Select the statement that is true. An isoquant divides the set of input bundles into three regions, the efficient production, inefficient production, extra efficient production. For the same technology, two isoquants cannot cross. For a given technology, there can be many different production functions representing that technology. An isoquant can slope upwards in the short run.
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- From the following production functions 1. Q= a1H + a2L + a3H2 + a4 L2 + a5HL, where ai> 0 2. Q = aH@ Ly, where a, @, y > 0 a. Derive the equation of the relevant isoquant. b. Find out whether the production function is well behaved. c. Examine whether the isoquant is well behaved and therefore represents the behaviour of a rational production. d. Derive equation which describes MRTS of 9ne factor. e. For each equation examine whether the production is homogeneous and if so, what is the degree of homogeneity. Is the equation characterized by IRTS, DRTS or CRTS.Suppose a soap-manufacturing production process is described by the following equation: Y = a + b log K + с log L Where, Y= Output (number of soaps produced) K=Capital L=Labor a, b and c are constants Suppose 0<a<1, 0< b<1 a. Find the Marginal Product of Labor (MPL) and Marginal Product of Capital (MPK) in the production of soap b. Is MPL diminishing, increasing or constant as L increases? c. Is MPK diminishing, increasing or constant as K increases?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
- Write about the production function with two and more than two variablesThe figure shows the production function of a farmer who produces grain by working certain hours each day. Which of the following statements is correct about this production function? a. The slope of the production function represents the marginal rate of substitution. b. The ceteris paribus assumption means that the farmer becomes more productive as he works more hours. c. A rightward movement from B along the production function implies that the farmer has better technology. d. This production function exhibits economies of scale. e. A technological improvement would shift up the production functionThe production function q = 9K0.8L0.1 exhibits: a. increasing retruns to scale b. constant returns to scale c. decreasing returns to scale d. none of the above The production function q = K1.2 + 3L1.2 exhibits a. increasing retruns to scale b. constant returns to scale c. decreasing returns to scale d. none of the above
- Identify the returns to scale in the functions below. Production Function a. q = 3L + 2K Returns to Scale constant increasing decreasingProblem 2 (a) Find an example of a production technology that is such that two inputs must be used in fixed proportions (hopefully a different one from the examples discussed in class). Explain why you chose this example. Draw a typical isoquant of the example you found. (b) Find an example of a production technology that is such that two inputs are completely inter- changeable. Explain why you chose this example. Draw a typical isoquant of the example you found. (c) Find an example of convexity of production technology. Explain why you chose this example. Draw a typical isoquant of the example you found.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…
- 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.…What is meant by an expansion path? Illustrate expansion paths for a normal input and an inferior input.