Let f: Rn → R be increasing returns to scale. Recall, this means that f(αx) ≥ αf(x) for all x ∈ Rn and all α ≥ 1. Further, assume for some vector of inputs, profits are strictly positive. Argue that there is no profit maximizing vector of inputs.
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Let f: Rn → R be increasing returns to scale. Recall, this
means that f(αx) ≥ αf(x) for all x ∈ Rn and all α ≥ 1. Further, assume for some vector of inputs, profits are strictly positive. Argue that there is no profit maximizing vector of inputs.
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- A company produces commercials. A 2-minute commercial, for example, needs exactly 5 minutes of filming and 8 minutes of editing. Let x1 denote the minutes of filming and x2 denote the minutes of editing. a) Write down the production function and state whether it has increasing, constant, or decreasing returns to scale b) Suppose that filming costs $45 per minute and editing costs $10 per minute. To produce a 5-minute commercial, how many minutes of filming and how many minutes of editing is needed to minimize cost? c) Suppose that filming costs w1 per minute and editing costs w2 per minute. Let y denote the length (in minutes) of commericals produced. derive the conditional factor demand functions x1(w1,w2,y) and x2(w1,w2,y) and its cost function c(w1,w2,y)Your firm is producing a unique product and the marginal product with respect to x1 in your function αf(x1,x2) exhibits a decreasing marginal product trend. Is it possible for the output of this function to have increasing returns to scale? Select one: a. Yes b. NoExercise 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…
- Production is described by the function f(K, L) = AL0.3K 0.3, A > 0.a. Interpret the exponents of the function f( K, L) and the parameter A. b. Explore the effects of scale of this production function. Does the answer depend on A?c. What is the degree of homogeneity of this function? Does the answer depend on A? d. Consider a production function given by F(K, L) = f 2(K, L ). How do the answers to thequestions in b. and c. change?e. Consider a production function given by F(K ,L) = f(K, L) + 2. How do the answers to thequestions in b. and c. changeWhat is meant by an expansion path? Illustrate expansion paths for a normal input and an inferior input.Yt = F(Kt, Lt, At) Explain through example how diminishing marginal products can occur in the production process? If the form of the production function is a Cobb-Douglas function, show the production equation for constant return to scale conditions!Do diminishing marginal products also apply here?
- A firm has a short-run production function as Q = 50 L + 6 L2 – 0.5 L3 Where Q = Quantity of output per week and L = Labor (number of workers) When does the law of diminishing returns take effect? Calculate the range of values for labor over which stages I, II and III occur. Draw the stages and indicate which stage will the firm consider as per optimal level of input?Identify the returns to scale in the functions below. Production Function a. q = 3L + 2K Returns to Scale constant increasing decreasingThe production function for the automotive and parts industry is q=L0 25 K0.16 M0.59 where M is energy and materials (based loosely on Klein, 2003). What kind of returns to scale does this production function exhibit? This production function exhibits constant returns to scale. The marginal product of materials, MPM, is O A. MPM = 0.59(q/M) O B. MPM = 0.59L0 25 K0.16M - 0.41 MPM =L0 25K0. 16MO.59 O D. both a and b. O E. all of the above.
- Suppose that a food manufacturing company produces two goods, A and B, using the same plant and labor. The total cost of producing A and B is give by: (in the picture) Is this total cost function consistent with the present of increasing or decreasing returnsto scaleThe law of diminishing returns happens when each additional unit of a variable input results in a decline inA firm has a production function f(x, y) = 1.80(x0.10 + y0.10)2 whenever x > 0 and y > 0. When the amounts of both inputs are positive, this firm has increasing returns to scale. increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1. increasing returns to scale if x + y > 1 and decreasing returns to scale otherwise. decreasing returns to scale. constant returns to scale.
