Write down the problem the car manufacturer solves to find the levels of 'K' and 'L' that minimize cost. What two equations are used to solve it? **Problem 10:**Consider a car manufacturer which uses capital $ K $ and labor $ L $ to produce $ q $ cars according to the production function:\[q = f(L, K) = L^{\frac{1}{8}} K^{\frac{3}{8}}\]This function expresses the output $ q $ in terms of the input quantities of labor $ L $ and capital $ K $, raised to the powers $\frac{1}{8}$ and $\frac{3}{8}$, respectively.

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Write down the problem the car manufacturer solves to find the levels of 'K' and 'L' that minimize cost. What two equations are used to solve it?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Write down the problem the car manufacturer solves to find the levels of 'K' and 'L' that minimize cost. What two equations are used to solve it?

**Problem 10:**

Consider a car manufacturer which uses capital $ K $ and labor $ L $ to produce $ q $ cars according to the production function:

\[
q = f(L, K) = L^{\frac{1}{8}} K^{\frac{3}{8}}
\]

This function expresses the output $ q $ in terms of the input quantities of labor $ L $ and capital $ K $, raised to the powers $\frac{1}{8}$ and $\frac{3}{8}$, respectively.

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