1

Lecture Notes

ECON 437/837: ECONOMIC COST-BENEFIT ANALYSIS

Lecture Seven

2

Economic Cost of Foreign Exchange (EOCFX) and Shadow Price of Non-

Tradable Outlays (SPNTO)

3

Definition of EOCFX and SPNTO

• These variables (EOCFX and SPNTO) are estimated to measure

the value of the distortions created when funds are sourced in the

capital market and used to purchase either tradable goods, or non-

tradable goods.

• These actions are repeated many times for each project and are

identical for such actions across projects.

• It is efficient to estimate these variables once for a country and use

the same values repeatedly as needed.

• To make the estimates we do not include the specific distortions on

the particular tradable or non-tradable good. These effects are

included when we estimate the economic cost of the specific item.

4

Estimation of EOCFX and SPNTO under two situations:

1. Project already has raised funds (e.g. foreign aid) and spends them on tradable and non-tradable goods.

2. Project raises funds in capital markets and spends funds on tradable and non-tradable goods

• When the values for the tradable inputs and outputs are expressed in units of

domestic currency at the domestic price level, the foreign exchange effect of

the change in the demand (or supply) of tradable commodities must be

converted into domestic currency.

• Conversion should take place at the “shadow exchange rate”, or economic

price of foreign exchange (Ee).

• If there are no distortions on the demand or supply of tradable goods, and if

the exchange rate is determined by market forces, then the economic price of

foreign exchange is equal to the market exchange rate (Em).

Economic Cost of Foreign Exchange

6

Partial Equilibrium Model: Distortions that affect international trade are

considered, but no account is made for how purchase of foreign exchange is

financed.

1.Trade Distortions: These distortions will change the demand and/or supply of

foreign exchange such that the market exchange rate no longer measures the

economic price of foreign exchange. For example,

– Tariffs: lower the market demand for foreign exchange and cause Em

to be less than Ee

– Export Taxes: Decrease the market supply of foreign exchange and

cause the Em to be greater than Ee

– Export Subsidies: Increase the market supply of foreign exchange

and cause the Em to be less than Ee

• Indirect taxes: This will impact the demand and supply of both tradable and

non-tradable goods

- Value added taxes

- Excise taxes

Economic Cost of Foreign Exchange with Distortions (cont’d)

7

• All goods are divided into three types:

1. Importable

2. Exportable

3. Non-Tradable Goods• Importable and exportable goods are referred to as

tradable goods.• Prices of tradable goods are determined by international

markets and expressed in units of a foreign exchange currency.

• Domestic prices of such goods are determined by multiplying the internationally given import price Pw

I or the

export price PwE by the market exchange rate EM, i.e.

PDI =EMPw

I, PDE=EMPw

E

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• As the world prices of these goods are fixed, their domestic

prices, and the quantity domestically demanded or

domestically supplied of these goods will depend on the

real exchange rate.

• These quantities can be expressed in units of foreign

exchange.

• Importable and exportable goods can be aggregated to

make market for tradable goods.

• Equilibrium in tradable goods market also means that there

is equilibrium in foreign exchange market.

• This market will determine the country’s real exchange

rate.

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Demand for Tradable Goods

• Equals demand for importable goods plus demand for exportable goods

Demand for Importable Demand for Exportable Demand for Tradable

Goods Goods Goods

EM EM EM

DT = DI+DE

DI DE

Q (FX) Importable Q (FX) Exportable Q (FX) Traded

• Because the world price of importable and exportable goods are given to country, the demand for tradable goods is a function of the real exchange rate.

10

Supply of Tradable Goods

• Equals domestic supply of importable goods plus domestic supply of exportable goods.

Domestic Supply of Domestic Supply of Domestic Supply of Importable Goods Exportable Goods Traded Goods EM S I EM SE EM ST=SI+SE

EM0 EM

0 EM0 DT

QSI QS

E QST

Q(FX) Importable Q (FX) Exportable Q (FX) Tradable

Exchange rate is determined by the demand and supply of tradable Goods.

QDT = QS

T

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Demand for Foreign Exchange

An equivalent way to see how the exchange rate is determined as to draw the demand for imports and supply of exports

Importable Market Demand for Imports

P SImportable EM

_

EM0 EM

0

EM1 DImportable E1 DM

QIS Import QI

D Importable(QFx) QFXD

The demand for imports = Demand for importable goods - Supply of importable goods

Demand for Foreign Exchange = Demand for Imports

QFxD = QI

D - QIS

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Supply of Foreign Exchange

Exportable Market Imports and Exports

P SExportable

SX

EM0

EM1 E1

DM

DExportable

QED Export QE

S Exportable(QFx) QFXD/S

QFxS = QE

S - QED = Supply of Foreign Exchange = Supply of Exports = SX

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Total Economy = Market for Tradable Goods plus Market for Non-Tradable Goods

Tradable Goods Non-Tradable Goods

EM ST SNT

E0 PNT

DT DNT

QT

0 Q(FX) QNT0

• Given the amount of capital and labor in country, GDP = Quantity Supplied of Tradable goods + Quantity Supplied of Non-tradable goods.

• Price of non-tradable goods is fixed as the numeraire price in the economy, real exchange rate becomes the relative price of tradable to non-tradable goods.

• Market equilibrium is determined by the relative prices.

• Changes in exchange rate will cause the demand and supply of non-tradable goods to shift. This is the relative price effect on demand for a good.

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Full Employment and Equilibrium in Tradable and non-Tradable Goods Markets

Tradable Goods Non-Tradable Goods

EM ST0 SNT

E0 PNT

DT0 DNT

QT0 Q(FX) QNT

0

GDP = QT0 + QNT

0 Full Employment

Think of tradable goods and non-tradable goods as two large composite goods

QST = QD

T QSNT = QD

NT

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Equilibrium in Foreign Exchange Market

Importable Exportable Market for Foreign Exchange

EM SI SX

SE

E0

DI

DE DX

QSI QD

I QDE QS

E QFX0

Import Export

• Equilibrium in tradable goods market and foreign exchange market.

QDI + QD

E = QDT, QS

I + QSE = QS

T

• In equilibrium, QDT = QS

T

• Hence, QDI+QD

E= QSI+QS

E QDI-QS

I = QSE-QD

E Imports = Exports

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Determination of Market Exchange Ratewith No Distortions

Exchange Rate: # of units of domestic currency per unit of Foreign Exchange

Quantity of foreign exchange US$

Ee=Em

S0fex

D0fex

Q0

Ee = Em

Em = Market Exchange Rate Ee

= Economic Exchange Rate

S0fex = Supply of foreign exchange as derived from supply of exports

D0fex = Demand for foreign exchange as derived from demand for imports

Ee = Ws*Em + Wd*Em

as Ws +Wd = 1 then

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Case One: Funds available to purchase foreign exchange

• Import Tariff = Tm

Quantity of Foreign Exchange Traded

Q0

D0

d1 QQ

Dt (net of tax)

s1

Dt+project

m1Em0

E

S0

Exchange Rate

E0m(1+Tm)

Ee = Ws * Em +Wd * Em(1+Tm)

Determination of Exchange Rate with Import Tariff

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Case Two:• Export Subsidy = kx

D0

S0

S0+export subsidy

Quantity of Foreign Exchange Traded

Exchange Rate

D0 + Project

Q0

s1QQ

d1

m1Em0

E

E0m(1+kx)

E1m(1+kx)

Ee = Ws*Em*(1+kx) + Wd*Em

Determination of Exchange Rate with Export Subsidy

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Case Three:• Export Tax = tx

D0

S0+export tax

S0

Quantity of Foreign Exchange Traded

Exchange Rate

D0 + Project

Q0

s1QQ

d1

m1Em0

E

E0m(1-tx)

E1m(1-tx)

Ee = Ws*Em*(1-tx) + Wd*Em

Determination of Exchange Rate with Export Tax

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Case Four• Current Account in Equilibrium• Import Tariff = Tm

• Export Tax = tx

Ee = Ws*Em*(1-tx) + Wd*Em*(1+Tm)

Quantity of Foreign Exchange Traded

Q0

D

d1

Q

Dt

G

F

Tariff

L

J

Export Tax

Qs1

Dp

m1Em0

E

St S

Exchange Rate

AB

H

Determination of Exchange Rate with Import Tariff and Export Tax

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Determination of Exchange Rate with Distortions and Capital Flows

Case Five:

• Balance of Payments Deficit Sustained through Capital Inflows

• Import Tariff = Tm

• Export Tax = tx

Ee = Ws*Em*(1-tx) + Wd*Em*(1+Tm)

Quantity of Foreign Exchange Traded

Conclusion: No change in basic estimation procedure.

St

Exchange Rate

H

Q

A

d1QQ

Dt

G

D

L J

s1

S

s0

F

K

MDP

B

Qd0

m1Em0E

N

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Economic Price of Foreign Exchange

Trade Distortions• An increase in demand for imported inputs will cause a (slight)

depreciation in the domestic currency, which in turn will cause a reduction in imports and an increase in exports.

• The economic value of the foreign exchange required by a project is determined by the economic values of the forgone imports and increased exports.

Example: The main trade distortions are tariffs on imported goods and taxes on exports. The economic price per unit of foreign exchange is

Ee = Ws*Em*(1-tx) + Wd*Em(1 + Tm)Where Ws = The proportion of an extra unit of foreign exchange that is met by an increased supply of exports:

Wd = The proportion of an extra unit of foreign exchange that is met by a reduction in other imports:

s

s - d * (Qd/Qs)=Ws

s - d * (Qd/Qs)

- d * (Qd/Qs)=Wd

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Calculation of Foreign Exchange PremiumUnder Special Conditions

If the elasticity of foreign exchange supply (s) is equal to the elasticity of foreign exchange demand (d): s = - d

Then, a simple way to calculate the foreign exchange premium is:

Tariff Revenues + Export Subsidies - Export Taxes

Value of Imports + Value of ExportsFEP =

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Application of Foreign Exchange Premium

• To value tradable goods at economic prices, the CIF prices of importable goods, or the FOB prices of exportable goods should be converted into domestic prices using the economic exchange rate (Ee).

In financial analysis: PfI = EmPw

I, PfE = EmPw

E

In economic analysis: PeI = EePw

I, PeE = EePw

E

• Alternatively, this valuation at economic prices can be achieved by adding a foreign exchange premium [(Ee/Em) - 1] per unit of foreign exchange demanded (or supplied) by a project.

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Premia for Foreign Exchange and Non-Tradable Outlays

-- A General Equilibrium Analysis --

Introduce Project Financing• Project funds come from capital market• Project costs 600• Funds obtained from the capital market for our project

displace 600 of other demands• Assume reduction in other demand is a reduction of 400

in tradable demand and a reduction of 200 in non-tradable demand.

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Premia for Foreign Exchange and Non-Tradable Outlays (cont’d)

-- A General Equilibrium Analysis --

Four alternative scenarios:

a) Project funds borrowed domestically and spent on tradable goods;

b) Project funds borrowed abroad and spent on tradable goods;

c) Project funds borrowed domestically and spent on non-tradable goods;

d) Project funds borrowed abroad and spent on non-tradable goods.

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Tradable Goods Markets-- Case A: funds borrowed domestically and spent on tradables --

Ts

0

Td0

Eu

Td1

E0 E1

QT1

Td2

QT2 QT

0 QNT1 QNT

0

NTd0

NTd1

NTs0

Exchange Rate

NTs1

QNT2

200 400

200

Price of Non-tradables

P0

QT QNT

80 120 80 120

A. Tradable Goods B. Non-tradable Goods

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Foreign Exchange Markets

Xs0

Md0

Qfxd Qfx

s

Id1

Id0

Jd0

Jd1

Xs1

Md2

Md1

Is0

Js0

Qsi0 Qdi

0 Qdi1 Qse

0 Qde0 Qde

1

E1

E0

Exchange Rate

200

Exchange Rate

Exchange Rate

Qfx Qi Qe

100 300 100 100 300

Importable Exportable Market for Foreign Exchange

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TABLE 1 CALCULATION OF ECONOMIC OPPORTUNITY COST OF FOREIGN EXCHANGE

600 of Project Funds Sourced in Capital Market And Spent on Tradables m

vt

m vh

Applicable m vt eis

Distortion Alone vh eia

Change Due To (exclusion for Capital Market investment Sourcing eis = 0.75)

Tradables Demand -400 vt = .20 n.a. -80 -20

Import Demand -300 m = .12 -36 -36 -36

Export Supply +100 - n.a. n.a. n.a. Nontradables Demand -200 vh = .05 n.a. -10 -2.5

Change Due To Real (exclusion for Exchange Rate investment Adjustment eia = 0.33)

Tradables Demand -120 vt = .20 n.a. -24 -16

Tradables Supply +80 - n.a. n.a. Import Demand -100 m = .12 -12 -12 -12

Export Supply +100 - n.a. n.a. Nontradables Demand +120 vh = .05 n.a. +6 +4

Nontradables Supply -80 - n.a. n.a. Total Distortion Costs (-), -48 -156 -82.5 Benefit (+) Distortion Cost/ Project Expend. .08 .26 .1375 = Premium on Tradables Outlays EOCFX/ 1.08 1.26 1.1375 Market Exchange Rate

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Case B: Funds Borrowed from Abroad and Spent on Tradables

Step 1: No impact on domestic capital market due to borrowing from abroad Step 2: More foreign exchange to purchase tradable goods for project

600

E

E0

Q

sT0 sT1

dT0

dT1

TQ0TQ1

Step 1Step 2

PNT

sNT0

dNT0

NTQ0

Tradable Goods Non-Tradable Goods

Supply of tradable goods (foreign exchange) increased by 600, Demand for foreign exchange increased by 600 with the Project.

No Impact on Non-Traded

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Market for Foreign Exchange

600

sX 0 sX1

dM 0

dM1

0Q 1Q

Step 1Step 2

FXQ

0E

E

No change in exchange rate as change in demand for FX of 600 is offsetted by additional supply of FX of 600.

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Tradable Goods Markets-- Case C: funds borrowed domestically and spent on nontradables --

NTd0

NTd1

NTd2

NTd3

NTs0

NTs1

Ts0

Td0

Td1

E0

E2

QNT2 QNT

0 QNT1 QT

0 QT1

Exchange Rate

QT QNT

400 200 400

Price of Non-tradables

PNT

240 160 160 240

QNT3

Tradable Goods Non-Tradable Goods

Assumption that |TD| =1.5 T

S

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Foreign Exchange Markets

100300

dM 0

dM1

200 200

FXQ0

2E

0E

sX1

sX 0E

FXQ

Assumption that |ID| = x

S

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TABLE 2 CALCULATION OF SHADOW PRICE OF NONTRADABLES OUTLAYS 600 of Project Funds Sourced in Capital Market And Spent on Nontradables

m

vt

m vh

Applicable m vt eis

Distortion Alone vh eia

Change Due To (exclusion for Capital Market investment Sourcing eis = 0.75)

Tradables Demand -400 vt = .2 n.a. -80 -20

Import Demand -300 m = .12 -36 -36 -36

Export Supply +100 - n.a. n.a. n.a. Nontradables Demand -200 vh = .05 n.a. -10 -2.5

Change Due To Real (exclusion for Exchange Rate investment Adjustment eia = 0.33)

Tradables Demand +240 vt = .2 n.a. +48 +32

Tradables Supply -160 - n.a. n.a. n.a. Import Demand +200 m = .12 +24 +24 +24

Export Supply -200 - n.a. n.a. n.a. Nontradables Demand -240 vh = .05 n.a. -12 -8

Nontradables Supply +160 - n.a. n.a. n.a. Total Distortion Costs (-), -12 -66 -10.5 Benefit (+) Distortion Cost/Project Expend. .02 .11 .0175 = Premium in Nontradables Outlays Shadow Price of Nontradables Outlays 1.02 1.11 1.0175

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Case D: Funds Borrowed from Abroad and Spent on Nontradables

• More foreign exchange available in the economy

• Impact on exchange rate

Change in demand for tradable goods is increased by 360, change in demand for non-tradable goods is decreased by 360.

Tradables

T0s

T1s

T0d

600

360 240

Q0T

NT0s

NT1s

NT0d

600

240 360

PNT

NT2d

Non-Tradables

NT1d

E0

E2

E

Q

E

Q

Assumption is that |TD| = 1.5 T

S

Market for Foreign Exchange

X0s

X1s

M0d

600

300 300

Q0T

E0

E2

E

QFX

600 excess supply of FX from foreign borrowing results in falling

real exchange rate to E2. This will cause the demand for imports

to rise by 300 and the supply of export to fall by 300.

Assumption that |ID| = x

S

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TABLE 3 CALCULATION OF SHADOW PRICE OF NONTRADABLES OUTLAYS

600 of Project Funds Sourced Abroad And Spent on Non-Tradables m

v t

m vh

Applicable m v t eis Distortion Alone v h eia

Change Due To (exclusion for Capital Market investment Sourcing eis = 0.75) n.a. n.a. n.a.

Change Due To Real (exclusion for Exchange Rate investment Adjustment eia = 0.33)

Tradables Demand +360 vt = .2 n.a. +72 +48

Tradables Supply -240 - n.a. n.a. Import Demand +300 m = .12 +36 +36 +36 Export Supply -300 - n.a. n.a. Nontradables Demand -360 vh = .05 n.a. -18 -12

Nontradables Supply +240 - n.a. n.a. Total Distortion Costs ( -), +36 +90 +72 Benefit (+) Distortion Cost/ Project Expend. -.06 -.15 -.12 = Premium on Nontradables Outlays Shadow Price of Nontradable Outlays 0.94 0.85 0.88

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TABLE 6 WEIGHTED AVERAGE PREMIA WITH “STANDARD”

CAPITAL MARKET SOURCING gd = fraction of project funds effectively sourced in the domestic capital market

gf = (1-gd) = fraction of project funds effectively sourced in the foreign capital market

PREMIA ON TRADABLES AND NONTRADABALES

Project Funds Sourced From: Both Markets gd = .7

Applicable Distortions Domestic Capital Market Foreign Capital Market gf = .3

m = .12

Project Funds Spent On Tradables .08 -0- .056 Nontradables .02 -.06 -.004 m = .12, vt = .20, vh = .05

Project Funds Spent On Tradables .26 -0- .182 Nontradables .11 -.15 .032 m = .12, vt = .20, vh = .05, eih = .75, eia = .33

Project Funds Spent On Tradables .1375 -0- .09625 Nontradables .0175 -.12 -.02375

TABLE 6 WEIGHTED AVERAGE PREMIA WITH “STANDARD”

CAPITAL MARKET SOURCING gd = fraction of project funds effectively sourced in the domestic capital market

gf = (1-gd) = fraction of project funds effectively sourced in the foreign capital market

PREMIA ON TRADABLES AND NONTRADABALES

Project Funds Sourced From: Both Markets gd = .7

Applicable Distortions Domestic Capital Market Foreign Capital Market gf = .3

m = .12

Project Funds Spent On Tradables .08 -0- .056 Nontradables .02 -.06 -.004 m = .12, vt = .20, vh = .05

Project Funds Spent On Tradables .26 -0- .182 Nontradables .11 -.15 .032 m = .12, vt = .20, vh = .05, eih = .75, eia = .33

Project Funds Spent On Tradables .1375 -0- .09625 Nontradables .0175 -.12 -.02375

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A Case of South Africa

• A General Equilibrium Analysis• Take into account:

- project funds sourced from the capital market (62.5% from displaced investment, 11.5% from household saving and 26.0% from foreign savings).

- all distortions in import tariff, subsidy, value-added tax, and other indirect taxes.

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Table 1 Impact of Capital Extraction and Spending on Project Inputs in South Africa

Capital Sourcing and Spending Importables Exportables Non-Traded Domestic Funds a) Project Demands for Importables +100.0

Displacement (K-Market) -39.0 -24.0 -37.0 Effect of Real Exch Rate on Demand -8.4 -6.9 +15.3 Effect of Real Exch Rate on Supply +7.6 +14.1 -21.7 Excess Demand for Goods +45.0 -45.0 0 Domestic Funds b) Project Demands for Exportables +100.0

Displacement (K-Market) -39.0 -24.0 -37.0 Effect of Real Exch Rate on Demand -8.4 -6.9 +15.3 Effect of Real Exch Rate on Supply +7.6 +14.1 -21.7 Excess Demand for Goods -55.0 +55.0 0 Domestic Funds c) Project Demands for Non-Tradables +100.0

Displacement (K-Market) -39.0 -24.0 -37.0 Effect of Real Exch Rate on Demand +14.3 +11.8 -26.1 Effect of Real Exch Rate on Supply - 12.9 -24.0 +36.9 Excess Demand for Goods -11.8 +11.8 0 Funds Borrowed from Abroad d) Project Demands for Non-Tradeables +100.0

Displacement (K-Market) - - - Effect of Real Exch Rate on Demand +22.7 +18.8 -41.5 Effect of Real Exch Rate on Supply -20.4 -38.1 +58.5 Excess Demand for Goods +43.1 +56.0 0

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Table 2 Externalities Generated from Project Funds Sourced from Domestic Markets and

Spent on Importables

Capital Sourcin g and Spending Importables Exportables Non-Traded Domestic funds a) Project Demands for Importables +100.0

Displacement (K-Market) -39.0 -24.0 -37.0 Effect of Real Exch Rate on Demand -8.4 -6.9 +15.3 Effect of Real Exch Rate on Supply +7.6 +14.1 -21.7 Excess Demand for Goods +45.0 -45.0 0 Total Distortion Costs: -8.21% Import Tariffs = (45-100)*3.6% = -1.98% Production Subsidies = -(-45)*0.6% = + 0.27% VAT = [(-39-24)*0.156 + (-8.4-6.9)*0.804]*11.36% +[(-37)*0.156 + (15.3)*0.804]*6.54% = - 2.09% Other Indirect Taxes = (-39-24-8.4-6.9)*5.63% = - 4.41%

Premia on Tradables and Non-tradables in South Africa (Percentage)

Funds Drawn from Funds Spent Funds Spent

on Tradables on Non-Tradables

Domestic Capital Source 8.21 3.06

Foreign Capital Source 0 - 5.15

Capital Market Weights 6.08 0.93

(D: 74%, F: 26%)42

Estimates of FEP and NTP for African Countries

Country Parameters Effective Tax and Subsidy Rates (%) Premiums (%)

D-Fund Imp/Tr in Cap-

Ext

ImportDuty

Export Tax

VAT-Trade

VAT-Nontrad

Excise Subsidy FEP NTP

VAT Countries

Ethiopia 0.74 0.92 7.00 0.00 8.05 1.89 2.25 0.26 6.64 -0.24

Ghana 0.68 0.92 8.50 0.42 9.34 2.20 3.64 0.06 7.87 -0.86

Ivory Coast

0.76 0.92 14.33 5.33 4.61 1.09 1.15 0.78 9.50 +1.54

Keynes 0.72 0.92 4.90 0.06 11.54 2.72 7.21 0.04 8.65 -0.57

Mauritius 0.76 0.89 3.79 0.00 12.75 3.00 2.94 0.52 5.71 -0.35

Rwanda 0.70 0.92 5.80 0.00 7.76 1.83 2.70 4.89 5.86 -0.52

Senegal 0.64 0.92 6.09 0.00 14.66 3.45 3.37 5.85 7.91 -1.68

Tanzania 0.68 0.92 3.75 0.00 14.08 3.31 0.54 0.00 3.94 -0.80

Uganda 0.76 0.92 4.10 0.05 8.29 1.95 0.05 0.00 8.46 0.00

Zambia 0.76 0.92 5.00 0.00 10.03 2.36 5.04 0.37 7.66 -0.05

Countries with General Sales Tax System

Egypt 0.78 0.92 4.00 0.18 6.20 1.93 2.00 8.93 5.07 +0.47

Seychelles

0.73 0.92 3.19 0.00 13.50 9.00 4.36 0.00 6.23 +0.72

Congo 0.65 0.92 7.71 0.44 4.96 1.86 1.50 0.00 7.78 +0.81

43