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Small town mentality in to kill a mockingbird

07/02/2022 Client: muhammad11 Deadline: 2 Day

SMò—âA – Mathematics for Economics
Fall òýÔ
Asst. Prof. Nelson Uhan
Lesson ÔÀ.

e Cobweb Model
ý Warm up
Example Ô.
Solve the dišerence equation
y
t
+
Ô
+
ç
y
t
=
¥
. Is
y
t
oscillatory or nonoscillatory? Is
y
t
convergent
or divergent?
Ô Overview

Market with single product

Supply in period
t
is decided
in
pe
riod
t

Ô and so is based on the price in period
t

Ô

e.g. agricultural production: planting must occur a long time before harvesting and selling

How does the price of the product change over time?
ò

e model

Variables:
P
t
=
unit price at period
t
Q
dt
=
quantity demanded at period
t
Q
st
=
quantity supplied at period
t

Parameters:
α
,
β
,
γ
,
δ
>
ý

Equations:
Q
dt
=
Q
st
Q
dt
=
α

β
P
t
Q
st
=

γ
+
δ
P
t

Ô
Ô
ç Solving and analyzing the model

Substituting the last two equations into the rst, we can reduce the model to:

Let’s rewrite this dišerence equation by shiŸing the time subscripts:

Note that in this case:

We can solve for
P
t
, where
P
ý
represents the initial price:

We can interpret
̄
P
=
α
+
γ
β
+
δ
as the intertemporal equilbrium price of the model, and write
P
t
as:

P
t
is convergent when

P
t
is oscillatory when
ò

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