1.1 Calculate Q when L = 60 and K = 210 [1] 1.2 Calculate Q when both inputs are increased by 10%. 1.3 Compare your answers when Q in 1.1 is increased by 10%. What does this imply about the level of returns to scale?
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- Economic1. For each of the following production functions, determine whether there areincreasing, constant or decreasing returns to scale. a)Q = 3K + 4L b)Q = K + L + KL c)Q = 18K^ 0.6 L^0.3Show that the following production function has constant returns to scale. It can be through a particular example or by demonstrating the general case. 1/21/2 y = 5x;"x;2Which of the following production functions represent increasing returns to scale? 1. f(K, L) = 2K + 3L II. f(K, L) =[K¹/² + [¹/2]³ III. f(K, L) = min{4K, L} IV. f(K, L) = 5KL-K²/2 - 1²/2 (1) only (II) only (II) and (IV) All of them (1) and (III)
- Which of the following production functions demonstrates constant returns to scale? I. Q=5L+2K п. Q-KL+L III. Q=4L(1/2)K1/5) II only I only I and III only II and III only I and II only Ш onlyQ1.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 markets9.7 Consider a generalization of the production function in Example 9.3: q = Bo +B1Vkl + B2k+ B31, where 0 < B; <1, i= 0,...,3. a. If this function is to exhibit constant returns to scale, what restrictions should be placed on the parameters Bo» ...,B3? b. Show that, in the constant returns-to-scale case, this function exhibits diminishing marginal productivities and that the marginal productivity functions are homogeneous of degree 0. c. Calculate o in this case. Although o is not in general constant, for what values of the B's does o = 0, 1, or o?
- a) The production function q = 9K0.8LO.1 exhibits [ increasing returns to scale, constant return to scale,decreasing returns to scale, none of the above ] b) The production function q = K1.2 + 3L1.2 exhibits [ increasing returns to scale, constant return to scale,decreasing returns to scale, none of the above] a) The production function q = 9KO.8L0.1 exhibits [ Select ] %3D b) The production function q = K1.2 + 3L1.2 exhibits [Select] %3DQ2. The economist for the ABC Truck Manufacturing Corporation has calculated a production function for the manufacture of their medium-size trucks as follows: Q = 1.3*(L^0.75)*(K^0.3) Where Q is the number of trucks produced per week, L is the number of labor hours per day and K is the daily usage of capital investment. 1. Does the equation exhibit increasing, constant or decreasing returns to scale? Why? 2. Calculate the marginal product of labor and marginal product of capital using the below data? 3. How many trucks will be produced per week with the following amounts of labor and capital? Labor Capital 100 50 120 60 150 75 200 100 300 150Which of the following production functions exhibit constant returns to scale? In each case y is output and K and L are inputs. (1) y = K 1/2 L 1/3 (2) y = 3 K 1/2 L 1/2 (3) y = K 1/2 + L 1/2 (4) y = 2 K + 3 L. O 1, 3, and 4 O 1, 2, and 4 2 and 4 2, 3, and 4 2 and 3
- 1. Assume that a firm has the following production function: q = L0.5K0.6 a. Calculate output when L = 64 K = 32. b. What returns to scale does this production function exhibit? c. Calculate output if technology utilized by the firm increases by 25%. d. Determine, both, the marginal product of labour and capital functions (ignore c.). e. Calculate, both, the marginal product of labour and capital when L = 64, K = 32 and interpret your answers. f. Calculate the marginal rate of technical substitution when L = 64, K = 32 and interpret your answer.Answer asap n correctly n give proper explanation of the question . (long run production) For each of the following production functions, determine whether it exhibitsdecreasing, constant, or increasing returns to scale. (In all production functions, M ismaterials, K is capital and L is labor.) Show your proof in mathematics as well as yourreasoning in words.(1) q = L + K(2) q = L0.60K0.40(3) q = M0.7K0.7L0.6A 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?