Constrained Optimization A firm wants to minimize the cost of producing 100 units of output given that the cost of labor (w) is $10 and the cost of capital (r) is $5. Output is produced according to the Cobb-Douglas production function: Q = 10L-5K-5. What is the mix of inputs that minimizes the cost of producing 100 units?

Constrained Optimization A firm wants to minimize the cost of producing 100 units of output given that the cost of labor (w) is $10 and the cost of capital (r) is $5. Output is produced according to the Cobb-Douglas production function: Q = 10L-5K-5. What is the mix of inputs that minimizes the cost of producing 100 units?

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter7: Production And Cost In The Firm

Section: Chapter Questions

Problem 21PAE

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part D E F urgently needed
II. Helping Conchita-Crem to minimize costs Suppose that the labor cost of Conchita-crem is $20 USD per hour, and the cost of capital is $5 USD per hour. Suppose the production function for conchas is q = 10L/2K2 a) José Antonio produces 1000 conchas. He is currently using 100 workers and 100 ovens. Is he optimizing his use of inputs of production? b) What is the rule to optimize the use of inputs of production? c) Find the optimal level of labor and capital for Conchita-Crem. What is its total cost? d) Now suppose that the rental price of ovens for Conchita-Crem increases 100%. Would the production change? What would be now the rule to efficiently use inputs of production? How much labor and capital be used? What is the total cost now? Compare it to your answer in c. e) Find the input demand functions for capital and labor. Remember these functions specify the amount of labor or capital that Conchita-Crem will use as a function of production level q. f) Suppose now that José Antonio…
part D E F
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oboard S Font Paragraph S Sensitivity Styles Editing Voice A Cobb-Douglas production function for new company is given by FF(KK, LL) = KK3/5LL2/5 where K represents the units of capital and L represents the units of labor. Suppose units of labor and capital cost $200 and $100 each respectively. If the budget constraint is $30,000, find the maximum production level for this company. VAAAWMMAA AAAAAAAAA SAAAAAAA
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Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.
A company produces commercials. A 2-minute commercial, for example, needs exactly 5 minutes of filming and 8 minutes of editing. Let x1 denote the minutes of filming and x2 denote the minutes of editing. a) Write down the production function and state whether it has increasing, constant, or decreasing returns to scale b) Suppose that filming costs $45 per minute and editing costs $10 per minute. To produce a 5-minute commercial, how many minutes of filming and how many minutes of editing is needed to minimize cost? c) Suppose that filming costs w1 per minute and editing costs w2 per minute. Let y denote the length (in minutes) of commericals produced. derive the conditional factor demand functions x1(w1,w2,y) and x2(w1,w2,y) and its cost function c(w1,w2,y)
A firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L^1/2M^1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400and another isocost line showing combinations that cost $200.2. Suppose that the firm wants to produce its output in the cheapest possible way. Find thenumber of machines it would use per worker. (Hint: The firm will produce at a point wherethe slope of the production isoquant equals the slope of the isocost line.)
Solve parts d and e please
When do we say that a firm is operating with least cost combination of inputs?
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