Answered: For the typical Cobb-Douglas function,…

For the typical Cobb-Douglas function, q= AKαLβ whereas APL /APK =1 , find out the marginal rate of technical substitution.

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter21: Production And Costs

Section21.3: Production

Problem 3ST

See similar textbooks

Related questions

Q: Pears are on sale for $1.49 a pound. Sara buys p pounds of pears for a total cost of c dollars.…

A: The complete expense incurred while buying or producing a certain number of products or services is…

Q: a) On the same graph, plot (with scale) the isoquants corresponding to output levels of q = 10, q =…

A: Isoquant illustrates the different combinations of two inputs that produce the same level of output.…

Q: What is the elasticity of substitution for the production function f(K, L) = K¹/4 [³/4? (a) o = (b)…

Q: The total cost function of a firm that produces its product on two assembly lines is given as TC…

A: Total cost is the sum of all expenses incurred by a firm in producing a certain level of output. It…

Q: I have seen solutions for this question that include solving by matrices and row reduction. Will…

A: Row reduction method is a generalized method that can be used for matrices of any integral…

Q: The chemical X-2000 is produced using two inputs, benzene (B) and labor (L) in the exact proportions…

A: Given: There are two inputs, benzene (B) and labor (L). Production function: qX = min[B, 0.5L]…

Q: After finding the optimal quantities of X1, X2 that maximize the function Z = (X1^0.2)*(X2^(1-0.2)),…

A: In the context of optimization problems, the term "optimal quantities" refers to the specific values…

Q: Isoquants have a v slope and, for Cobb-Douglas production functions, are The MRTS is v and is the v…

A: In an economy, the connection between total output to the amount of total input used in the…

Q: A retail store in Makkah, receives shipments of a particular product from Jeddah and Taif. Let X be…

A: a.) total=y+x on the grounds that it will be the amount of the two shipment amounts.

Q: in part b, how do we know that is the cost function? where are those variables coming from?

A: In part B of the question, you are asked to find expressions for the cost-minimizing levels of labor…

Q: Consider the Lagrangian function L=q%q,+(Y-p,9, -P292)- Which of the following expressions is NOT a…

Q: Suppose Honda operates a car engine manufacturing plant in Canada and one in Mexico. Suppose further…

A: Given,The production function of Honda's car engine manufacturing unit in Canada is The production…

Q: The marginal rate of substitution of both of them are not correct.

A: Marginal rate of substitution (MRS): it is the slope of the indifference curve, and it tells us that…

Q: Let X = R. Suppose that u represents p>0, M > 0, ū> 0, and r(p, M) >0. if necessary. (1) Show that…

A: - Utility Function:A utility function is a concept commonly used in economics and decision theory to…

Q: A software firm has only two inputs to production: domestic programmers based in the firm's U.K.…

A: A production function states the mathematical link of quantities of production factor and the…

Q: A farmer can produce f(x,y) = 208-√4x² + y² units of produce by utilizing x units of labor and y…

A: To calculate the marginal productivity of labor at a specific point, we can take the partial…

Q: Suppose that a furniture manufacturer produces tables. The manufacturer's production function is…

A: Cost minimizing is a process where firm chooses their desired level of output and using optimal…

Q: Round the answers to 2 decimal places. Travis Scott spent x thousands of dollars on advertising and…

A: a) To find the maximum revenue, we need to find first-order differentiation, set it equal to 0 to…

Q: (i) Write down the first order necessary condition and the second order sufficient condition for…

A: Extremum is the maximum or minimum value of function.

Q: Given that f(x) = b^x for b > 0, determine the values of b that will make the function f an…

A: This can be described as a concept that shows when an individual, firm, or any entity uses an…

Q: Which of the following production functions exhibits constant returns to scale (refer to activities…

A: This can be described as a concept that shows when an individual, firm, or any entity uses an…

Q: Write the technical rate of substitution expression for f(x1, x2) = (x1 - 1)0.25 x20.5

A: The marginal rate of technical substitution (MRTS) is an concept that explains the rate by which one…

Q: a) Given that a firm has a production technology, y= (x² + x²) ²³/₁ derive the MRTS12

A: The production function shows the rrealtionship between the input used and the outtput produced.…

Question

For the typical Cobb-Douglas function,

q= AK^αL^β

whereas AP_L /AP_K =1 , find out the marginal rate of technical substitution.

Definition Definition Rate at which one factor of production is decreased in order to maintain the same level of output when another factor of production is increased. MRTS allows for the substitution between factors of production: labor (L) and capital (K) in order to maintain a given level of output.

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 3 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

Write the technical rate of substitution expression for f(x1, x2) = (x1 - 1)0.25 x20.5
Does the output maximization level of input use exist for the following function? If yes, then what is the exact input-use level? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23
Please only do, d,e,f please!
Suppose that a furniture manufacturer produces tables. The manufacturer's production function is Q(KL)- 2K0.8 0.2 where Kis the number of wood saws and L is the number of labor hours used to produce tables. The prevailing wage rate is $10 per hour and the rental rate associated with wood saws is $50. The manufacturer has a goal to produce 1,000 units. What Lagrangian equation can be used to solve the manufacturer's cost minimization problem? Oa. C = 2K12 s.t. 1,000 = 50K + 10L b. = Oc L = Od. L = 10K + 50L s. t. 1,000 = 2K08102 50K + 10L s.t. 1,000= 2KL02 2K10 s. t. 1,000= 10K + 50L
Please can I get some help with this question
Al's production function for deer is f(x1,x2) = (2x1 + x2)^1/2, where x1 is the amount of plastic and x2 is the amount of wood used. If the cost of plastic is $4 per unit and the cost of wood is $3 per unit, then the cost of producing 5 deer is a) $55 b) $10 c) $50 d) $75
in part b, how do we know that is the cost function? where are those variables coming from? thx
Isoquants have a v slope and, for Cobb-Douglas production functions, are The MRTS is v and is the v of the slope of the isoquant.
Number
The technical rate of substitution between factors x2 and x1 is −4. If you desire to produce the same amount of output but cut your use of x1 by 3 units, how many more units of x2 will you need?
Could I have some help deriving the solutions? I’m confused given that it isn’t a standard cobb Douglas function
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.