6. Optimize the Cobb-Douglas production function given the following parameters. The maximum about of money available to spend is $1, 600 where the price of K = 12 and the price of L = 6. That is P = 12 and P = 6. The function is given as q = K0.4L0.6. Using the Lagrangian method, what are the optimal values of Ko and Lo?
Q: Consider a competitive, closed economy with a Cobb-Douglas production function with parameter α =…
A: The production function shows the relationship between the inputs and the output. In other words, it…
Q: We consider a CES production function. Y = A + (1 – a)L̟º Q1: As o → 1, prove the Cobb-Douglas…
A: Given production function Yt=AαKtσ-1σ+(1-α)Ltσ-1σσσ-1
Q: A firm can manufacture a product according to the production function Q = F(K, L) = K0.5L0.5. (a)…
A: We are going to calculate average product of labour and marginal product of labour
Q: H8. Which of the following production functions exhibit(s) constant returns to scale?I. Q = Min…
A: There are CRS if the doubling the all inputs result in the double of output.
Q: The following is a Cobb-Douglas production function: Q = 1.75K0.6L0.5. What is correct here? *…
A: Since the sum of coefficient of L and K is higher than 1 (= 0.5 + 0.6 = 1.1), there are increasing…
Q: Given the production function Q=20L+8K and cost budget = 1000JD; w (Price per unit of labor)=8;…
A: Production function exhibits the relationship between the input and the output. The production…
Q: In a certain country, output is produced using only labor and land. The production function is…
A: Given information Y = AXα L1-αSubstitute x = 100 and L = 30 Y = A100α 301-α
Q: Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 70L0.6 K0.4 where L…
A: Production function P(L,K) = 70L0.6K0.4 ...... (1) Where L is the labor units and K is the…
Q: Suppose that firms face the following production function: Q = 10 + L+K+2L/2K1/2, This production…
A: please find the answer below.
Q: Which of the following production functions exhibit constant returns to scale? In each case y is…
A: Given: The production functions are: 1y=K12L132y=3K12L12(3)y=k12+L12(4)y=2K+3L
Q: A firm has a short-run production function as Q = 50 L + 6 L2 – 0.5 L3 Where Q = Quantity of…
A: The short-run is the time period where at least one factor is fixed and others are variable. In…
Q: combination of labor and capital maximizes output with a cost of Birr 720? b. What is the maximum…
A: With the given production function, it can be inferred that the firm uses two inputs labor (L) and…
Q: increasing, decreasing
A: A production function tends to relate the physical output of a production process to factors of…
Q: Given the production function: Q = 0.5C ^ 2 + 12CL + 1.5L and the total acceptance function: TR =…
A: Production Function Q = 0.5C2 + 12CL + 1.5L DIfferentiate Q with respect to C to get Marginal…
Q: > The production function for gadgets is: Q = Q(L, G) = L½ + G½ ne price of L is w = $2. The price…
A: A production function has Diminishing returns to scale when change the inputs changes the output by…
Q: With a production function of if r = $4 and w = $4, how many units of capital and labor will be…
A: Profit maximizing firm would employ labor and capital at the point where the marginal productivity…
Q: Consider the production of some output Q using capital K and labour L. a) Assume K is fixed. Draw a…
A: Production function refers to that function which provided maximum level of output for given level…
Q: Show whether the following production functions exhibit decreasing returns to scale (DRS), constant…
A: Production function shows the output produced in an economy by using the available factors of…
Q: 4. LR and SR: Returns to Scale and Diminishing Returns Q- LaK > Consider a general Cobb-Douglas…
A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…
Q: Margeʹs Hair Salon production function is Q = f(K, L) = K0.5L0.5 where K is the number of hair…
A: 2.1 Prove, with the aid of mathematics, the type of returns to scale exhibited by this production…
Q: A firm's production function is: q = 20L1/2K1/2 where q is the firm's total product, L is the…
A: Given firm's production function is: q = 20L1/2K1/2 Price of labor is $25 per unit and the price of…
Q: 1. For each of the following production functions, determine whether there areincreasing, constant…
A: A production function shows the maximum level of output that can be produced with the help of…
Q: Ricardo-Viner Model a. Consider a manufacturing firm where total cost (TC) equals the product of the…
A: Given information Manufacturing firm is working under perfect competition. Total cost is cost…
Q: Given the production function f (L K) = L2 / 3. K1 / 3, where L is the working hours and K is the…
A: Cost is minimised at a point where marginal rate of technical substitution is equal to the price of…
Q: The Cobb-Douglas production function for a particular product is N(x,y) = 80x0.60 4 where x is the…
A:
Q: A firm produces output according to a production function: Q = F(K,L) = min {4K,8L}. a. How much…
A: Q = min[4K, 8L] a) K = 2 , L = 3 Q = min[4(2), 8(3)] = min[8, 24] Q = 8units
Q: The manager of Dixie Furniture Company estimates that the daily output of her factory (in thousands…
A: a.) Daily output of the factory can be calculated as follows: If X = 81,000 and Y = 265,000 Thus,…
Q: Optimize the Cobb-Douglas production function given the following parameters. The maximum about of…
A: (Q) Optimize the Cobb-Douglas production function given the following parameters. The maximum about…
Q: Question 3 The board of a firm wanted to get value for money by employing the right number of…
A: We are going to use single variable maximisation method to answer this question.
Q: 600 2100 2500 2600…
A: Capital is a fixed factor. A fixed amount is assumed to be invested, the interest on which is 10%…
Q: There are three factors of production, capital, K, skilled labour L; and unskilled labour Ly. Which…
A: a production function gives the technological relation between quantities of physical inputs and…
Q: 6. A general version of the Cobb-Douglas production function can be written as f(#1,..,In) = '.…
A: The Technical Rate of Substitution (TRS) is the rate at which one input must decrease so that the…
Q: Draw labeled graph according to the question: The change in the optimal capital-labor ratio if both…
A: If both the inputs(labour and capital) are perfect complements in production, they are to be used…
Q: Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r…
A: Note: Since, you've posted a question with multiple sub-parts, we will solve the first three…
Q: subject to the budget constraint 5L + 10K = 75; where L is labour and K is capital. Derive the…
A: The production function shows the relationship between the output and inputs. The equilibrium is…
Q: Under what conditions do the following production functions exhibit decreasing, constant, or…
A: When an increase in inputs results in a proportional increase in output, there occurs constant…
Q: In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm…
A:
Q: Q=L3/4.K1/4 Find out the optimal quantities of the two factors using Lagrangian method, if it is…
A: Production function is Q=L3/4×K1/4 Wages = Rs.6 Capital = Rs.3 Total Cost = Rs.120 Find: Optimal…
Q: Consider the following production function: f (A, B) = gamma multiply A^alpha multiply B^Beta. where…
A: We are going to use function separability theorem to answer this question.
Q: A firm has two opportunities for a new plant location, one is in China and the other is in Mexico.…
A: A firm has two opportunities for a new plant location, one is in China and the other is inMexico The…
Q: 0.7 The Cobb-Douglas production function for a particular product is N(x,y) = 80xyo, where x is the…
A: Production function: N (x,y) = 80x0.7y0.3 Wage per labor (w) = $80 Rent per capital (r) =…
Q: Q3, A firm operates with the following Cobb-Douglas production function where Q is output, L is…
A: Given information Production function Q = 5(L1/3K2/3) Wage rate= $ 40 per hour Rent=$10 per hour The…
Q: Consider the following Cob-Douglas production function: f(k.1) = K°P°, where a 20 and > 0. 1. Show…
A: a) f(k,l) = kαlβf(nk,nl) = (nk)α(nl)β f(nk,nl) =nαkαnβlβf(nk,nl) =nα+β*(kαlβ)It is given that α>0…
Q: Returns to scale in production: Do the following production functions exhibitincreasing, constant,…
A: Note: Since you have asked multiple parts, we will solve the first 3 parts for you. If you want any…
Q: In the short run, we assume that capital is a fixed input and labor is a variable input, so the firm…
A:
Q: 1) Suppose a firm uses capital, K, and labor, L, to produce output. Verify whether the following…
A: Note; Since we can only answer up to three subparts, we'll answer first three please repost the…
Q: For the production function q = f(K, L) the ratio of the percentage change on with PK is called…
A: cobb douglas production function:- Q=ALαKβ in the cobb douglas production function, we have…
Q: Assume labor (L) is the only variable input used in the production process, a firm’s production…
A: Production refers to the process in which the output is produced using the factors of productions.…
show all working.
Step by step
Solved in 2 steps
- Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.Suppose there are two inputs for production, labor and capital. The firm’s production process isdefined by the following production functiony=f(L,K).Howdoweinterpretthefirm’smarginalrateof technical substitution? a)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same cost level b)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm produces one more unit of output c)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same level of production d)a) and b) are correct e)a) and c) are correct
- Does the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?(04.Suppose we are given (he constant returns to scale (CES) production function q= { ßa + aa }1/a a. Show that the marginal product of Beta is (g/B) and marginal product of Alpha (q/a)** b. Show that RTS = (2/B); I lence or otherwise shov that the ò =-1/(1-a) 1-aIf output is produced according to Q = 4LK, the price of K is $10, and the price of L is $40, then the cost minimizing cost minimizing combination of K and L capable of producing 64 units of outputlis L O and K 64 (please put your answers in numerical value with no comma or decimal place)
- Please don't copy ans Economics You are the owner of a motorbike company that currently has two different factories, an old one and a new one. The old factory uses an old technology that requires large amounts of labor to produce motorbikes. The production technology for the old firm is given by Fo(L) = m*L^1/2 . The new factory uses a much more modern production technology given by Fn(L) = n*L^1/2 . a. What are costs as a function of output for each individual factory? b. Suppose that you want to produce 1000 motorbikes. How many motorbikes will you produce at the old factory and how many will you produce at the new factory? c. Derive an expression for the total cost of producing y motorbikes (assuming that you always divide production between the factories in the optimal way). How does this cost function compare to the individual factory cost functions? d. It turns out that you can upgrade your old factory to make it just as efficient as the new factory. To pay…A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the unit is $760 per month, all the unit will be filled, but 1 unit will become vacant for each $20 increase in this monthly rate. If the monthly cost of maintaiing the apartment building is $12 per rented unit, what rent should be charged per month to maximize the profit? $ =A firm face the production function:Q=120L+200K-L2-2K2It can buy L at N5 a unit and K at N8 a unit with a budget of N70. Use any method ofyour choice to find the maximum output the firm can produce.
- Question: Orla manages a loom that produces flags (F) using thread (T) and dye (D) as inputs. Herproduction function is given by: Q(T,D) = (T1/2 D1/2)1/2*For this problem, assume F, T, and D are infinitely divisible so you don’t need to worryabout restricting to whole-number answers. a.) Does Orla’s production function exhibit increasing, constant, or decreasing returns toscale? Explain. b.) Set up Orla’s cost-minimization problem to find the lowest-cost combination of inputsrequired to produce a specific level of output (bar Q) given factor prices PT and PD. (Note: You can write this either as a minimization subject to constraints or in Lagrangian form. *You do not need to solve it.)Very short answer ...Given the following data on input and output levels. Suppose the output price is $2 and input price is $3. Find the values of AVP and MVP when X = 2: %3D X. Y 1 10 2. 25 3 45 4 60 70 75 $30 and $50 $30 and $30 $4 and $50 $25 and $30