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4.4.3 A firm's output Y is related to capital input K, labour input L and natural re- source input R by the production function Y = 2K/2L/3R'/6 |3D Write down a linear relationship between the logarithms to base 10 of Y, K, L, R.

4.4.3 A firm's output Y is related to capital input K, labour input L and natural re- source input R by the production function Y = 2K/2L/3R'/6 |3D Write down a linear relationship between the logarithms to base 10 of Y, K, L, R.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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I need help with question 4.4.3
QUADRATICS 76 (4.10) Logarithms in economics: an example faking logarithms (all to the same base) and applying L1 and L2, log Y -log 5+ log (K0.4)+log (L0.6). production function Let y = log Y, k= log K andl = log L. Then by L4, y = 0.4k +0.6l- log 5. (4.11) Equation (4.11) is a linear relationship between the logarithms of the economic variables. For this reason, relations such as (4.10) are said to be log-linear. The pro- cedure of transforming a non-linear relationship into a linear one by taking logarithms is a very useful one, and we shall return to it in Chapter 9. Exercises 4.4.1 Evaluate, without using a calculator, the following: (a) logs 125, (b) log3(1/125), (c) logg 64, (d) logg 4, (e) logs 256. 4.4.2 Use the properties of logarithms to show that log = 1/ log a. 4.4.3 A firm's output Y is related to capital input K, labour input L and natural re- source input R by the production function Y = 2K/2L/3R'/6 Write down a linear relationship between the logarithms to base 10 of Y, K, L, R. Problems on Chapter 4 4-1. Solve simultaneously the equations q = 5 – p², q = 2p – 3. Now suppose p represents price and q quantity, and that the equations represer demand and supply curves respectively. Sketch the parts of the curves which là in the non-negative quadrant state the equilibrium price and quantity. 4-2. This problem is concerned with a class of functions which are not quadrati can be minimised by completing the square
Transcribed Image Text:QUADRATICS 76 (4.10) Logarithms in economics: an example faking logarithms (all to the same base) and applying L1 and L2, log Y -log 5+ log (K0.4)+log (L0.6). production function Let y = log Y, k= log K andl = log L. Then by L4, y = 0.4k +0.6l- log 5. (4.11) Equation (4.11) is a linear relationship between the logarithms of the economic variables. For this reason, relations such as (4.10) are said to be log-linear. The pro- cedure of transforming a non-linear relationship into a linear one by taking logarithms is a very useful one, and we shall return to it in Chapter 9. Exercises 4.4.1 Evaluate, without using a calculator, the following: (a) logs 125, (b) log3(1/125), (c) logg 64, (d) logg 4, (e) logs 256. 4.4.2 Use the properties of logarithms to show that log = 1/ log a. 4.4.3 A firm's output Y is related to capital input K, labour input L and natural re- source input R by the production function Y = 2K/2L/3R'/6 Write down a linear relationship between the logarithms to base 10 of Y, K, L, R. Problems on Chapter 4 4-1. Solve simultaneously the equations q = 5 – p², q = 2p – 3. Now suppose p represents price and q quantity, and that the equations represer demand and supply curves respectively. Sketch the parts of the curves which là in the non-negative quadrant state the equilibrium price and quantity. 4-2. This problem is concerned with a class of functions which are not quadrati can be minimised by completing the square
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