You manage a firm that has the production function q = 18L1/3K1/2. You can hire labor (L) at a wage of $15 per unit oflabor and rent capital (K) at a rate of $6 per unit of capital. Your boss gives you a budget of $1800.Write your budget constraint in terms of inputs (L and K):What is your optimal amount of L and K?L =K =Does the firm have increasing, decreasing or constant returns to scale?How much output (q) can you make when operating at peak efficiency given these constraints? Round your answer to 2decimal places as necessaryq=

Approach to solving the question: Detailed explanation:budget constraint in terms of inputs (L and…

Answered: You manage a firm that has the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q₂ A production function is given by q = 500L + 700K. The price of capital is $120 and the price of labor is $100. If the firm wants to produce 1,400 units of output, how many units of labor should it use? Your Answer: Answer
Find the MRTS for a firm with production function f(L,K)=(L)^2+vK. Is it diminishing?
ASAP!!
Consider the following production functions• F(L,K) = LK^3 For each for these production functions: (a) Draw the corresponding graph (b) Calculate the marginal product of labor and capital (c) Discuss if each marginal product is diminishing, constant or increasing (d) Calculate the marginal rate of technical substitution (e) Calculate if the function exhibits constant, increasing, or diminishing returns to scale*Just solve d and e
Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1 and the cost of a unit of capital is $3. The manager of this firm is interested in finding the following information: a) Type of returns to scale and the marginal products of labor and capital. b) The marginal rate of technical substitution of labor for capital. Graph the isoquant map. c) The firm is currently producing 100 units of output. Find the optimal cost-minimizing quantities of labor and capital. Graphically illustrate this optimal solution using isoquants and isocost lines. What is the minimum total cost? d) The manager now wants to know the K/L ratio to produce anyoutput level at the minimum total cost. Represent graphically the expansion path in the long run.
Which of the following statements is (are) TRUE?I. If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line.II. If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped.III. If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output. IIII, II, and IIIII and II Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Suppose you are the production manager of a firm that has a production function: Q = (K )(L^0.5) where Q represents the firm’s level of output, K is the number of units of capital you utilize, and L is the number of units of labour you hire. The rental rate of a unit of capital is given by r = $100, and the wage rate for a unit of labour is given by w = $10. The firm operates in a competitive market where its output can be sold for $100 per unit. (a) Suppose the firm is operating in the short run, with its capital fixed at K = 1. What level of Q will maximize its profits? (b) Now suppose that in the long run, the firm can set its capital to be either K=1 or K=2. What would you recommend in order to maximize profit?
Suppose the production of Scooby Snacks at x units of labor and y units of capital is given by the Cobb-Douglas production function P(x, y) = kx"y" where m, n, k are known positive constants and m+ n = 1. The company can spend only p dollars for the production of Scooby Snacks. The cost of one unit of labor is b dollars, while the cost of one unit of capital is c dollars. Using Lagrange multipliers, find an expression for x and y where maximum production will occur?
The Cobb-Douglas production function for a particular product is N(x,y) = 40x0.6.0.4, where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $40 and each unit of capital costs $120. Answer the questions (A) and (B) below. (A) If $300,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. (B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $50,000 is budgeted for the production of the product. (A) If $300,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. Production will be maximized when using units of labor and units of capital.
Suppose that the production function for Hannah and Sam's home remodeling business is Q = F(L,K) Q = 10L0.1K0.4.Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $1,000 per week.a. What is the least-cost input combination for remodeling 400 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places. $ .revised jrl 08-11-2011
Lesson 8 - Costs Question 3
Suppose a firm uses a single input to produce a single output according to a production function f(x) = 10√x where x is the number of units of input. The output initially sells for £120 per unit. The input costs £20 per unit. A change in the market causes the product price to increase from £120 per unit to £200 per unit, all else equal. How does this change in product price affect the firm's profit maximizing level of profits? a. Profits increase by £16,000 Ob. Profits do not change Profits increase by £8,000 d. None of the other answers is correct Profits increase by £9,000 f. Profits increase by £18,000 g. Profits increase by £50,000 h. Profits increase by £32,000 C. e.

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