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Updated:16 Jan. 2007 Lecture Notes ECON 622: ECONOMIC COST-BENEFIT ANALYSIS Lecture Nine

Updated:16 Jan. 2007 Lecture Notes ECON 622: ECONOMIC COST-BENEFIT ANALYSIS Lecture Nine. ECONOMIC OPPORTUNITY COST OF LABOR.

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Updated:16 Jan. 2007 Lecture Notes ECON 622: ECONOMIC COST-BENEFIT ANALYSIS Lecture Nine

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  1. Updated:16 Jan. 2007 Lecture Notes ECON 622: ECONOMIC COST-BENEFIT ANALYSIS Lecture Nine

  2. ECONOMIC OPPORTUNITY COST OF LABOR

  3. The Economic Opportunity Cost of Labour (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

  4. Estimation of the Economic Opportunity Cost of Labor • Two approaches for the estimation of the EOCL: • value of marginal product of labor foregone; & ii) supply price of labor

  5. Value of Marginal Product of Labor Foregone 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 that project (marginal product foregone). • and then adjusting for differences in other costs & benefits.

  6. 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

  7. Example: Comparing the Value of Marginal Product Foregone 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: • Difference in cost of living (C) • 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)

  8. Example (cont’d) Marginal Product Approach • EOCL = prior wage – change in cost of living - worker preferences = Wc - (Cc - Co) – So = 20 - (6 - 3) – 2 • EOCL = $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

  9. Structure of Analysis • Labor prices can vary greatly • Determinants of the economic cost of labor to the project: • Type of Labor (Skilled vs. Unskilled) • Regional Variations and Domestic Migration • Type of Job (Permanent vs. Temporary) • International Migration • Type of Labor Market (Protected vs. Unprotected)

  10. Calculations: Supply Price Approach • Determine the minimum gross-of-tax wage (W) needed to attract sufficient unskilled labor to the positions available on the project. • Identify the distortions in the labor market such as 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.

  11. 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 foregone marginal product for unskilled labor

  12. Example 1: Rural Labor Case without Seasonal Variation in Demand • Assume: • no distortions in the unskilled labor market, • no taxes paid by the employer (demand side), • no income taxes paid by the worker (supply side), • 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 that the EOCL is estimated using the market supply price (WS) not the project wage (Wp).

  13. Example 2: Rural Labor Case with Seasonal Variation in Demand • Assume: • no distortions in the unskilled labor market, • no taxes paid by the employer (demand side), • no income taxes paid by the worker (supply side), • market wage varies due to seasonality in demand. Number of workers needed for project Wages Qp Patterns of project’s demand for labor during the year Pattern of wage rate for unskilled labor during the year Wi Feb April June Aug Oct Dec

  14. n EOCL = å (Kt*Wt) t=1 • 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 (Kt) 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.

  15. 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.

  16. Example: Sugar Production Projects hires Unskilled Labor in a Rural Area • A labor-intensive sugar project • Project requires unskilled workers on a temporary basis • Project pays a wage of 180 dollars per month (Wp) • Project working conditions are identical to those prevailing in the labor market.

  17. Month Market Wage (W) ($/month) Person-months required (Kt) (1) (2) (3) (4) Economic cost of labor for period ($) 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 • 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.

  18. EOCL =  (Kt*Wt) = [120*18 + 100*18 +… + 150*9 + 180*9] = $ 12,690 n=12 t=1 • 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

  19. 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.

  20. Situation 1: Labor Market without Distortions or Regional Migration • Assume: • No distortions in the labor market • No migration • 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

  21. Situation 2: Workers Migrate to Project from Distorted Regional Labor Markets • Assume: • A proportion of the project’s labor (Hd) is induced to migrate from alternative labor markets where they were employed. • Project pays a wage equal or higher than the gross-of-tax supply price (WgS) 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).

  22. Wage Rate D1 D Q2 - Q1 Hs = Q0 - Q1 S Q0 - Q2 W = Hd A Q0 - Q1 B E Wp F C 1 W a W a Qt 1’ W (1 - T) a W Quantity of labor required for project (1 - T) a MARKET FOR A TYPE OF SKILLED LABOR IN SENDING REGION S1 S Wage Rate D D1 S1 S Q1 Q2 Q0 Hs Hd Regional Interaction Between Skilled Labor Markets

  23. Explanation of Figure • Workers migrate from other regions to the project. Supply curve in the sending region (SS) shifts leftward to (S1S1). • At original net-of-tax wage (Wa(1 - T)), migration to the project will cause a decrease in the available supply from Q0 to Q1. • Wage increases to Wa1 (1 - T) to bring about an equilibrium. Higher wage in the sending regions causes employers to reduce the quantity they demand. • 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. • 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. • Reduction in the quantity of labor demanded results in a loss of taxes (ABCE).

  24. 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 market or 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 (WgS) 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 (WgST), 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.

  25. The EOCL (skilled) hired by the project in the area is: EOCL = WgS - (WgS 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 WgS 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.

  26. Labor Externality • Labor externality can be expressed as: LEi = Wp - WgS + (WgST - 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 - Hd WaT • Thus, of the total of externalities created by the employment of workers by a project, labor will gain additional income 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.

  27. Example: Skilled Labor Hired for Sugar Production 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.

  28. The EOCL can be estimated by determining: (1) the taxes to be paid on the supply price of skilled labor for the project, (2) the taxes foregone by the workers in their alternative employment. (1) Taxes on the Supply Price of Labor Taxes on Supply Price = WgST = 1,200(0.20) = $240 per month  (2) Taxes Foregone in Alternative Employment • Assume that the supply of labor in these occupations in the economy is relatively inelastic as compared to the demand for that labor and let Hd = 0.90 and HS = 0.10. • The foregone taxes from the previous employment of the workers are calculated as follows:   Taxes Foregone = Hd Wa T = 0.90 * 900 * 0.20 = $162/month

  29. The EOCL for this project is calculated: EOCL = WgS - (WgST - Hd WaT) = 1,200 - ((1,200 * 0.20) - (0.90 * 900 * 0.20)) = $1,122/month • The difference between the economic opportunity cost of labor in these skilled occupations and the value of the project's labor externality per month of labor employed. • The labor externality can be expressed as: LEi = Wp - WgS + (WgST - HdWaT) = Wp (1 - T) - WgS(1 - T) + WpT – HdWaT

  30. It is possible to determine how these labor externalities are 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 • Thus, 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.

  31. Two Measurements of the EOCL • EOCL for a person who has job over 12 months of calendar time but not full-time • EOCL for a person who has job of 12 months of work Case of Labor for a Person Employed Less than Full Year in Market Activities- May be thought as the EOC of a migrant from another region of a country Assume: • Each worker can spend part of each year working and part of each year in non-market activities or unemployment. • Workers are employed in market activities for a proportion (Pp) of the year if they work for the project (assuming that (Pp<1)). • If not associated with the project, workers are employed a different proportion (Pa ) of the year. No taxes on non-market activities • 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.

  32. EOCL = PpWgS - (PpWgS T - HdPaWaT) 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. • 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). The taxes lost in alternative market activities arises because there is a net reduction in employment of this type of workers elsewhere (Hd of the total). • The economic opportunity cost of these workers is the expected gross-of-tax supply price less the expected net change in tax payments:

  33. EOCL for Different Types of Jobs Case of 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 unemployment insurance 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.

  34. EOCL of Permanent Jobs • 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, Hdt, and some hired from those who are currently out of labour force, Hs. • Hdp + Hdt + Hs = 1 • For those sourced from permanent sector externality of taxes lost of HdpWpT. • For those sources from the temporary sector there is loss in taxes, HdTPtWtT, and a gain in reduced unemployment insurance payments Hdt(1-Pt) fU (1-T) • No externalities for share Hs sourced from outside labour force.

  35. EOCL of Permanent Jobs • If unemployment insurance: EOCLP = WgS(1 – T) + HdpWpT + Hdt[PtWtT – (1 – Pt)f U (1 – T)] • If no unemployment insurance: EOCLP = WgS(1 – T) + HdpWpT + HdtPtWtTt

  36. 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’, Hdt’, Hs’ permanent, temporary employment and Hs of 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 labour services sourced from the permanent sector there will be 1/Pt individuals and (1 – Pt)/Pt period of unemployment and f [(1 – Pt)/Pt] periods of paid unemployment insurance compensation.

  37. EOCL for Temporary Sector Jobs • EOCL of 12 months of temporary sector job is: EOCLT = WgS(1 – T) + (Hdp/Pt) [WpT + (1 – Pt) f U (1 – T)] + Hdt Wt(T) + (Hs/Pt )(1-Pt) f U (1 – T) Where Hdp = workers sourced from the permanent sector Hdt = workers sourced from the temporary sector Hs = workers sourced from those out of the labor force Pt = proportion of time that person works in a temporary sector job during a year • In the case where the supply price Wgs the same for both permanent and temporary job then EOCLT > EOCLP. • Labor sourced from permanent sector jobs will now experience (1-Pt) / Pt periods of time as unemployed and they will collect unemployment insurance. This will give rise to (1-Pt) / Pt periods of paid unemployment insurance compensation (UIC). Additional cost of tax lost from permanent employment plus the additional UIC now as these workers become eligible for unemployment insurance payment. • For labor services sourced from the temporary sector, loss in taxes will be same as before for the same length of time to the time working on the project and UIC will be same as before for the same amount of unemployed time. Only additional cost is the amount of taxes lost from working in alternative temporary job. • Labor sourced from these now out of the labor force (Hs / Pt) have additional costs now of unemployment insurance that will now be paid to them when they become unemployed from the new temporary job

  38. Economic Opportunity Cost of Labor if International Migration Flows Case 1. 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 economic opportunity cost of labor must not only take into consideration 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 will be factored into the worker’s supply price to the project.

  39. Ee Em EOCL= WgS(1 - T) + HdWaT + Hf R( – 1) • 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 as a fraction of the value of amount that would otherwise have been remitted.

  40. 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 value-added tax (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.

  41. EOCLF = WF(1 - Th) - WF(1 - Th)(1-R)tVAT+ WF(1–Th)R(Ee/Em–1) + N • 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= Value-added tax levied on consumption R = proportion of the net-of-tax income repatriated by foreign labor Ee = economic exchange rate (explained in chapter 10, section V) Em = market exchange rate N = value of benefits gained by foreign workers from subsidies

  42. EOCLF = WF(1 - Th) - WF(1 - Th)(1-R)tVAT+ WF(1–Th)R(Ee/Em–1) + N • WF(1–Th) represents the net-of-tax wage paid to the foreign worker. • WF(1–Th)(1–R)tVAT represents the amount of VAT revenue created by the foreign workers’ consumption in the country while working on the project. • WF(1–Th)R(Ee/Em–1) is the premium on foreign exchange associated with the repatriated portion of the income. • N is the value of the subsidy consumed by the foreign workers. • If the EOCLF is greater than the financial cost of labor to the project, the economic opportunity cost of hiring foreign labor is greater than the project wage. If the economic opportunity cost of foreign labor will is lower than the market wage, this means that the country is benefiting economically from the presence of foreign labor.

  43. Example: A Multinational Corporation Employing Foreign Labor • 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 market exchange rate (Em) is held constant by the government at 39.00 pesos to the dollar, while the economic exchange rate (Ee) is estimated to be 15% higher at 44.85 pesos per dollar. • Assume that there are no subsidies paid by the government with respect to these workers, i.e. N=0.

  44. Estimation of the EOCL: • EOCLF = 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 $9 less than the net-of-tax wage of $150. • Hence, there is a beneficial externality created if the project uses foreign labor. EOCLF = WF(1 - Th) - WF(1 - Th)(1-R)tVAT+ WF(1–Th)R(Ee/Em–1) + N

  45. Effects of a Protected Sector on the Economic Opportunity Cost of Labor • 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.

  46. Wage Rate O S p W 1 T S Do O W S A1 A B C Quasi-voluntary Unemployed Open Market Employment Protected Employment O QQV QPr Q • 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, independent of their supply prices, 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. EOCL in the Protected Sector and No Migration

  47. 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 actively seek jobs in the protected sector, and will consider themselves involuntarily unemployed. They are seeking work which will pay the protected sector wage (W), but are unable to find it.

  48. Wage Rate T S 1 O S S p W 1 O W Do S B1 A1 C E A B • Project in Protected Sector • 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. • 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, then 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.

  49. 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 both the protected and open sectors, there is an additional economic cost to hiring workers from the open sector over and above the worker's supply price (i.e. the net-of-tax wage WO). • The value of this distortion can be expressed in terms of the net-of-tax supply price, [WO (t/(1 - t))]. For the quasi-voluntary unemployed hired by the protected sector, their economic opportunity cost is still the average of the net-of-tax open and protected sector wages because they pay no taxes when unemployed: EOCLP=[WO(1-T)QO/(QO+QQV)]+[(WO+W1P)/2 (1 – T)][QQV/(QO +QQV)]

  50. Wage Rate Wage Rate Before Project After Project S1 O S O S p p W W 1 1 T T p S S W 2 O O W Do O W D S S A B C H A1 F G A B C Case 2: EOCL with Two Protected Sectors • The protected sector can contain a series of segmented markets, with different protected sector wages, W1, W2, ..., Wn.

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