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. <= 70,000 L, C >= 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!

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. <= 70,000 L, C >= 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!

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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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…
The Cobb - Douglas production function is a classic model from economics used to model output as a function of capital c. and labor. It has the form f(L,C) = c_L" C² where co, 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 c₁ = 5, c₁ = 0.25, and c = 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $80,000 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. 25L +75C 80000 L,C>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 L3,000 and 0 C1,000. Round your answers to the nearest integer when necessary.) units at (L,C) = (x)
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)=²1C²2 where 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. Max s.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)=(
Which of the following equations does not represent a plausible production function? a.F(K,L) = 2KL b.F(K,L) = 2K-2L c.F(K,L) = 2(KL)0.5 d.F(K,L) = KL
Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?
Suppose that a rock star gives concerts. The production function of the concert is the following: Q(C, A,G) = (C – 10)/ªAª/4G+/4 where C represents hourly contribution of guitarist Chris; A represents hourly contribution of guitarist Ataman and G represents hourly contribution of guitarist George.
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.
A lot of companies use the marginal cost function for their business models to determine the production level to minimize total costs. As we all know, if C (x) represents the total cost of producing x units of a product, then the average cost per unit at this production Let assume C (x) is differentiable on all x > 0 . This implies that the C(x) level is average cost function is also differentiable for all x > 0 since C(x) can be written as C (x) · - , and both C (x) and are differentiable for all x > 0. Suppose you go to an interview and the chairman of the interview committee gives you the following questions: In our company , we use marginal cost to determine the production level to minimize the costs. However, there is another useful model in business, the average cost function, that we also track. 1. Is it true or not that the marginal cost C '(x) is equal to the average cost at the critical points of the average cost function? Please elaborate and explain to us. 2. This year, the…
Suppose the production function is given by Q = 3K + 4L. What is the average product of capital when 5 units of capital and 10 units of labor are employed.