A manufacturer's production ismodelled by the function f(x, y) = 100x 34 y 14 where xуrepresents the units of labourand y represents the units ofcapital. Each labour unit costs $200 and each capital unit costs $250. The total expenses forlabour and capital must be $50, 000. Find the maximumproduction level.

The objective of the question is to find the maximum production level given the cost constraints for…

Answered: A manufacturer's production is modelled…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i. e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i. e. MPL = 1000). The price of a man- hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $25 per hour. How does this change the answer from part 1?
Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 600 bottles per day (i. e. MPK = 600). An additional man-hour of labor would increase output by 1200 bottles per day (i. e. MP₁ = 1200). The price of a man-hour of labor is $40 per hour. The price of a machine-hour of fermentation capacity is $8 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally choosing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $20 per hour. How does this change the answer from part 1?
Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost.a) Find the marginal product of each input.b) Determine whether the production function exhibits diminishing marginal product to each input.c) Find the marginal rate of technical substitution(MRTSLK)d) How does MRTSLK change as more L, is used holding output constant.e) Find the least costly combination of labor and capital to produce 3000 units
Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?
A firm’s production is represented by the following function: Q = L1/4 K3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs?b. How much capital and labor should be used to produce 400 units of output? What is the total cost?c. What is the short run total cost if output is decreased to 300 units?d. How would the capital labor choice and total cost change in the long run?e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternativelocation assuming relocation is costless?
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.
Suppose a firm is producing computer monitors utilizing the following technology: Q=F(K,L)=L1/3K2/3 Q – weekly output L – labor hours K – hours of capital use Would the firm with the above production function be able to produce monitors using only capital (no labor)? Explain.
A firm estimates its long-run production function to be Q = -0.0050 K3L3 + 15 K2L2 Suppose the firm employs 10 units of capital. At units of labor, average product of labor begins to diminish? A) 350 B) 66.67 C) 100 D 150 E) 1500

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