The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the formf(L, C)=²1C²2where co. ₁, and care constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital.(a) In this example, assume co5, c, 0.25, and c₂-0.75. Assume sach unit of labor costs $25 and each unit of capital costs $75. With $70,000 available in the budget, devalop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output.Maxs.t.L, CZO€ 70,000(b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0S LS 3,000 and 0 s Cs 1,000. Round your answers to the nearest integer when necessary.)units at (L. C)=(

The Cobb-Douglas production function refers to the mathematical model that helps in establishing the…

The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form FL, C) = CpL²1C²2 where cu c, and c, are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume c, 5, c, -0.25, and c,-0.75. Assume sach unit of labor costs $25 and each unit of capital costs $75. With $70,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output Max st. LCZO $70,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0 SLS 3,000 and 0 scs1,000. Round your answers to the nearest integer when necessary.) units at (L. C)=(

The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form FL, C) = CpL²1C²2 where cu c, and c, are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume c, 5, c, -0.25, and c,-0.75. Assume sach unit of labor costs $25 and each unit of capital costs $75. With $70,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output Max st. LCZO $70,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0 SLS 3,000 and 0 scs1,000. Round your answers to the nearest integer when necessary.) units at (L. C)=(

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 7E

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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…
The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C) = c₂LC1C²2 C2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co 5, C₁ = 0.25, and c2₂ 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $90,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. = = where co, C₁, and Max s.t. L, C ≥ 0 A ≤ 90,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Put bound constraints on the variables based on the budget constraint. Use L ≤ 3,000 and C ≤ 1,000 and use the Multistart option as described in Appendix 8.1. (Round your answers to the nearest integer when…
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.…
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 = 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 AverageProduct 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. 4. 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? 5. Assume Kia Head Office is considering hiring more laborers either at their Gwadar plant 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 = 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…
The amount of fish caught per week an a trawler is a function of the crew size assigned to operate the boat. Based on past data, consider the following production function identifying the relationship between output and labor input. You may assume that capital is fixed at 10 units.Labour Input (No of. Workers) (L) Total Product TPL (Q). From the table below :-(a) Calculate APL and MPL. (b) Graph APL and MPL. Do they have the expected shape? (c) On your graph, identify the three stages of production Labour input (No of Workers) (L) Total Product TP L (Q) 0 0 1 80 2 170 3 300 4 450 5 540 6 620 7 700 8 770 9 830 10 880 11 920 12 950 13 970 14 980 15 985 16 988 17 988
100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.
Suppose the production function for widgets is given by KL – 0.5K2 – 0.1 L2 , where q represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labor input. (a). Suppose K=5; what is the average productivity of labor (Average product of Labor, MPL) (b). Suppose K=10; at what level of labor input does the total output reach the maximum?
The Cobb - Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C) = COLc1Cc2 where c0, c1, and c2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a)In this example, assume c0 = 5, c1 = 0.25, and c2= 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $70,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. = 0 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0 < = L < = 3,000 and 0 <= C <= 1,000. Round your answers to the nearest integer when necessary.)________ units at (L, C) = Please use Excel to get answers. Show steps on Excel Please!
Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?