MANAGERIAL/ECON+BUS/STR CONNECT ACCESS
9th Edition
ISBN: 2810022149537
Author: Baye
Publisher: MCG
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Question
Chapter 5, Problem 13PAA
To determine
To find: The profit maximizing output, labor and maximum profit.
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You are a manager for Herman Miller, a major manufacturer of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is
Q = 2(K)1/2(L)1/2 where K represents capital equipment and L is labor. Your company has already spent a total of $8,000 on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. If workers at the firm are paid a competitive wage of $120 per day and chairs can be sold for $400 each, what is your profit-maximizing level of output and labor usage? What is your maximum profit?
You are a manager for Herman Miller—a major manufacturer of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is:Q = 2(K)1/2(L)1/2where K represents capital equipment and L is labor. Your company has already spent a total of $8,000 on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. If workers at the firm are paid a competitive wage of $120 and chairs can be sold for $400 each, what is your profit-maximizing level of output and labor usage?Output: Labor: What is your maximum profit?$
You are working to model your production function and you are interested in the equation of the line tangent to the production function at a specific level of production. You know that the equation of the tangent line will be first derivative of the production function. Given this information,
Previously, a consultant had estimated that your production function could be estimated as
f(x) = -1,000 + 26 hours - 0.2 hours^2
Given that you firm is planning to use 97 hours in the production process, what is the value of the equation of the tangent line at 97?
Chapter 5 Solutions
MANAGERIAL/ECON+BUS/STR CONNECT ACCESS
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- 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.arrow_forwardAssume that you are a manager for Haworth —one of the major manufacturers of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is Q = 2(K) 1/2 (L)1/2 where K represents capital equipment and L is labor. Hanworth has already spent a total of $10,000 on the 4 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. The workers at the firm are paid a competitive wage of $100. Also, the chairs can be sold for $200 each. Given the competitive wage of workers which is $100 and the price of chairs, what is your profit-maximizing level of output and labor usage? what is your maximum profit?arrow_forwardAssume that you are a manager for Haworth —one of the major manufacturers of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is Q = 2(K) 1/2 (L)1/2 where K represents capital equipment and L is labor. Hanworth has already spent a total of $10,000 on the 4 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. The workers at the firm are paid a competitive wage of $100. Also, the chairs can be sold for $200 each. Suppose that Hanworth aims to produce 200 units of chair, how much is the optimal level of capital(K) needed in the production to maximize your profit?arrow_forward
- The Cobb-Douglas production function for a particular product is N(x,y) = 80x0.6.0.4, 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 $60. Answer the questions (A) and (B) below. (A) If $150,000 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. C (A) If $150,000 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.arrow_forwardA firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $20 per worker-hour and the cost of capital is $10 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 28,800 plastic bins? Hint: The marginal products are MP, = K and MPg = L.arrow_forwardCost minimization when output is known and total costs are unknown. A factory that you are managing has an hourly production process that can be represented by the following Cobb Douglas Production function: Q = 2K0.50L 0.5 The price of one unit of capital per hour is $20 and the price of one unit of labour per hour is $20. You have been instructed to produce 200 units per hour or Q = 200. Find the optimal amount of labour and capital that you will be using, and compute the total cost.arrow_forward
- Q3, A firm operates with the following Cobb-Douglas production function where Q is output, L is labor hours per week, and K is machine hours per week. Cobb-Douglas Production Function: Q = 5(L1/3K2/3) The firm intends to produce 5,000 units of output per week by contracting employees for $40 per hour and renting machinery for $10 per hour. Determine the cost minimizing combination of labor and capital for the firm. Based on your solution in part (a), calculate the firm’s total cost of producing 5,000 units of output per week.arrow_forwardConsider a company that operates with a production function that coordinates units of work (L) and units of machines (K). The quantity of products produced in a month is given by the function Q = 3KL. Each machine is used at a monthly cost of $15,000 and each unit of work at a cost of 5,000 per month. The cost of the products is given by the labor cost, the cost of the machines and an additional $500 of raw materials per unit of product. Considering that the factory has 10 leased machines in operation (Fixed Cost) and could hire any amount of work each month. Ask if: a) Indicate the Average and Marginal Productivity functions of L b) Indicate the short-run total, average and marginal cost functions of this factory as a function of Q (quantity of product). c) How many units of work are required to produce 300 units of product? What is the average cost per product? d) What is the marginal cost of unit 300, calculated in (c)? e) What is the marginal rate of substitution for K and L? In…arrow_forwardThe Cobb-Douglas production function for a particular product is N(x,y) = 80x0.6y0 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 $100. If $500,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production. Production will be maximized when using units of labor and units of capital.arrow_forward
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