Explanation Given information: The production function is q = c K α L β , Where q is the quantity produced per month, K is the amount of capital invested, L is the amount of labour available each month and c , α , β are positive constants. L is the measure in man-hours per month, and that each man-hours costs the company w rubles. Formula used: The profit π ( q ) is the difference between the revenue, R ( q ) , and the cost, C ( q ) , of supplying that quantity. ⇒ π ( q ) = R ( q ) − C ( q ) The revenue is given by R = q . p , where q is the quantity and p is the price of the product. Calculation: q = c K α L β (Given) The revenue is given by R = q . p . ⇒ R ( L ) = c K α L β p Since, L is the measure in man-hours per month, and that each man-hours costs the company w rubles, the cost is C ( L ) = w L . The profit is π ( L ) = R ( L ) − C ( L ) ⇒ π ( L ) = c K α L β p − w L Differentiating with respect to ‘L’, we get π ' ( L ) = c β K α L β − 1 p − w To find the critical point, equate π ' ( L<

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 4.4, Problem 34P

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To calculate:

The man-hours of labour per month should the company use in order to maximize the profit.

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Chapter 4 Solutions

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The man-hours of labour per month should the company use in order to maximize the profit.

Solution Summary: The author calculates the man-hours of labour per month that the company should use to maximize the profit.

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To calculate: The man-hours of labour per month should the company use in order to maximize the profit.

Chapter 4 Solutions

To calculate:

The man-hours of labour per month should the company use in order to maximize the profit.