3 Production Many Variable Inputs Ch 7

3 Production Many Variable Inputs Ch 7 - Production and...

Info iconThis preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
Production and Cost: Many Variable Inputs
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
In most real situations, firms have the ability to vary more than one input during the relevant time period. They can substitute more of one input for less of another. We can illustrate all the different combinations of inputs that yield the same level of total output as a production isoquant.
Background image of page 2
Example: Our Courier Recall: y = courier services measured in km z 1 = driver’s time measured in hours z 2 = gasoline measured in litres The production function is y = (1200z 1 z 2 ) 1/2 Suppose we want to cover 120 km. 120 = (1200z 1 z 2 ) 1/2 14400 = 1200z 1 z 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
There are all kinds of input bundles that will satisfy this equation. For example, 2 hrs driving and 6 litres gas 4 hrs driving and 3 litres gas, etc. Suppose we want to cover 240 km. 240 = (1200z 1 z 2 ) 1/2 57600 = 1200z 1 z 2 48 = z 1 z 2
Background image of page 4
For 240 km, can drive 6 hrs with 8 litres gas drive 4 hrs with 12 litres gas… We can graph all the combinations of driving time and gas usage that will result in 120 and 240 km covered, respectively, on an isoquant map.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The higher the isoquant, the greater the quantity of output.
Background image of page 6
Marginal Rate of Technical Substitution, MRTS The MRTS measures the rate at which one input can be substituted for the other, with output remaining constant. The MRTS is the absolute value of the slope of the isoquant. It tells us the rate at which we must increase the qty of input 2 per unit decrease in qty of input 1. Example: if MRTS = 2.5, if we decrease input 1 by 1, we must increase input 2 by 2.5.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Note that MRTS uses a marginal reduction in qty of input 1. That is, since the slope is z 2 / z 1 , let z 1 r 0. Generally, it becomes progressively harder to substitute one input for another. You need more and more of input 2 to compensate for each unit decrease in input 1. MRTS gets smaller – diminishes – as we move from left to right along an isoquant.
Background image of page 8
MRTS and Marginal Product When the qty of input 1 is decreased by z 1 , the change in total output y is approximately the MP of input 1 multiplied by z 1 y = MP(z 1 ) z 1 or z 1 =r y / MP(z 1 ) The change in input 2, z 2 , must yield a corresponding change in output y y = MP(z 2 ) z 2 or z 2 = y / MP(z 2 )
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Since MRTS, the |slope of the isoquant|, is z 2 / z 1 , Then, MRTS = z 2 / z 1 = [ y / MP(z 2 ) ] / [ y / MP(z 1 ) ]
Background image of page 10
Numerical Example A production function is given by F(z 1, z 2 ) = 16z 1 z 2 MP(z 1 ) = δ F(z 1, z 2 ) / δ z 1 = 16z 2 MP(z 2 ) = δ F(z 1, z 2 ) / δ z 2 = 16z 1
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MRTS ( z 1 , z 2 ) = MP(z 1 ) / MP(z 2 ) = 16z 2 16z 1 = z 2 / z 1 In general, for any Cobb-Douglas production function of the form F(z 1 ,z 2 ) = Az 1 α z 2 1 – α MRTS (z 1 ,z 2 ) = α z 2 (1 - α ) z 1
Background image of page 12
Inputs are perfect substitutes when one input can always be substituted for the other on fixed
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/18/2011 for the course ECON 2X03 taught by Professor Jamesbruce during the Fall '10 term at McMaster University.

Page1 / 84

3 Production Many Variable Inputs Ch 7 - Production and...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online