's profit maximization problems and solve for the optimal K*, L*, and 7* (profits) in terms of parameters(12 points) iii) What's the ** when a + b =...
Question 7 rding to the production function: uses labor and machines to produce output according to...
Question 7 rding to the production function: uses labor and machines to produce output according to the where Lis ALK) = 41/212, ere is the number of units of labor used and K is the amount of capita or is $40 per unit and the cost of employing capital is $10 per unit. mount of capital employed. The cost (0): On the graph below, draw an isocost line for this firm that includes combin capital and labor that cost $400...
2. To produce 18 units of output a firm can hire either 9 workers or 3...
2. To produce 18 units of output a firm can hire either 9 workers or 3 machines. a. Let L denote workers and K denote machines. Write down a production function that represents this firm's production technology. (2 points) b. Let w denote the wage rate and r denote the rental rate of capital. Suppose wir = 0.4. Derive the firm's long run factor demand functions for labor and capital and the firm's long run cost function. (4 points) C....
q=L^0.5+K^0.5, assuming r=w=$8. Suppose this perfectly competitively firm horizontal demand curve with p=$48, calculate the quantity...
q=L^0.5+K^0.5, assuming r=w=$8. Suppose this perfectly competitively firm horizontal demand curve with p=$48, calculate the quantity this firm will decide to produce. Find the amount of L and K the firm will hire. Is this firm making a profit or loss, how much it it?
SM 3. A firm uses capital K, labour L, and land T to produce units of...
SM 3. A firm uses capital K, labour L, and land T to produce units of a commodity, where Q=K2/3+ 1/2+/3 Suppose that the firm is paid a positive price p for each unit it produces, and that the positive prices it pays per unit of capital, labour, and land are r, w, and q, respectively. (a) Express the firm's profits as a function of (K,L,T). Then, find the values of K, L, and T, as functions of the four...
Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production...
Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which carn be combined to produce Y units of out put according to the following production function: Y-30K+10L The firm wants to produce 600 units of out put 1. Draw the isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and K on the vertical axis 2....
Please show all work. Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two...
Please show all work.
Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which carn be combined to produce Y units of output according to the following production function: Y = 30K + 10L The firm wants to produce 600 units of output. 1. Draw the isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and...
1. A firm uses labor and machines to produce output according to the production function f(L, M) 2L2 M , where L is the number of units of labor used and M is the number of machines. The cost of labor is $20 per unit and the cost of using a machine is $5. a. Suppose that the firm wants to produce its output in the cheapest possible way. Find the input demand functions for machines and workers. Please show...
1. A firm uses labor (L) and machine (K) to assemble garden benches. The firm has the pro- duction function Q = F(L,K) = 207LVK, where L is the number of full-time workers the firm hires per day and K is the number of machines the firm uses per day. Both L and K can be non-integers (for example, a worker can work for half a day). Each worker costs $100 a day and each machine costs $200 a day....
Suppose that the production function for your firm is given by: F(L,K)=L12K1/2 w=$1 and r=$1. In the long-run, how many workers and capital should you hire in order to produce Q units of output? Select one: a. L=2Q; K=Q b. L=Q; K=Q2 c. L=0.5Q; K=0.5Q d. L=Q; K=Q e. None of the above
Consider a representative firm that produces using capital (K) and labor (N). The firm hires workers at wage w and rent capital at rental rate r. Suppose the firm has the production function: F(K, N) = K™NB with a + ß < 1 and a, ß E (0,1) ii) Set up the firm's profit maximization problems and solve for the optimal K*, L*, and 7* (profits) in terms of parameters(12 points) iii) What's the ** when a + b =...
Question 7 rding to the production function: uses labor and machines to produce output according to the where Lis ALK) = 41/212, ere is the number of units of labor used and K is the amount of capita or is $40 per unit and the cost of employing capital is $10 per unit. mount of capital employed. The cost (0): On the graph below, draw an isocost line for this firm that includes combin capital and labor that cost $400...
2. To produce 18 units of output a firm can hire either 9 workers or 3 machines. a. Let L denote workers and K denote machines. Write down a production function that represents this firm's production technology. (2 points) b. Let w denote the wage rate and r denote the rental rate of capital. Suppose wir = 0.4. Derive the firm's long run factor demand functions for labor and capital and the firm's long run cost function. (4 points) C....
SM 3. A firm uses capital K, labour L, and land T to produce units of a commodity, where Q=K2/3+ 1/2+/3 Suppose that the firm is paid a positive price p for each unit it produces, and that the positive prices it pays per unit of capital, labour, and land are r, w, and q, respectively. (a) Express the firm's profits as a function of (K,L,T). Then, find the values of K, L, and T, as functions of the four...
Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which carn be combined to produce Y units of out put according to the following production function: Y-30K+10L The firm wants to produce 600 units of out put 1. Draw the isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and K on the vertical axis 2....
Please show all work.
Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which carn be combined to produce Y units of output according to the following production function: Y = 30K + 10L The firm wants to produce 600 units of output. 1. Draw the isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and...
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