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.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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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