4. Suppose a firm makes a single output using a single input. Think of the input as labor. Denote quantities of these outputs and inputs by q and I respectively. Suppose that the firm's production function f is given by f(10 = 0 if I < 1 and f(1) = 1-1 otherwise. Clearly draw a diagram of this firm's production set. Be sure to label the axes.
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- 2. The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3K1/3, where P is the number of anvils produced when L is the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. c. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. Only need paVAS e and flThe Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1Consider a production process where flowers are grown (the output) using gardeners (labor) and greenhouses (capital). The quantity of flowers grown per day with various combinations of labor and capital are shown in the table. Fill in the marginal product of labor in the table below. (Enter your responses as integers.) Labor 0 1 2 3 4 5 Capital 1 1 1 1 1 1 O A. are experienced when the second worker is hired. OB. are experienced when the fifth worker is hired. O C. are experienced when the fourth worker is hired. O D. are experienced when the third worker is hired. O E. are never experienced. Output 0 160 480 640 720 760 Does the production of flowers experience the effects of the law of diminishing returns? The effects of the law of diminishing returns Marginal Product of Labor 160 320 160 80 40
- If capital and labour are perfect complements then the marginal products of capital and labour are undefined A True Faise Question 16 A firm uses 10 units of labour and 20 units of capital to produce 10 units of output. The marginal product of labour is 0.5. If there are constant returns to scale the marginal product of labour must be 0.25 True B False Question 17 Afirm uses 10 units of labour and 30 units of capital to produce 10 units of output. The marginal product of labour is 05. If there are constant returns to scale the marginal product of labout must be 0.25 A True FalseProblem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…A firm uses Labour (L) and Capital (K) to produce commodity (Y). The quantities of the inputs and outputs are shown in the table below. L 3 2 90 250 4 5 6. 10 K 90 90 885 90 90 90 90 90 90 90 90 Y 100 420 560 675 760 820 860 900 a. Calculate the average and marginal product of labour and plot them. What economic factors explain the shape of these curves? What is the range of output corresponding to the second stage of production? b. Assuming that the wage rate is Rs.3407- and the rental rate on capital is Rs.0.5/-, calculate the short run average variable cost, marginal cost, average fixed cost, average total cost, total variable cost, total fixed cost and total cost. Plot all these curves. c. Does the average variable cost cuts the marginal cost at the minimum point of the marginal cost? Why is this always the case? What is the relationship between the marginal cost and average variable cost in the second stage of production.
- Suppose a production function for a firm takes the following algebraic form: Q = 4KL - (0.2)L", where Q is the output of sweaters per day. Now suppose the firm is operating with 12 units of capital (K = 12) and 11 units of labour (L = 11). What is the output of sweaters? ign O A. 108 sweaters per day Hot O B. 467 sweaters per day OC. 459 sweaters per day ke a O D. 526 sweaters per day O E. 504 sweaters per day Clear all Check answer Etext pages Grapher Ask my instructor Review Resume MacBook Pro * & # $ % @ 7 8 1 2 3 4 Y Q W E J K A S D F M Z C V この つ エ くOA firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L1/2M1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400and another isocost line showing combinations that cost $200.2. Suppose that the firm wants to produce its output in the cheapest possible way. Find thenumber of machines it would use per worker. (Hint: The firm will produce at a point wherethe slope of the production isoquant equals the slope of the isocost line.)Digging calms by hand in Sunset Bay requires only labor input. The total number of calms obtained per hour (q) is given by :Q = 100√LWhere L is labor input per hour. A. Graph the relationship between q an LB. What the average productivity of labor in Sunset Bay? Graph this relationship and show that output per unit of labor input diminishes for increase in labor input. C. It can be shown that the marginal productivity of labor in Sunset By is given by:MPL =50√LGraph this relationship and show that labor’s marginal productivity is less than average productivity for all values of L . Explain why this is do.D. Explain the concept of diminishing returns to labor and how this concept related to increasing marginal costs.
- Question: Orla manages a loom that produces flags (F) using thread (T) and dye (D) as inputs. Herproduction function is given by: Q(T,D) = (T1/2 D1/2)1/2*For this problem, assume F, T, and D are infinitely divisible so you don’t need to worryabout restricting to whole-number answers. a.) Does Orla’s production function exhibit increasing, constant, or decreasing returns toscale? Explain. b.) Set up Orla’s cost-minimization problem to find the lowest-cost combination of inputsrequired to produce a specific level of output (bar Q) given factor prices PT and PD. (Note: You can write this either as a minimization subject to constraints or in Lagrangian form. *You do not need to solve it.)Question 14 of 20 Output Marginal Labor (Q) Product 15 1 2 50 15 4 70 5 60 In the table above, when the firm increases its Labor from 4 to 5, the Marginal Product of Labor is: O - 10 15 10 O - 159 Output Marginal Labor (Q) Product i of 20 1 20 50 2 3 100 10 5 130 6 135 In the table above, what is output (Q) when L = 2? Select one: а. 55 b. 65 C. 50 d. 70