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)=(

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). Can we say that the production function satisfies the law of decreasing marginal returns of labor?True False
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Problem 1: Your firm has employed an economist to estimate your firm's production function. After gathering the appropriate data, the economist estimates that your is of the form shown below. You also know that capital is fixed at 8 units in the short run. 12 Q=K³L²³ a. Calculate the average product of labor when 27 units of labor are utilized and interpret your result. b. Calculate the marginal product of labor when 27 units of labor are utilized and interpret your result. c. Suppose the firm can hire labor at a wage of $5 per hour and output can be sold at a price of $15 per unit. Determine the profit-maximizing levels of labor and output. d. What is the maximum price of capital at which the firm will still make nonnegative profits?
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…