Short-Run Income Models

Chapter 7

Production Possibilities Curve

Two linear production possibilities curves showing

comparative advantage

Keynesian Model

• Y = C + I + G + (X−M)

• C = a + bYd,

• Yd = Y−T

• M = d + mYd

• Exogenous Spending: (a + I + G +X –d)

Regional income multiplier

•

• Marginal Propensity to consume locally: (b – m)

)(1

1

mb

spending. Exogenous)(1

1

mbY

Location Quotients

EE

ee

i

i

Interpreting Location Quotients

• LQ > 1: export industry

• LQ = 1: produce for local consumption

• LQ < 1: import industry

Employment Multiplier

Employment Basic

Employment Total

Calculating Basic Employment

eEE

ee

Xii

i

Direct, indirect and induced effects on a production possibilities curve

Input-Output Analysis

• Total output (by rows): Xi = zi1 + zi2 + . . .  + zii + . . .  + zin + Yi

• Total spending (by columns):

• Xj = z1j + z2j + . . .  + znj + Vj =

 

Vz j

n

iij

. XX ji

Sellers

Buyers

Table 7–2. Hypothetical Transactions Table

  Interindustry Flows of Goods

A B C D EFinal

demand

Gross regional output

A 12 35 85 22 12 540 706

B 25 34 25 1 26 350 461

C 45 25 32 11 5 338 456

D 155 42 44 56 25 266 588

E 24 255 25 4 251 563 1,122

3,333

Value added 445 70 245 494 803 — —

Imports 25 3 20 25 35 — —

Total spending 706 461 456 588 1,122 — 3,333

Technical (or direct) coefficients

• Technical (or direct) coefficients (aij)

• Technical coefficients show the quantity of output from each industry needed to produce final demand (the first round effect)

X

zaA

j

ijij

Table of Technical Coefficients

Table 7–3. Table of Technical Coefficients

Industries

Industries A B C D E

A 0.017 0.076 0.186 0.037 0.011

B 0.035 0.074 0.055 0.002 0.023

C 0.064 0.054 0.070 0.019 0.004

D 0.220 0.091 0.096 0.095 0.022

E 0.034 0.553 0.055 0.007 0.224

Value added 0.595 0.145 0.493 0.798 0.684

Imports 0.035 0.007 0.044 0.043 0.031

Total spending 1.000 1.000 1.000 1.000 1.000

Leontief matrix and powers

• Direct effect is represented by [I−A]

• Direct effect + Indirect effect: I−A + A2 + A3 + . . . + An

• The production needed to satisfy an increase in final demand (X): multiply the vector of final demand (Y) by the inverse of the Leontief matrix, X = [I−A]−1 Y

Table of Multipliers

Table 7–4. Table of Multipliers

A B C D E

A 1.047 0.116 0.223 0.048 0.021

B 0.047 1.109 0.078 0.006 0.034

C 0.080 0.080 1.100 0.026 0.011

D 0.270 0.168 0.183 1.121 0.042

E 0.088 0.803 0.144 0.018 1.315

Type I Multipliers 1.533 2.276 1.727 1.219 1.422

Input-Output Multipliers

.Direct

Induced Indirect Direct :Multiplier II Type

Direct

Indirect Direct :Multiplier I Type

Shift-Share Analysis

• dij = gij + mij + cij,

• gij = Eij0 rB,

• mij = Eij0 (riB – rB)

• cij = Eij0 (rij – riB) • (Eij0 is the number of employees in industry i within

region j during time 0)

• dij = Eij1 – Eij0

Shift-Share Analysis

E

EEr

B

BBB

0

01

E

EEr

iB

iBiBiB

0

01

E

EEr

ij

ijijij

0

01

Esteban-Marquillas Extension

• Redefine Competitive Effect: cij′ = E′ij0 (rij – riB) where E′ij0 is homothetic employment:

• E′ij0 = Ej(EiB/EB)• Allocative effect:

aij = (Eij0 – E′ij0) (rij – riB) – Specialization effect (Eij0 – E′ij0)– Measure of comparative advantage

(rij – riB):

Policy implications of Esteban-Marquillas extension

Short-Run Model of an Open Economy

• E = C + I + G + (X – M)

• In equilibrium, income (or output or actual expenditures) = Desired Expenditures: Y = C + I + G + (X – M)

• C = a + bYd

• Yd=Y – T

• T = tY

• M = d + mYd.

Finding the multiplier

• E =

• a + b (1 – t)Y + I + G + X – (d + m (1 – t) Y)

• E = (b – m) (1 – t) Y +(a +I +G +X – d)

• Since in equilibrium, Ye = E, dXGIa

tmbY

)1)((1

1

Xtmb

Y

)1)((1

1

Keynesian Cross

Modeling Interregional Dependencies

• Two regions c (core) and p (periphery)• Yi = Ci + Ii + Gi + (Xi−Mi)• Ci = ai + bYdi

• Ydi=Yi−Ti

• Ti = tiYi

• Mi = di + mYi

• Xc = Mp; • Xp = Mc