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

See similar textbooks

Related questions

Q: Consider the following production function: q = (KL)ª, where a > 0. Answer the following questions:…

A: Given Production function: q=KLα where α>0 ............ (1)

Q: On separate axes, draw typical production isoquants for each of the following production functions.…

A: For Isoquants, we have to take f(x,y)= c a constant

Q: a) Determine whether the following production functions exhibit increasing, constant, or decreasing…

A: If Q(tF,tK)=ta Q(F,K), then, when a>1, the firm is earning increasing returns to scale when a=1,…

Q: You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run…

A: “Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: Question 2 A firm's short-run production function is given by Q=L(11 + L L²) where L is units of…

A: The average product of labor measures the output produced by each worker on average. The marginal…

Q: A firm can manufacture a product according to the production function Q = 2(K)1/2 (L)1/2 where K…

A: The marginal productivity of labor can be found by differentiating the production function with…

Q: Consider the following production functions • F(L,K) = LK^3 For each for these production…

Q: The Cobb - Douglas production function is a classic model from economics used to model output as a…

A: a) Maximize f = 5L0.25C0.75 s.t. 25L + 75C ≤ 80,000 L, C ≥ 0 b)The results for such…

Q: When production function q= 0.4 LK+ 3 L^2K- 0.07 L^3K and K= 12 are given, find amount of labor at…

A: The production function in short-run will be given as below if the value of K (capital) = 12 (fixed…

Q: 1. A firm’s production function is Q = L1/2 K1/2 They have 16 units of capital (which is fixed in…

A: Inputs are resources that benefits the production unit in developing goods and services. In the…

Q: Production is described by the function f(K, L) = AL0.3K 0.3, A > 0.a. Interpret the exponents of…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: A firm faces the production function: q=10L^0.32 K^0.56 (a) What kind of returns to scale does…

Q: Solve the exercise with a production function with diminishing returns: In this case, production…

Q: If a firm’s production function is Y = KαL1-α, show that it can earn at most zero profit. Use this…

A: Production function highlights the relationship between the different combinations of inputs used to…

Q: Consider the following production functions • F(L,K) = LK^3 For each for these production…

A: In this case, we have to discuss the production function. Production function is actually showing…

Q: Consider the following Cobb-Douglas production function: Y = 10L04K04. Suppose that the price of…

Q: y = F(L,K) = min(L,3K) Show if the leontie

A: Here, we have to find constant returns to scale.

Q: Show using math and logic that for constant returns to scale production functions, MRTS between…

A: Production function and productivity: The production function determines all the input bundles that…

Q: I am having trouble understanding how to answer the last part of this question. I am providing the…

A: According to the law of diminishing marginal product, the marginal output decreases when one more…

Q: If the production function is Q = 30 + 22L + 30K, what's the most you can produce with 5 workers (L)…

A: As given Production Function Q = 30 + 22L + 30K Also K( capital) = 7 units L(workers) = 5

Q: Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal…

A: Economics refers to the study of scarcity and its implications for the use of resources, production…

Q: Give me answer

A: The objective of the question is to determine the conditions under which the given production…

Q: The Constant Elasticity of Substitution (CES) production function is a flexible way to describe how…

A: (A)Given, that the question states that the firm's objective is to maximise the present discounted…

Q: Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a)…

A: The production function for widgets is given by:

Question

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)=(

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Define cobb-douglas production function

VIEW

Step 2: a. Represent the maximization problem

VIEW

Step 3: b. Find the optimal solution

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Consider the production function f(x1, X2) = 4x1x2, where x1 and x2 are the quantities of inputs 1 and 2, respectively. One of the following statements is true. %3D Which statement is true? The production function exhibits: А Constant returns to scale. Increasing returns to scale. C Decreasing returns to scale.
The following equations represent the long-run production functions for four different technologies, where capital and labor are both variable inputs. For each function, indicate whether it exhibits increasing, decreasing, or constant returns to scale. Clearly show your derivations. (Note that in parts a and c, the exponents are decimals.) f(L,K)= 8L²K4 b. f(L,K)= L+7K c. f(L,K)= L³K d. f(L,K)= 4L+K? а. с.
How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether α1 + α2 is larger than, smaller than, or equal to one?
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is: q=min{L/3, K0.5}, where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice. a) Draw isoquants for q = 1, q = 2 and q = 3 on a graph with labour on the horizontal axis and kiwi fruits on the vertical one. = $5 per kg. b) Let the price of labour-hour be given by w = $18 and the price of fruit by p What is the optimal amount of labour and fruit to produce q bottles of juice if Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q) and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines. c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the expansion path, i.e., K as a function of L. How does it depend on the wage and the price of kiwi?
Q = A Lx Ky (Quantity, A, Labor, Capital) If A; X; Y are all positive numbers, does the production function exhibit Increasing return to scale, Constant return to scale or Decreasing return to scale?
Consider the production function q=√L+8K^(3). Starting from the input combination (3,6), does the production function exhibit increasing, constant or decreasing returns to scale if inputs double?
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
Consider the production function: F(L, K) = L0:2K0.7. %3D The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. (a) Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. What is the marginal productivity of labour and the marginal productivity of capital for (L, K) = (1,1)? Would a firm (which minimises costs) use this combination of labour and capital? Explain. If your answer is yes, then what would be the quantity of production for which the company would use this combination? r (b) Compute the quantity of labour and capital that this firm would use to produce y = 2 at the minimum cost. How much would this cost be? What is the average cost and the marginal cost for that production level? Hint: for this part, you can use directly (without providing the derivation) any results derived in the lecture or tutorials. (c) Derive the equation of the isoquant for y = 2 (with K in the…
The function Q = L0.3 + K0.7 is an example of _____ returns to scale of production.
***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?…
Suppose the production function for T-shirts can be represented as q = L0.25 K0.75. Show that the production function has constant returns to scale.
How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether β is larger than, smaller than, or equal to one?