Production functions Economists model the output of manufacturing systems using production functions that have many of the same properties as utility functions. The family of Cobb-Douglas production functions has the form P = f(K, L) = CKa L1–a, where K represents capital, L represents labor, and C and a are positive real numbers with 0 < a < 1. If the cost of capital is p dollars per unit, the cost of labor is q dollars per unit, and the total available budget is B, then the constraint takes the form pK + qL = B. Find the values of K and L that maximize the following production functions subject to the given constraint, assuming K ≥ 0 and L ≥ 0.
55. Given the production function P = f(K, L) = KaL1–a and the budget constraint pK + qL = B, where a, p, q and B are given, show that P is maximized when K = aB/p and L = (1 – a)B/q.
Trending nowThis is a popular solution!
Chapter 12 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage