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 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)
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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Transcribed Image Text: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)
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