Identify the returns to scale (increasing, constant, or decreasing) for the following production functions. 1) Q =100K²L² 2) Q = 2K +3L 3) Q =2K% +21%
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- Determine the returns to scale for the following production functions. a) ? = K + 7L b) ? = KL33 1 Y = 2X} X} WHICH OF THE FOLLOWING ASSUMPTIONS APPLY TO THIS RELATIONSHIP. INCREASING RETURN TO SCALE DECREASING INCOME TO THE SCALE FIXED RETURN TO THE SCALEDetermine the returns to scale of this production function: F(x1, x2) = [xỉ + x3]!/2 %3D A. Constant return to scale B. Increasing return to scale C. Decreasing return to scale
- 12. Which of the following production function shows decreasing returns to scale? (a) f(r) = min{x1, 12}. 1/4 (b) f(z) = xỉ + x}/2 1/4 1/2 (c) f(x) = r1 + xj"x (d) f(x) = VE +a3.4) Does these production functions exhibit decreasing, constant, or in- creasing returns to scale? Prove your answer. a) q= b) KL (K+L) q=100√ML+M+LFor the production function Qs = K0.4L0.1 find the returns to scale, recall that a doubling of inputs that doulbes output is a CONSTANT returns to scale = 1.0 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
- What is the elasticity of substitution of f(K, L) = KL²? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1 (e) 3/2 (f) 2 Which of the following represents increasing returns to scale? (a) f(K, L) = (K² + L²)¹/2 (b) f(K, L) = (K¹/2 + [¹/2)² (c) f(K, L) = (K + L) (d) f(K, L) = (K + L)² Suppose the production function for good q is given by q = (k¹/2+1¹/2)2. Consider the following three statements about this function: I. The function exhibits constant returns to scale. II. The function exhibits diminishing marginal productivities in both inputs. III. The function has a constant rate of technical substitution. Which of these statements is true? (a) All of them (b) None of them (c) I and II, but not III (d) II and III, but not IThe total cost of producing 1 unit of a product is ху C(x, y) = 28 + 4x + 6y + 56 dollars where x is the cost per pound of raw materials and y is the cost per hour of labor. (a) If labor costs are held constant, find the function that describes the rate at which total cost increases for each increase of $1 per pound in material cost. (b) If material costs are held constant, find the function that describes the rate at which total cost increases for each $1 per hour increase in labor costs.The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?
- 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)A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy
