InputOutput model

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Tourism Industry AnalysisHA449/HA649Lecture
2-1Introduction to Basics of Input-Output Model
for Tourism Industry Analysis
Tad Hara, PhD SHA, Cornell University
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Basic Algebra Quiz (1) Welcome Back!
How about these?
This is absolute minimum to understand I-O model,
which earned Nobel Prize in Economics!
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Input Output Model

• Inter-industry needs Final Demands Total
  Output
• Tire Factory
• Sales to consumer (you I)
• Sales to car company
• Computer Hard-Disk Factory
• Sales to consumer (you I)
• Sales to Hewlett Packard
• Vegetable Farm
• Sales to consumer (you I at Farmers Market,
  Ithaca)
• Sales to Statler Hotel
• Airlines
• Sales to guests (you and I)
• Sales to Wholesalers

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Input-Output model

• Total Output (X) consists of
• Inter-industry needs (AX), (0ltAlt1)
• Final Demand (Y)
• Also, I ?Identity Matrix (just like 1)
• (1) AX Y X
• Inter-industry needs final demand Total
  Output
• (2) Y X AX
• (3) Y (I-A) X

(4)
(5)
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Input-Output model (2)

• ASSUME Total Output (X) 10
• Final Demand (Y) 5
• Proportion of Inter-industry needs in the Total
  Output (A) 0.5
• I ?Identity Matrix (just like 1)
• (1) AX Y X
• Inter-industry needs final demand Total
  Output
• (2) Y X AX
• (3) Y (I-A) X
• (4)

(5)
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Input Output Model (3)

• Industry consists of many sectors.
• Simplify into 3 sectors (3 x 3) in our case
• Value Added (lower left-side)
• Labor, Capital etc
• Final Demand (upper right-side)
• Consumption by household, Govt. etc

Sectors on the Row (left side of the matrix)
produces goods services. Sectors on the
Column (upper side of the Matrix) receives goods
and services. Lets put the numbers and see how
it works.
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Input Output Model (4)
So, we put some numbers based on available macro
economic data Then take out the industry column
only.
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Input Output Model (5)
Standardize each elements in the matrix
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Input Output Model (6)
This standardized inter-industry transactions
(blue) part is called A-Matrix
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Input-Output Model (alternative explanation-1)
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Input-Output Model (alternative explanation-2)
Then, (I-A)
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Input-Output Model (alternative explanation-3)
Recall, Y (I-A) X
Final demands (proportion of Total Output left
over after inter-industry needs) Multiplied by
Total Output
Inverse of (proportion of Total Output left over
after inter-industry needs) Multiplied by CHANGE
IN FINAL DEMAND CHANGE IN TOTAL OUTPUT
LEONTIEF INVERSE MULTIPLIER
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Input-Output Model (alternative explanation-4)
LEONTIEF INVERSE MULTIPLIER
alpha, not a Sorry for confusion
Change in final demand Expressed in column
vector Y. Change in Total Output Expressed in
column Vector X
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Basic Algebra Quiz (2) Welcome (Back?)!
How about Basic Matrix Operations?
You must attend Lab 1 to understand matrix
operations! (attendance Checked)
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Basic Algebra Quiz (3) Welcome (Back?)!
How about Basic Matrix Operations?
You must attend Lab 1 to understand matrix
operations! (attendance checked)
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Basic Algebra Quiz (4) Welcome (Back?)!
How about Inverse Matrix?
This is to fulfill your curiosity to show how you
can calculate the inverse of matrix (2 x 2) by
head hands. If you think this is horrible, Use
Excel (Lab 1). To solve Assignment 1, you have to
calculate (15 x 15) matrix! No easy task by head
hands!