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Multipliers and Input-Output Models
创建日期：2024-06-17 15:56:59
所属分类：经济Economics
标签： econmice
Multipliers and Input-Output Models

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Chapter 5: Urban Econ Growth

PART 1: Multipliers and Input-Output Models
Normally, growth is measured in per capita terms of income or local GDP, etc.
Most of these measures, e.g., GDP, are the product of price and quantity
That is, growth may be driven by P or by Q.
To avoid the problem that growth is simply inflation driven we will mainly refer to
growth as “growth in employment” --- Income growth expressed in $ is simply
converted into employment growth by assuming an avg job is the equivalent of a certain
amount of $ (e.g., one job equals $50,000)
Local Production Function
A firm’s production function is given by
q= q(k,l,r,t) where q denotes output, k capital, l labor, r natural resources and t
technology.
Similarly, a region’s production function is given by
Q = F(K,L,R,T) where Q stands for aggregate supply/output.
Regional growth results from a change in one of these factors
City-Specific Innovation can’t be fully internalized
The Figure below shows two identical cities with a population of 6m people each. At the
beginning, both cities are at point I and both experience a utility of u=70.
Now, assume one of the two cities is very innovative and shifts up its utility curve
enabling it to reach point j with a utility of U=80. However, this point is not a stable
equilibrium. People in the less innovative city have string incentives moving to the
innovative city and reap its benefits. Due to this, the more innovative city will grow to a
population of 7m and its utility per worker will fall. The less innovative city will shrink
to a population of 5m and its utility per worker will decline. People will move from until
the utility per worker is identical at both locations, which is the case at point s and b.
à the benefits of innovation cannot be internalized but spread into space.
Multiplier Process
Assumption:
There are two kinds of products
(a) export (or basic) production (e.g., steel)
(b) local (or non-basic) production (e.g., bread)
growth is caused by additional income coming from exports
This income goes to
- workers (as labor income)
- land owners (as rent)
- capital owners (as interest)
- the fraction of income that stays within region/city will multiply within economy.
- the fraction of income that is spent on imports will not multiply within region
The Table below shows how a $1000 increase in export sales (steel) multiplies the local
income. Since the recipients of the initial income gain of $1000 (i.e., workers, capital and
land owners) spend part of their income on local goods, the increase in exports also
increases local sales. Assuming that 60% of the increase will be consumed locally and
40% will be spent on imports, there will be a further local consumption increases by $600
while $400 is spent on imported goods.
In round 2. $360 of the additional $600 is spent locally, $240 is spent on imports. In
round 3, again, 60% of the additional $360 is spent on local goods (i.e., $126), and $144
is spent on imported goods. After three rounds the initial income impulse of $1000 has
multiplied to now $1960. Of course, this process does not end after 3 rounds. After an
infinite number of rounds there will be a total income increase by $2,500.
Increase in Round 1 Round 2 Round 3 After 3
Rounds
After an infinite
Number of
Rounds
Local income $1,000 $600 $360 $1,960 $2,500
Local
consumption 600 360 216 1,176 $1,500
Import 400 240 144 784 $1,000
The overall income effect DY depends on
- the size of the initial impulse DX (increase in export sales) and
- the income fraction consumed locally (=marginal propensity to consume locally m)
DY = DX + mDX + m(mDX) + m(mmDX) + m(mmmDX) + …….
which equals
DY = DX + mDX + m2DX + m3DX + m4DX + …….
The change in total income is the sum of an infinite series and can be written as
INCOME CHANGE ∆ = ∆ ∙ "
Applied to the example above we thus get ∆ = , ∙ − . = ,
From the income change we derive the income multiplier
INCOME MULTIPLIER
∆∆ = %
The income multiplier in our example above equals (1/(1-0.6) = 2.5
An initial income impulse of $1,000 will multiply by 2.5 fold.
à Assuming a fixed number of jobs per $1,000 income one can transform income
multipliers into employment multipliers.
The Table below provides recent employment multiplier estimates for the Portland (OR)
Metropolitan Area:
Predicting Growth with Input Output Tables
A common way to predict regional growth and/or show the effect of a certain industry on
the regional economy is based in Input-Output Analysis
Compared to assuming a constant local multiplier as shown above, Input-Output analyses
draw on industry-specific m-values
Input-Output analyses are based on Input-Output Tables (see example below)
Producers Exports TOTAL
Inputs Cars Steel Local
Merchants
Households
Cars 0 300 150 180 1,370 2,000
Steel 400 0 0 0 600 1,000
Local 0 0 0 2,500 0 2,500
Labor (households) 1,000 600 2,000 0 0 3,600
Imports 600 100 350 920 0 1,970
Total 2,000 1,000 2,500 3,600 1,970
Input-Output Tables report inter-industrial relations and show who buys from whom.
The buying industry is on top, the input industry is on the left hand side. For instance, car
firms buy steel worth $400, labor worth $1,000 and import goods worth $600. Overall,
car firms spend $2,000. Similarly, steel producers spend a total of $1,000 ($300 on cars,
$600 on labor and $100 on imported goods).
Input-Output Tables can be converted into Input-Coefficient Tables.
Input-Coefficient Tables report the percentage of all industry-specific inputs (see Table
below).
Producers
Inputs Cars Steel Local Merchants Households
Cars 0.00 0.30 0.06 0.05
Steel 0.20 0.00 0.00 0.00
Local 0.00 0.00 0.00 0.69
Labor (households) 0.50 0.60 0.80 0.00
Imports 0.30 0.10 0.14 0.26
Total 1.00 1.00 1.00 1.00
For instance, 20% of all expenditure of computer firms goes to wire producers; 50% is
spent on labor. Input-Coefficient Tables allow to track the effect of growth in one
industry on all other industries and calculate multiplier effects.
The following Figure shows the economic effect of a $100 export growth for computer
firms.
initial
impulse
round
1
round
2
round
3
sum of induced
changes
overall ΔY
after 3 rounds
TOTAL 100.00 70.00 55.00 44.50 169.50 269.50
cars 100.00 -- 8.50 2.67 11.17
steel -- 20.00 -- 1.70 21.70
local -- -- 34.50 8.28 42.78
labor (wages) -- 50.00 12.00 31.85 93.85

Round 1: The increase in computer sales increases wire production by $20 and wages by
$50.
Round 2: The $20 increase in wire production increases computer sales by an additional
$6 and wages by an additional $12.
Round 3: The increases in computer sales, wages and local sales cause additional
$100 car exports
$20 steel
$50 wages
$1.25 wages
$27.60 wages
$3.00 wages
$12.00 wages
$6.00 cars
$2.50 cars
$2.07 cars
$0.60 cars
$1.20 steel
$0.50 steel
$8.28 local
$34.50 local
increases in wire sales, wages computer sales and local consumption.
Main Limitations of Input-Output Analysis
The assumption of constant multipliers is unrealistic
• Wages and other input prices change as these production factors get scarce.
Therefore, price effects will eat up part of the multiplier effect (see also the Figure
under “Labor Equilibrium” Ch. 5 Part 2)
• As Input prices change and firms substitute less expensive inputs for more
expensive inputs (there is more plastic in cars now than 30 year ago; why?)
input-output analysis assumes constant input coefficients, but these relations
change over time.
• Regional multipliers are multipliers increase with city size (because of the
increasing marg. prop. to consume locally grows with city size; for instance, a
State’s multiplier will always be larger than the one of any single city in that
State)
In addition, not all growth is export-driven, there is also “endogenous” growth from an
increase in trade; (the comparative advantage example shows how both parties can
benefit from trade). A good example for non-export-driven growth is the growth of the
world economy. There has been tremendous growth without any extra-terrestrial exports
PART 2: Urban Labor Market
Wages and employment level (i.e., prices and quantities) of the urban labor market are
determined by the demand for labor and the supply of labor.
A. Labor Demand
slopes down because of
(1) output effect: one input more expensive --> less output
w↑ --> C↑ --> market area ↓ --> Q↓ --> need fewer workers
(note: the links between all steps can be very lose)
(2) substitution effect: increasing wages drive the substitution of capital for labor
drawing microeconomic theory we will get
- downward sloping demand curves for partial substitutes
- vertical demand curves for perfect complements
- two vertical demand curves for perfect substitutes
Shifts in Labor demand curve if
(1) demand for exports changes
(2) labor productivity increases
option 1: productivity↑ à goods cheaper à more exports à more workers
Labor demand shifts to the right
option 2: more productive could also mean à less workers for same quantity
Labor demand shifts to the left
(3) business taxes (higher taxes shift labor demand to left and vice versa)
(4) land-use policies (higher land cost shift labor demand to left and vice versa)
B. Labor Supply
General assumption: slopes up because of
migration effect:
w ↑ --> more people from outside the cluster move in
However, there are two potential problems:
(1) it is unproven that the labor supply curves slopes up for all employees
For unskilled labor (NYC Taxi Drivers) Camerer et al. (1997)1 show that the labor supply
curve may not slope up. It seems that drivers have a certain revenue-per-shift-goal in
mind, which results in less driving time during busy hours and vice versa. As a result, the
labor supply curve may slope down!
Here, a scatterplot of their three samples:
1 Camerer, C., Babcock, L., Loewenstein, G., and Thaler, R. (1997). Labor Supply of
New York City Cab Drivers: One Day at a Time. Journal of Quarterly Economics,
112(2), 407-441
And here are the resulting regressions:
(note, the numbers in parentheses are not t-statistics but standard errors; one can easily
calculate t-statistics as the ratio of (coefficient/std error).
Most equations suggest that the (log of) hours worked (=labor supply) is a negative
function of the (log of) the wage.
Note, the numbers in parenthesis under the coefficients are standard errors.
The t-statistics are calculated as (coefficient / standard error)
(2) Macro-Micro Puzzle:
for the entire economy labor supply is vertical
micro – macro puzzle:
why do single product supply curves slope up but LRAS (long-run aggregate supply) is
vertical? If LRAS curve is the average supply curve for all goods, must there be some
goods that have a falling supply curve? No.
à changes in relative prices lead to shifts in resources
example: a firm has a fixed amount of resources (K,L,R) and produces two goods A and
B; prices are given by PA and PB
now assume PA increases changing the relative price ratio and making it more profitable
to produce A. The firm will thus shift some of its resources from B towards A and
produce more A (and less B). As a result: both supply curve slope up. A falling relative
price of B leads to a decline in production; a rising relative price of A leads to increasing
production
result in the regional context:
labor supply slopes up because workers move from location to location in search of gains
Causality between wage and labor supply and cost effects
an upward sloping labor supply curve reflects a positive relation between wage and labor
supplied. However, there is no clear causality
either w ↑ à SL↑ or SL↑ à w↑
more labor supplied (i.e., more people N) means
(1) higher housing cost (housing cost elasticity with respect to population e(H,N) = 0.35)
(2) higher cost of living (living cost elasticity with respect to population e(L,N) = 0.20)
(3) wage increases with cost of living
(wage elasticity with respect to population e(W,N) = 0.20)
10% increase in employment will cause wage increase by 2%
(4) other way ‘round: wage increase of 2% will cause 10% more employment
(labor supply elasticity with respect to wages e(N,W) = 5.0)
Shifts in Labor Supply
(1) environmental quality (improvements shift LS to right and vice versa)
(2) residential taxes (reduction shifts LS to right and vice versa)
(3) residential public services (improvements shift LS to right and vice versa)
. Labor Equilibrium
In the Figure below, incomes are translated into jobs. That is, it shows employment
multipliers rather than income multipliers. The multiplier analysis, as discussed above,
suggests that the demand for worker will increase from 50 to 75. In other words, the total
effect (25) is 2.5 times as high as the initial impulse (20). That is, the employment
multiplier is 2.5.
However, this disregards the labor supply curves and assumes constant wages. In
contrast, together with the labor supply curve we will get the following equilibrium
outcome:
The labor equilibrium is now at 66 and not at 75. Monthly wages are up from $1,000 to
$1,200. As a result, the actual multiplier is not 2.5 but just 1.6.
Public Policy and Urban Growth
in general: any shift in one or both LS and LD curves can change the equilibrium outcome.
The Figure below shows the effect of two simultaneous policies: (1) a tax on companies
is imposed in order to (2) decrease pollution and improving the quality of living in the
city.
The tax causes a left (or downward) shift in the labor demand curve
(t↑ --> C↑ --> Q↓ --> L↓)
The environmental improvement causes a right (or downward) shift in the labor supply.
People are willing to take a pay-cut in lieu for a better quality of living.
As a result, wages are down and the number of jobs is up.
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COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 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