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Problem 3. The marginal product of labor (i.e., the increase in total output if one more worker is employed) is equal to 5,000/x+2000 where x is the number or employees. Currently the firm employes 500 people and produces 1200 units of product. a) Using integrals, find the production function Q(x), i.e., find how much the firm will produce (Q) as a function of how many people it employs (x). b) If the wage is equal to $100 per worker and the firm is able to sell its product for $70 per unit, how many people the firm needs to employ to maximize its profit? Note that the profit is equal to π =70Q-100x. Note also that you will have to use the knowledge from previous chapters. c) Without performing any calculations, state how your answer to part (b) will change (increase, decrease, or stay the same) if the firm with 500 employees would have produced 1300 units of product instead of 1200. Assume all other information remains the same.

Problem 3. The marginal product of labor (i.e., the increase in total output if one more worker is employed) is equal to 5,000/x+2000 where x is the number or employees. Currently the firm employes 500 people and produces 1200 units of product. a) Using integrals, find the production function Q(x), i.e., find how much the firm will produce (Q) as a function of how many people it employs (x). b) If the wage is equal to $100 per worker and the firm is able to sell its product for $70 per unit, how many people the firm needs to employ to maximize its profit? Note that the profit is equal to π =70Q-100x. Note also that you will have to use the knowledge from previous chapters. c) Without performing any calculations, state how your answer to part (b) will change (increase, decrease, or stay the same) if the firm with 500 employees would have produced 1300 units of product instead of 1200. Assume all other information remains the same.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.3: Rates Of Change
Problem 6E: Find the average rate of change for each function over the given interval. y=3x2 between x=1 and x=2
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Problem 3. The marginal product of labor (i.e., the increase in total output if one more worker is employed) is equal to 5,000/x+2000 where x is the number or employees. Currently the firm employes 500 people and produces 1200 units of product. a) Using integrals, find the production function Q(x), i.e., find how much the firm will produce (Q) as a function of how many people it employs (x). b) If the wage is equal to $100 per worker and the firm is able to sell its product for $70 per unit, how many people the firm needs to employ to maximize its profit? Note that the profit is equal to π =70Q-100x. Note also that you will have to use the knowledge from previous chapters. c) Without performing any calculations, state how your answer to part (b) will change (increase, decrease, or stay the same) if the firm with 500 employees would have produced 1300 units of product instead of 1200. Assume all other information remains the same. d) A competitor firm has access to a better technology and has a larger marginal. (5,000/x+2000 + e -0.001x). By how much the total output of this firm will product of labor of increase if it increases its current staff from 700 to 1000 employees. Round your answer to the nearest integer number.
Transcribed Image Text:Problem 3. The marginal product of labor (i.e., the increase in total output if one more worker is employed) is equal to 5,000/x+2000 where x is the number or employees. Currently the firm employes 500 people and produces 1200 units of product. a) Using integrals, find the production function Q(x), i.e., find how much the firm will produce (Q) as a function of how many people it employs (x). b) If the wage is equal to $100 per worker and the firm is able to sell its product for $70 per unit, how many people the firm needs to employ to maximize its profit? Note that the profit is equal to π =70Q-100x. Note also that you will have to use the knowledge from previous chapters. c) Without performing any calculations, state how your answer to part (b) will change (increase, decrease, or stay the same) if the firm with 500 employees would have produced 1300 units of product instead of 1200. Assume all other information remains the same. d) A competitor firm has access to a better technology and has a larger marginal. (5,000/x+2000 + e -0.001x). By how much the total output of this firm will product of labor of increase if it increases its current staff from 700 to 1000 employees. Round your answer to the nearest integer number.
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