Let y = f(x1, x2)=x112+x1X2 be a firm's production function, where x120, x220. e a. Write down the firm's production possibility set, and its input requirement set. b. Is this production function concave, quasi-concave? - c. Is this production function homogenous, homothetic? e d. Find its returns to scale when x1=1, and x2=1.“
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- A firm’s production function is - y = f(X1, X2)= X11/2 + X1X2 , Where X1≥0, X2≥0 1. Write down the firm’s production possibility set, and its input requirement set. 2. Is this production function concave, quasi-concave? 3. Is this production function homogenous? 4. Find its returns to scale when X1=1, and X2=1Problem 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…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.)
- Exercise A.5 A company operates with production function q-K¹/2 [1/2 a) What type of returns to scale does this production function present? As production varies, how would you expect long-term average costs to evolve? b) Assume that the firm's capital equipment is fixed and equal to K = 100 units. Find the firm's short-run production function and the marginal productivity of labour and graph these functions. As production varies, how would you expect marginal costs to evolve in the short term? c) If the prices of capital and labour are r = 8€ and w = 2€ respectively, obtain the expression of the short-run total cost function of the firm. b) Obtain the expressions of the functions of short-term average total costs, average variable costs and marginal costs of this company. Find the production level for which the average total cost is minimized and the corresponding average total cost level. d) Indicate the value of the average total cost, the average variable cost and the marginal cost…4. Show that the law of diminishing marginal productivity holds for the production function Q=6L² - 0.2L'Q1.The following is a Cobb-Douglas production function: Q = 1.75K0.6L0.5. What is correct here? * -This production function displays constant returns to scale -This production function displays increasing returns to scale -A one-percent change in L will cause Q to change by one percent -This production function displays decreasing returns to scale Q2. For studying demand relationships for a proposed new product that no one has ever used before, what would be the best method to use? * -consumer surveys, where potential customers hear about the product and are asked their opinions -double log functional form regression model -ordinary least squares regression on historical data -market experiments, where the price is set differently in two markets
- 3. Frisbees are produced according to the production function q = 2K+L where q = output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquant defined in part a and part b. What is the RTS along this isoquant? Explain why the RTS is the same at every point on the isoquant. d) Graph the q = 50 and q = 200 isoquants for this production function also. Describe the shape of the entire isoquant map. e) Suppose technical progress resulted in the production function for frisbees becoming q = 3K+ 1.5L. Answer part a through part d for this new production function and discuss how it compares to the previous case.1. Suppose that a producer has the following production function: -1/3 Where Q is output, and L and K are man-hours and machine-hour the two inputs used in the production process. IB) (8 Points) Detemine the cost-minimize ratio of inputs where capital costs $1 per machine hour and labor costs $4 per lab-hour.24. A specific production process can be represented by the production function, f(x1, x2) = (x 1/2 + x 1/3) 3. A. How much x₁ could the firm give up if it wanted to use 1 extra unit of x2 and still wanted to produce an identical level of output? B. Labeling everything and being precise, draw the isoquant corresponding to q = 4. = 9. C. On the same graph, draw the isoquant corresponding to q D. Between the isoquants you just drew, does the production technology display decreasing, increasing, or constant returns to scale? E. Analytically determine whether the production process has global returns to scale that match your local results from part D. Recall that in order to claim global returns to scale, your result must hold for ALL possible values of x1 and x2.
- 2. Which of the following production functions with inputs K, L, and H exhibits Constant Returns to Scale (CRS)? (Assume Ā > 0 is a constant) a) Y = AK/2L/2 b) Y = ĀK/2L/3H/4 c) Y = ĀK/2 – L/H d) Y = ĀKL/2H\/2For a firm to maximize profit, it must minimize the cost of producing whatever quantity it produces. Use the isocost and isoquant tools to present a firm that is choosing the optimal levels of labor and capital (i.e., tools) to produce a certain quantity and a certain cost. Then, show in your diagram how this firm would respond if it were to expand and spend more on its inputs, assuming it is best for the firm to become more “capital intensive” as it grows. Comment on WHY a firm might best become more capital intensive as it expands, even when the relative prices of labor and capital remain unchanged.The 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=1
