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Lecture Notes

ECON 437/837: ECONOMIC COST-BENEFIT ANALYSIS

Lecture Eight

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ECONOMIC OPPORTUNITY

COST OF LABOR

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• The Economic Opportunity Cost of Labor (EOCL) is the value to the economy of activities given up by workers including non-market costs (benefits) associated with the change in employment.

• Labor is not a homogeneous input.

• An externality (LEi) is created by any project, if the EOCLi differs from the wage rate (Wpi) paid by the project. Externality for a specific type of labor (i) can be expressed as:

LEi = Wpi - EOCLi

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Project Location Level of Skill

Acquired

Sources of

Workers

Project Wagea

Prevailing Market Wagea

EOCL Ratio of EOCL to Project Wage

UrbanUrbanRuralRuralUrbanUrban

Outside of Polokwane

Urban

Unskilledb

Unskilledc

Unskilledd

Unskillede

Skilledf

Skilledg

Skilledh

Skilledi

LocalLocalLocalLocal

Elsewhere

Elsewhere

UrbanForeign

6511,490468

1,49015,02016,72918,43836,667

651651468468

15,02015,02018,43836,667

651897468668

14,652

14,652

16,860

26,592

1.000.601.000.450.980.880.910.73

Estimates of the EOCL in Limpopo Province (South Africa) (Rands per month)

Note:a. Project wage or prevailing market wage refers to the gross wage including tax, social security payments, and fringe benefits.b. Unskilled worker employed in informal urban labour market.c. Unskilled worker employed in unionized urban labour market.d. Unskilled worker employed in informal rural labour market.e. Unskilled worker employed in unionized rural labour market.f. Senior Site Engineer technician employed in urban area.g. Senior Site Engineer technician employed in urban area, earning higher than market wage.h. Senior Site Engineer technician employed in rural area, earning market wage for region.i. Engineer with skills that had to be sourced from abroad.

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Estimation of the Economic

Opportunity Cost of Labor

• Two approaches for the estimation of the EOCL:

i) value of marginal product of labor forgone;

ii) supply price of labor

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Value of Marginal Product of

Labor Forgone Approach

• Using this approach, the EOCL is determined by:

- starting with the gross-of-tax alternative wage (Wa) earned in previous employment by the labor hired for the project (marginal product forgone); and

- and then adjusting for differences in other costs & benefits.

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Supply Price of Labor Approach

• Supply price is defined as the minimum gross-of-tax wage rate the project needs to pay to attract the necessary labor.

• Supply price accounts for a worker's preferences for location, working conditions, etc.

• Using the supply price approach, the EOCL is determined by:

- starting with the market wage (the supply price) required to attract sufficient workers to the project; and

- then adjusting for distortions such as taxes and subsidies.

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Example: Comparing the Value of Marginal Product Forgone and Supply Price Methods

• Unskilled farm workers move from (c) where they were cutting sugar cane to a more pleasant place (o) harvesting oranges.

• No distortions in the labor market• Other factors influencing the relocation:

1. Difference in cost of living (C)2. Preference (S) of the workers for a more pleasant region.

 

Wo = $ 15.00 per day Wc = $ 20.00 per day

Co = $ 3.00 per day Cc = $ 6.00 per day

So = $ 2.00 per day (value of the preference for the warmer region)

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Example (cont’d)

Marginal Product Approach

• EOCL = prior wage - change in cost of living - worker preferences

= Wc - (Cc - Co) – So = 20 - (6 - 3) - 2

= $15.00 per day

Supply Price Approach

• Supply price in (o) accounts for the cost of living difference (Cc - Co) and worker's preference for the better climate (So).

• EOCL = Wo = $15.00 per day

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Structure of Analysis

• Labor prices can vary greatly • Determinants in the cost of labor to the

project: 1. Type of Labor (skilled vs. unskilled)

2. Regional Variations and Domestic Migration

3. International Migration

4. Type of Labor Market (Protected vs. Unprotected)

5. Type of Job (Permanent vs. Temporary)

The Economic Opportunity Cost of Unskilled Rural Labor

• EOCL of unskilled rural labor is not zero.

• The prevailing daily or weekly wage rate, W, (the supply price of unskilled labor) is a reflection of the marginal productivity of this type of activity.

• W is an effective measure of the value of forgone marginal product for unskilled labor.

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Supply Price Approach: Calculations

• Determine the minimum gross-of-tax wage (market supply price) needed to attract sufficient unskilled labor to the positions available on the project.

• Identify the distortions in the labor market such as personal income taxes or unemployment insurance benefits.

• The EOCL can be determined by adjusting the market wage to compensate for the distortions caused by those factors.

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The Economic Opportunity Cost of Unskilled Labor

Example 1: Rural Labor Case without Seasonal Variation in Demand

• Assume:1. no distortions in the unskilled labor market, 2. no taxes paid by the employer (demand side), 3. no income taxes paid by the worker (supply side), 4. no fluctuations in wages or labor demand over time.

• The supply price of labor (WS) is equal to the prevailing market wage (W).

EOCL = W = Supply Price of Unskilled Labor

• Note: The EOCL is estimated using the market supply price (WS) not the project wage (Wp).

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Example 2: Rural Labor Case with Seasonal Variation in Demand

• Assume:1. no distortions in the unskilled labor market, 2. no taxes paid by the employer (demand side),3. no income taxes paid by the worker (supply side), 4. market wage varies due to seasonality in demand.

Feb April June Aug Oct Dec

Wages

Wi

Number of workers needed for project

Qp

Patterns of project’s demand for labor during the year

Pattern of wage rate for unskilled labor during the year

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• Due to seasonal fluctuations in the wage rate, the EOCL at any point in time is equal to the market wage rate (Wt) at that point in time.

• The total EOCL used by a project over a year is the sum of the product of the quantity of labor hired in each season (Qt) times the corresponding market wage rate (supply price, Wt) for the period:

where: “n” is the total number of periods; and “t” is the period of time.

EOCL = (Qt*Wt)n

t=1

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Note:

• The project wage (Wp) paid does not play a

role in the estimation of the EOCL.

• Basis of estimation of the EOCL is the supply price of labor as reflected in the market wage (W).

• The difference between the financial cost paid by the project (Wp) and the EOCL is the

value of the labor externality.

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• A labor-intensive sugar project

• Project requires unskilled workers on a temporary basis.

• Project pays a wage of $180 per month (Wp).

• Project working conditions are identical to those prevailing in the labor market.

Example: Sugar Production Projects hires Unskilled Labor in a Rural Area

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• Table shows the project's monthly labor requirement, the monthly market wage rates (W) that labor would be willing to work for on this project and the EOCL for each period.

Month Market Wage (W)($/month)

Person-monthsrequired (Qt)

EOCL for period ($)

(1) (2) (3) (4)

January 120 18 2,160

February 100 18 1,800

March 180 18 3,240

April 180 9 1,620

May 100 9 900

June 150 0 0

July 180 0 0

August 120 0 0

September 150 0 0

October 110 0 0

November 150 9 1,350

December 180 9 1,620

Total   90 $12,690

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• The EOCL is calculated as follows:

• Labor externality = Financial Cost – EOCL = 180*90 – 12,690

= $3,510

• Labor externality is a net gain to labor.

EOCL = (Qt*Wt)

= [120*18 + 100*18 +….. + 150*9 + 180*9] = $ 12,690

n=12

t=1

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The Economic Opportunity Cost of

Skilled Labor 

• Skilled labor is not a homogeneous factor.

• Conversion factor for one type of occupation may not necessarily be the same for other occupations.

• Often labor must be induced with higher wages and improved benefits to migrate to other areas.

• Increase or decrease in the supply price of labor as it moves from one location to another will depend upon the magnitude of the consumer surplus lost or gained.

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Situation 1: Labor Market without Distortions or Regional Migration

• Assume:

1. No distortions in the labor market

2. No migration

3. Project working conditions are identical to those prevailing in the labor market.

• The economic opportunity cost of labor is equal to the local market wage (W) which in this case is the supply price (Ws): 

EOCL = W = Ws

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Situation 2: Workers Migrate to Project from Distorted Regional Labor Markets• Assume:

1. A proportion of the project’s labor (Hd) is induced to migrate from alternative labor markets where they were employed.

2. Project pays a wage equal or higher than the gross-of-tax supply price (Wg

s) to attract the necessary workers.

• EOCL = the supply price to the project, (Wgs)

- taxes paid by project workers, (WgsT)

+ taxes lost from the workers’ previous

employment, (HdWaT).

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1. Workers migrate from other regions to the project. Supply curve in the sending region (SS) shifts leftward to (S’S’).

2. At original wage (Wa), migration to the project will cause a decrease in the available supply from Q0 to Q1.

3. Wage increases to Wa’ to bring about an equilibrium.

Higher wage in the sending regions causes employers to reduce the quantity they demand.

4. Higher wage also induces some skilled workers to enter the formal labor force, thereby increasing the quantity of skilled labor supplied from Q1 to Q2.

5. Net effect: a proportion of the labor (Hs) ultimately comes from the newly induced supply and a proportion (Hd) comes from the reduced demand for workers elsewhere.

6. Reduction in the quantity of labor demanded results in a loss of taxes (ABCE).

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• When calculating the EOCL, only the tax distortion resulting from the reduced demand (Hd) need be

accounted for, because we assumed that the increased supply (Hs) of labor is coming from non-

market activities where there are no taxes or other distortions.

• Thus, the EOCL for the project in such cases is the gross-of-tax supply price (Wg

s) of workers induced to

move to the area minus the difference between the income taxes the workers would pay on this gross-of-tax supply price of labor (Wg

sT), which are gained by

the government, and the income taxes previously paid by the workers in their alternative employment (HdWaT), which are lost by the government.

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• The EOCL hired by the project in the area is:

EOCL = Wgs - (Wg

s T – HdWa T)

where:- Hd is the proportion of the project's demand for labor obtained from taxed employment activities in the alternative labor market,- Wa is the gross-of-tax wage of labor from alternative sources,- Wg

s is the gross-of-tax supply price of labor,- T is the income tax rate levied on workers in all regions,- Hs = (1 - Hd) includes both the supply of labor coming to the region from untaxed market and non-market activities, as well as increases in the labor force participation and the number of hours worked.

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Labor Externality

• Labor externality can be expressed as:

LEi = Wp - Wgs + (Wg

sT - HdWaT)

= Wp (1 - T) - Wgs(1 - T) + WpT – HdWaT

• We can determine how these labor externalities are distributed

between the workers and the government:

Labor benefits = Wp(1 - T) - Wgs(1 - T)

Government benefits = WpT - HdWaT

• Thus, of the total of externalities created by the employment of

workers by a project, labor will gain an additional income earnings

while the government will capture additional taxes.

• The distributional analysis provides a means of evaluating the

financial gains and losses affecting groups in the economy other

than the owners of the project.

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Example: Skilled Labor Hired for a Project

• In addition to the unskilled workers hired for the sugar project, the

government requires each year 1,000 person-months of labor with

skilled occupations.

• The project will have to attract skilled labor from the urban areas.

• These workers earn a monthly gross-of-tax salary (Wa) of $900 in the

urban area, they will not work for less than $1,200 gross-of-tax for

the project (Wgs). These wage rates reflect the gross-of-tax supply

prices of the workers in the two markets, respectively.

• There is a policy of encouraging more workers in these occupations

to migrate to the rural areas, so the project is required to pay a

salary (Wp) of $1,500 per month for such labor, or $300 more than

the market supply price.

• All skilled workers pay 20% of their wages in income taxes.

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Example : Skilled Labor (cont’d)

• The EOCL for this project is calculated:

EOCL = Wgs - (Wg

sT - HdWaT) = 1,200 – [(1,200 * 0.20) - (0.90 * 900 * 0.20)] = $1,122/month

 • The labor externality can be expressed as The

difference between the EOCL of these skilled workers and the value of the project's wage:

LEi = Wp - EOCL = 1,500 – 1,122 = $378/month

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Example : Skilled Labor (cont’d)

• These labor externalities can be distributed between the workers and the government:

Labor benefits = Wp(1 - T) - Wgs(1 - T)

= 1,500(1 - 0.20) - 1,200(1 - 0.20)= 1,200 - 960 = $240/month

Government benefits = WpT - Hd WaT = 1,500(0.20) - (0.90 * 900 * 0.20)= 300 - 162 = $138/month

 • Of the total of externalities created per month by the

employment of workers by a project, labor will gain an additional $240 per month while the government will capture $138 per month in additional taxes.

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EOCL if International Migration Flows-- Case 1: Retained or Returned Migrants --

Project is created inside the country and additional labor is hired, a part of this labor is sourced from a reduction in the outflow of international migration.

• The availability of additional jobs in the country may induce some workers to return from abroad to seek local employment.

• The EOCL must take into consideration not only the adjustment of the demand and supply of labor in the local markets, but also any distortions associated with the retention or return of domestic workers who would have been employed abroad.

• Some citizens work abroad and send back a stream of payments in the form of personal savings or remittances to relatives. The reduction in remittances themselves is not an economic cost, because they are factored into the worker’s supply price to the project.

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• An adjustment needs to be made to the supply price of labor, since the foreign remittances are made in foreign exchange and a foreign exchange premium exists in most countries.

• The expression for the EOCL becomes: 

where Hd = proportion of the project’s demand for a given type of labor

obtained from taxed employment activities in the domestic market.

Hf = proportion of the project’s demand for a given type of labor obtained from reduced international out-migration.

R = the average amount of remittances (measured in local currency) that could have been made per period if this type of worker had been employed abroad.

(Ee/Em – 1) = rate of the foreign exchange premium.

EOCL= Wgs(1 - T) + HdWaT + HfR(Ee/Em – 1)

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EOCL if International Migration Flows-- Case 2: Economic Opportunity Cost of Foreign Labor --

• There is an economic opportunity cost associated with hiring foreign labor (EOCLF) which should be included in the project assessment.

• The EOCLF is the net-of-tax wage paid to the foreign worker plus adjustments to the amount of foreign exchange associated with the repatriated portion, and adjustments to the amount of VAT associated with consumption by the foreign workers using the non-repatriated portion of that wage, plus any subsidies the foreign workers may benefit from while in the country.

• Foreign workers’ consumption in the country should be accounted for as an economic benefit to the country while the host-government subsidies to foreign workers on a variety of items such as food, fuel, housing and health care are an economic cost.

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Case 2 (cont’d)

• The economic opportunity cost of foreign labor can be expressed as:

where:WF = gross-of-tax wage of foreign labor

Th = personal income tax levied by the host country on foreign labor

tVAT = VAT rate levied on consumption

fr = proportion of the net-of-tax income repatriated by foreign labor

Ee = economic exchange rate

Em = market exchange rateN = value of benefits gained by foreign workers from subsidies

• If EOCLF is lower than the market wage, this means that the country is benefiting economically from the presence of foreign labor.

EOCLF = WF(1-Th) - WF(1-Th)(1-fr)tVAT + WF(1-Th)fr(Ee/Em-1) + N

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• A multinational corporation considering an electronic assembly project in an urban area discovered that there was insufficient local labor.

• Import skilled workers from a nearby country

• 50 workers who will be paid $200 per month

• 25% personal income tax.

• Each worker is expected to repatriate 30% of her net-of-tax income to support family members at home.

• The VAT rate is 15%.

• The economic value of foreign exchange is estimated to be 6% higher than the market value of exchange rate.

• Assume that there are no subsidies paid by the government with respect to these workers, i.e. N = 0.

Example: A Multinational Corporation Employing Foreign Labor

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Example (cont’d)

• Estimation of the EOCL:

= 200(1 - 0.25) - 200(1 - 0.25)(1 - 0.30)0.15

+ 200(1 - 0.25)0.30[(44.85/39) – 1]

= 150 - 15.75 + 6.75

= 141

• The economic opportunity cost of each worker will be $59 less than the gross-of-tax wage of $200.

• Hence, there is a beneficial externality created if the project uses foreign labor.

EOCLF = WF(1-Th) - WF(1-Th)(1-fr)tVAT + WF(1-Th)fr(Ee/Em-1) + N

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Effects of a Protected Sector on the EOCL

• There is a segmentation of the urban labor market between a protected sector and an unprotected or open sector.

• The protected sector is usually made up of the government agencies, foreign companies, and large local firms which provide wages (Wp) above the market clearing wage.

• Employment in the protected urban labor force is highly desired, with a variety of rationing methods used to select the people to fill the limited number of positions.

• The open labor market is affected by fewer distortions to the supply price of labor (Wo). Wages are determined competitively in the marketplace where there are fewer barriers to entry, lower wages and less security of employment.

• While workers may be initially attracted to this labor market by the hope of finding a job in the protected sector, they often end up working in the open labor market.

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EOCL in the Protected Sector (cont’d)

• Overall supply of labor is given by (SST)• Total number of workers available for

work at the protected sector wage of W is

point C. • The number of protected sector jobs

available is much more limited at QPr.• There is an excess supply of labor

available at the protected sector wage, as

shown by the quantity B .• If the selection of workers for employment

in the protected sector is done in a random

fashion from the available workers, the

supply of labor available to the open

market will be a fraction (B/C) of the total

labor supply SST at each wage rate. This

labor supply is shown as the curve SSO.

Wage Rate

Wp

ST

SO

Protected Employment

Quasi-voluntaryUnemployed

Open MarketEmployment

A1 A B C

O QQV QPrQS

WO

1

Do

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EOCL in the Protected Sector (cont’d)

• Demand for labor in the open sector is perfectly elastic at a wage

rate of WO, intersection of the demand for labor in the open sector

(WODO) with the supply (SSO) determines the quantity employed in

the open market. This quantity is indicated by point A1.

• The quantity of labor classified as unemployed (QQV) is determined

from the difference between points A1 and B. These quasi-

voluntary unemployed are those workers that will not choose to

take jobs in the open market sector because their basic supply

price of labor is above the open market wage (WO).

• Workers who actively seek jobs in the protected sector will

consider themselves involuntarily unemployed. They are seeking

work which will pay the protected sector wage (W), but are unable

to find it.

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• The number of workers willing to take jobs in the open sector will fall from A1 to E.

• When workers are attracted from the unemployed and open sectors in proportion to their numbers in the labor pool, in the absence of any distortions, the economic opportunity cost of labor to this project is a weighted average of the open sector wage (WO), and the average supply price of the quasi-voluntary unemployed [(WO + WP)/2].

• The relevant weights are the proportions that people in each of those categories will be chosen for the protected sector jobs.

Wage Rate

Wp

ST

SO1

S

E A B

A1

S

B1

1

WO

C

Do

Project in Protected Sector (cont’d)• Adding a project to the protected sector increases the size of the protected sector

from (C-B) to (C-B1). If additional workers (B-B1) are selected randomly from those remaining who want to work in the protected sector, the supply of labor to the open market will now shift to the left from SSO to SS1.

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Project in Protected Sector (cont’d)

• The expression for the economic opportunity cost of protected sector

jobs as:

EOCLP = WO [QO/(QO+QQV)]

+ [(WO+W1P)/2] [QQV/(QO+QQV)]

• When income taxes are levied on wages in the open sector, there is

an additional economic cost to hiring workers from this open sector

inclusive of income taxes.

• For the quasi-voluntary unemployed hired by the protected sector,

their economic opportunity cost is the average of the net-of-tax open

and protected sector wages in which the latter pay no taxes when

unemployed.

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EOCL with Two Protected Sectors

• The protected sector can contain a series of segmented markets, with different protected sector wages, Wp

1, Wp2, ...Wp

n.

Wage Rate

ST

SO

Wage Rate

Wp

ST

SOS1

A B C

S S

WO

1

Wp2

Wp1

C H A1 F G A B

D O

WO

Do

Before Project After Project

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EOCL with Any Protected Sector

• Under these conditions of a linear supply curve and a perfectly elastic

demand for labor at the open wage of WO, the EOCL for any protected

sector paying a wage, Wi, can be expressed as:

• The EOCL for any protected sector is simply a weighted average of

- the open sector wage, WO, and

- the average of the specific protected sector wage and the open sector wage.

• The weights can all be expressed as functions of the original total

market supply of labor ST{Wi}.

EOCLiP = [ ]WO+ ( )

ST{WO}ST{Wi

P}ST{WO}] Wi

P+WO

2[(ST{Wi

P}-

ST{WiP}

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EOCL When Labor Not Employed Full Time-- Labor Employed Less than Full Year in Market Activities --

Assume:

1. Each worker can spend part of each year working and part in non-market activities or unemployment.

2. Workers are employed in market activities for a proportion (Pp)

of the year if they work for the project.

3. If not associated with the project, workers are employed a different proportion (Pa) of the year. No taxes on non-market

activities.

4. Wgs is the gross-of-tax supply price of skilled labor in the area

of the project; and Wa is the alternative wage which reflects

this labor's other opportunities.

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EOCL When Labor Not Employed Full Time (cont’d)

• The EOCL is equal to the gross-of-tax expected supply price

for labor (Wgs), but only working a portion of the year on the

project (Pp), minus the additional tax payments that the worker

would incur if earning her supply price wage Wgs on this

project.

EOCL = PpWgs - (PpWg

s T - HdPaWaT)

• This additional tax is the difference between the tax paid on

the project (PpWgsT) and the tax previously paid in the

alternative mix of market activities (HdPaWaT).

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EOCL When Labor Not Employed Full Time-- Permanent and Temporary Jobs with an

Unemployment Insurance System and Labor Migration --

• We differentiate between those engaged in full-time and part-time employment.

• People in the permanent (or full-time) employment sector are almost never unemployed. Workers employed by temporary sectors such as tourism or construction are in jobs that are expected to be associated with repeated spells of employment.

• The type of employment created by a project is important.

- Temporary jobs can have a higher economic cost than permanent job when UI payments are paid to these workers when they are unemployed but engaged in non-market activities.

- These support payments affect the EOCL associated with a job.

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EOCL of Permanent Jobs

1. When project creates new permanent jobs they will generally be filled

by individuals already working in alternative permanent sector job,

Hdp, other temporary sector jobs, Hd

t, and some hired from those who

are currently out of labor force, Hs. Thus, Hdp + Hd

t + Hs = 1.

2. For those sourced from permanent sector externality of taxes lost of

HdpWpT.

3. For those sourced from the temporary sector there is loss in taxes,

HdtPtWtT, and a gain in reduced UI payments, Hd

t(1-Pt)fU(1-T), where

f denotes the proportion of time an unemployed worker expects to

collect UI benefits and U denotes the amount of UI benefits.

4. No externalities for share Hs are sourced from outside labor force.

Thus,

EOCLP = Wgs(1 – T) + Hd

pWpT + Hdt[PtWtT – (1 – Pt)fU(1 – T)]

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EOCL of Permanent Jobs (cont’d)

• If unemployment insurance :

EOCLP = Wgs(1 – T) + Hd

pWpT + Hdt[PtWtT – (1 – Pt)fU(1 – T)]

• If no unemployment insurance:

EOCLP = Wgs(1 – T) + Hd

pWpT + HdtPtWtTt

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EOCL for Temporary Sector Jobs

• Creation of 12 months of temporary sector employment

is equal to a person year job.

• Workers sourced in proportions, Hdp’, Hd

t’, Hs’ permanent,

temporary employment and supply of labor who were

previously out of the labor market.

• Pt is the proportion of time a person actually works per

year in a temporary sector job per year.

• For each period of labor services sourced from the

permanent sector there will be 1/Pt individuals,

(1–Pt)/Pt period of unemployment, and f[(1–Pt)/Pt]

periods of paid UI compensation.

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EOCL for Temporary Sector Jobs (cont’d)

• EOCL of 12 months of temporary sector job is:

EOCLT = Wgs(1 – T) + (Hd

p/Pt) [WpT + (1 – Pt)fU(1–T)]

+ HdtWt(Tt) + (Hs/Pt )(1-Pt)fU(1 – Tt)

• In the case where the supply price Wgs is the same for

both permanent and temporary job then EOCLT >

EOCLP for a 12-month job.

• A greater amount of taxes will be lost if temporary jobs

and UI increased.