Let c(x) be the cost of producing a product of x units. Given that c(x) follows the experience cost curve, c(x)= k(1 – b) xb-1 where k and b are constants and 0 < b < 1. Show that c(x) is a decreasing function, in this case. production costs show a downward trend with an increase in the number of products produced! Is this function a convex function? Explain!
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Let c(x) be the cost of producing a product of x units. Given that c(x) follows the experience cost curve, c(x)= k(1 – b) xb-1 where k and b are constants and 0 < b < 1. Show that c(x) is a decreasing function, in this case. production costs show a downward trend with an increase in the number of products produced! Is this function a convex function? Explain!
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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)Qno1. You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Required. a) .Find the ranges of the three stages of production. b) .Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above . c). At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital.Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2,do you observe increasing, decreasing or constant returns to scale? d). Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…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…
- A firm has the production function f(X, Y) = x²/2 y1/2, where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew Select one: O a. is vertical. b. is horizontal. c. is a ray through the origin with slope 3. d. is a ray through the origin with slope 4. O e. has a negative slope.You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L^2 – 0.5L^3 where L is variable input labor, Q is output of Cars assembled a. Find the ranges of the three stages of production. b. Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above. c. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L^.30K^.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? d. Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant.…You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled 1.Find the ranges of the three stages of production. 2.Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above 3.At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? 4.Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…
- Suppose the production function is Cobb-Douglas and f(x1;x2)=x11/2x23/2 Write an expression for the marginal product of x1. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain What is the the technical rate of substitution between x2 and x1? What is the type of returns to scale of this production function? (Increasing, decreasing, constant)A firm has a production function of ?(?,?) = ??.???.? a) Explain the concept of returns to scale. Does the function provide increasing, decreasing, or constant returns to scale? b) Provide an example of a typical sector with increasing returns to scale. c) Explain the concept of MRTS and argue whether the MRTS for this production function is diminishing. Please also provide a graphical illustration using numbers.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. change
- You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Find the ranges of the three stages of production. Demonstrate the relationship between Total Production, Marginal Product and Average Product in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively…Solve the exercise with a production function with diminishing returns: In this case, production increases as workers are added, but it increases less and less. a) Calculate the amount of production for each worker and add it to the table, taking into account the production function K 10 1 9. 2 8 3 7 4 6. 4 7 3 8 2 9 10 b) Explain why the production function exhibits diminishing returns to scale.Consider a firm that produces a good using capital and labor. We denote by L the quantity of labor and by K the quantity of capital. In the short term, the firm has a fixed amount of capital K. The short-run production function of the firm is given by f (K; L). Graphically, we measure the amount of work on the abscissa and the output on the ordinate. The average product of labor is (a) the slope of the production function. (b) the area that is below the production function. (c) Both of the above answers are correct. (d) None of the above is correct.