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AGEC 335 Lecture 4

The document discusses production models with two inputs, focusing on isoquants and the marginal rate of substitution (MRS). It explains how isoquants represent combinations of inputs yielding the same output and the implications of their slopes on input substitution. Additionally, it covers concepts like ridge lines and the relationship between marginal products and the MRS.

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9 views9 pages

AGEC 335 Lecture 4

The document discusses production models with two inputs, focusing on isoquants and the marginal rate of substitution (MRS). It explains how isoquants represent combinations of inputs yielding the same output and the implications of their slopes on input substitution. Additionally, it covers concepts like ridge lines and the relationship between marginal products and the MRS.

Uploaded by

tanvirtutorial99
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Production with two

inputs
Chapter 5

Ripon Kumar Mondal, PhD

LECTURE 4
Model with two inputs

Model with two inputs

 y = f(x1, x2)
 y = f(x1, x2⃓x3,x4,….,xn )

Ref: p 82 (textbook)
Isoquant and
marginal rate
of
substitution
 Any point on the
isoquant gives the
same output with
different combination
of two inputs
 Isoquants are convx to
the lower left-hand
corner

Ref: pp 86-89
Isoquant and
marginal rate
of
substitution
 Slope of Isoquant is known
as MRS/MTS/MRTS
 How well one input
substitutes for another as
one moves along a given
isoquant
 The MRS might also
measure the inverse slope
of the isoquant. E.g.
change in x1 due to
change in x2

Ref: pp 86-89
Marginal rate of substitution

 The terminology MRSx2x1 is used to describe the inverse slope of the


isoquant.
 If, x2 is the replacing input, and x1 is the input being replaced, as one
moves up and to the left along the isoquant.
 The MRSx2x1 is equal to 1/MRSx1x2.

Ref: p 88-89 (textbook)


Marginal rate of substitution

 The slope of an isoquant can also be defined as ∆𝑥2ൗ∆𝑥1


 Then 𝑀𝑅𝑆𝑥1 𝑥2 = ∆𝑥2ൗ∆𝑥1
1
 𝑀𝑅𝑆𝑥2 𝑥1 = ∆𝑥1ൗ∆𝑥2 =
𝑀𝑅𝑆𝑥1 𝑥2
 Isoquants are usually downward sloping, but not always.
 If the marginal product of both inputs is positive, isoquants will be
downward sloping.
 It is possible for isoquants to slope upward if the marginal product of one of
the inputs is negative.

Ref: p 89 (textbook)
Marginal rate of substitution

 Isoquants are usually bowed inward, convex to the origin, or exhibit


diminishing marginal rates of substitution, but not always.
 The diminishing marginal rate of substitution is normally a direct result of
the diminishing marginal product of each input.
 There are some instances, however, in which the MPP for both inputs can be
increasing and yet the isoquant remains convex to the origin.

Ref: p 89 (textbook)
Isoquants and
Ridge Lines
 A line could be drawn that connects all
points of zero slope on the isoquant map.
Thisline is called a ridge line and marks
the division between stages II and III for
input x1
 Now suppose that a level for x2 is chosen
of x2* that is just tangent to one of the
isoquants.
 The point of tangency between the line
drawn at x2* and the isoquant will
represent the maximum possible output
that can be produced from x1 holding x2
constant at x2*.

Ref: pp. 93-95


Marginal rate of substitution and
Marginal Product
 ∆𝑦 = 𝑀𝑃𝑃𝑥1 ∆𝑥1 + 𝑀𝑃𝑃𝑥2 ∆𝑥2
 0 = ∆𝑦 = 𝑀𝑃𝑃𝑥1 ∆𝑥1 + 𝑀𝑃𝑃𝑥2 ∆𝑥2
 𝑀𝑃𝑃𝑥2 ∆𝑥2 = −𝑀𝑃𝑃𝑥1 ∆𝑥1
 𝑀𝑃𝑃𝑥2 ∆𝑥2ൗ∆𝑥1 = −𝑀𝑃𝑃𝑥1
∆𝑥2 𝑀𝑃𝑃𝑥1
 ൗ∆𝑥1 = − 𝑀𝑃𝑃
𝑥2
𝑀𝑃𝑃𝑥1
 𝑀𝑅𝑆𝑥1 𝑥2 = −
𝑀𝑃𝑃𝑥2
Ref: pp 95-96 (textbook)

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