8. Consider a Firm producing a given output in the long run; the inputs employed in production are labour L, which costs w > 0 per unit, and capital K, which costs r > 0 per unit. The Firm produces a quantity Q according to the following production function: Q(K, L) = 4K/3 L²/3. Suppose the Firm's target is to produce 1,000 (Q = 1,000). (a) Find the cost-minimising combination of inputs K* and L' when w = 160 and r = 80, then compute the corresponding long-run cost of production. (b) Suppose that the rental price of capital decreases to w' 20. Find the new cost-minimising input combination. (c) Use your answers to points a) and b) to calculate the firm's price elasticity of demand for capital over this range of prices (rounded to two digits).

8. Consider a Firm producing a given output in the long run; the inputs employed in production are labour L, which costs w > 0 per unit, and capital K, which costs r > 0 per unit. The Firm produces a quantity Q according to the following production function: Q(K, L) = 4K/3 L²/3. Suppose the Firm's target is to produce 1,000 (Q = 1,000). (a) Find the cost-minimising combination of inputs K* and L' when w = 160 and r = 80, then compute the corresponding long-run cost of production. (b) Suppose that the rental price of capital decreases to w' 20. Find the new cost-minimising input combination. (c) Use your answers to points a) and b) to calculate the firm's price elasticity of demand for capital over this range of prices (rounded to two digits).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.3P

See similar textbooks

Similar questions

2. Suppose a producer's production function is F(X,L) = 3K-L2 The cost of K is 20 (r-20) and the cost of L is 80 (w = 80) The firm wants to produce 30 units of output. a. What is the cost-minimizing way for the firm to produce 30 units of output? How many units of capital and how many units of labor should be used? b. Suppose the firm has committed itself to 4 units of capital (K) and therefore is operating in the short run. What combination of inputs is the least costly way for it to produce 30 units now?
6 A production function is given by f(x1,x2)=(max{x1,x2})^0.5. Prices of inputs are p1=10 and p2=20. What is the lowest cost of producing 10 units of output?
Problem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…
4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…
4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…
1) Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q = 4K L where q is the number of reams produced, Kis the quantity of capital rented, and L is the quantity of labor hired. For this production, MP, = and MP, = The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost What ratio of capital to labor minimizes Miguel and Jake's total costs? (Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital and labor.) b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week? How much will hiring these inputs cost them?
8
7. A fast-food company in Hermanus has the following cost function: TC = 10 + 3K + 2L, where L is the number of labour hours and K is the number of machines they have to use. They have a production function of Q = 2KL, where Q represents the number of meals produced per day. The company has to make at least 75 meals every day. Using the Lagrangian method of production optimization, calculate the optimal number of labourers and machines needed to meet this quota. (6)
1. Let y = f(x1, x2)=x11/2+ X1X2 be a firm's production function, where x20, x220. - a. Write down the firm's production possibility set, and its input requirement set.“ b. Is this production function concave, quasi-concave? c. Is this production function homogenous, homothetic? + d. Find its returns to scale when x1=1, and x2=1.e
3. Suppose a production function is given by F(K, L) = KL?; the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes the cost of producing any given output?
2. A firm faces the production function 1 Q = f(K,L) = 80 [0, 4K-0,25 +0,4L-0,25] 0.25. It can buy the inputs K and L at prices per unit of 5 TL and 2 TL respectively. What combination of L and K should be used to maximize output if its input budget is constrained to 150 TL?
Please answer fast and Arjent please