3 Consider the production function of candles, with capital (K) and labour (L) as inputs: Q=K0.1L0.9 3.1 Show that both additional labour and additional capital increase production at a decreasing rate by computing and referring to some of the second derivatives of Qe 3.2 Now consider the production function of an additional product, electrical generators, de- fined by the following function: Qeg = K0.6L0.4 Show, using the Jacobian derivative matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units, would approximately change production of both goods. Start from an initial combination of K = 100 and L = 50.
3 Consider the production function of candles, with capital (K) and labour (L) as inputs: Q=K0.1L0.9 3.1 Show that both additional labour and additional capital increase production at a decreasing rate by computing and referring to some of the second derivatives of Qe 3.2 Now consider the production function of an additional product, electrical generators, de- fined by the following function: Qeg = K0.6L0.4 Show, using the Jacobian derivative matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units, would approximately change production of both goods. Start from an initial combination of K = 100 and L = 50.
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter7: Production Economics
Section: Chapter Questions
Problem 10E
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Transcribed Image Text:3 Consider the production function of candles, with capital (K) and labour (L) as inputs:
Qc = K0.1 L0.9.
3.1 Show that both additional labour and additional capital increase production at a decreasing
rate by computing and referring to some of the second derivatives of Qe.
3.2 Now consider the production function of an additional product, electrical generators, de-
fined by the following function: Qeg
= K0.6 L0.4. Show, using the Jacobian derivative
matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units,
would approximately change production of both goods. Start from an initial combination
of K = 100 and L = 50.
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