A CALCULATION OF

SHADOW PRICES

FOR TANZANIA

by

Armeane M. Choksi

Eastern Africa IA

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A CALCULATION OF SHADOW PRICES FOR TANZANIA

CONTENTS

Page Number

CHAPI'ER I - INTRODUCTION

The Valuation of Traded and Non-Traded Goods . Private Consumption versus Government Income . The Choice of Numeraire and the Associated Choice

of Discount Rate . The Income-Distribution Weights Summary of the Values of the Shadow Prices A Summary of the Calculations

CHAPI'ER. II - CONVERSION FACTOR

The Standard Conversion Factor (SCF) ... 'Q .. The Conversion Factor for Consumption Goods ( \ ) The Conversion Factor for Capital Goods ( f k). • The Conversion Factor for Intermediate Goods ( ~I) The Conversion Factor for Non-Tradeables (CFnt) •

CHAPTER III - THE MARGINAL PRODUCT OF CAPITAL (q)

The Incremental ~utput/Capital Ratio (k). The Marginal Product of Labour (mn) . • • The Incremental Employment/Capital Ratio (1)

CHAPI'ER IV - THE MARGINAL PROPENSITY TO SAVE (s)

CHAPTER V - THE CONSUMPTION RATE OF INTEREST (CRI)

CHAPTER VI - THE SUMMARY DISTRIBUTION MEASURE (D)

CHAPTER VII - THE SOCIAL VALUE OF PUBLIC INCOME

Method I • • • • • • The Critical Consumption Level (CCL) The Consumption Distribution Weight (d) The CCL Revisited. The Value of Public Income Revisited Method II. Method III

CHAPTER VIII - THE ACCOUNTING RATE OF INTEREST (ARI)

Method I • Method II ' .

1 1

2 2 2 3

4

5 6 7 7 7

10

10 11 11

13

14

16

17

19 21 21 22 23 24 24

25

25 26

CONrENTS (cont'd)

Page Number

CHAPTER IX - THE SHADOW WAGE RATE FOR RURAL WORKERS (SWR)

CHAPTER X - CONCLUSIONS

Data Constraints • The Use of Distributions Weights The Choice of the Utility Function • The Pure Rate of Time Preference

27

29

29 29 30 31

ANNEX - LI ST OF THE TABLES REFERRED TO IN THE TEXT

REFERENCES

I. Introduction

1 . 1 This is an application of the Revised Draft of "Economic Analysis of Projects" (June, 1974) to Tanzania. It is not intended to be a comprehensive manual on how to perform cost-benefit analysis, but merely to indicate a method of calculation of the relevant shadow (accounting) prices which are NOT project-specific. Project-specific parameters will have to be calculated by the project economist on a case-by-case basis. However, if any project economist feels that any particular shadow price does not accurately reflect the true one, the relevant section will indicate to him the manner in which his estimates of certain parameters may be used to obtain a different shadow price.

1 . 2 One can distinguish the main elements in this method of shadow pricing:

(i) the valuation of traded and non-traded goods;

(ii) private consumption versus government income;

(iii) the choice of numeraire and the associated discount rate;

(iv) the income-distribution weights

The Valuation of Traded and Non-Traded Goods

1.3 These goods are usually expressed in danestic market prices which nonnally overstate their true social values. They must either be revalued at border prices or be converted to border prices by multiplying them by their conversion factors in order to reflect their opportunity cost to the country. (see para. 2.1 - 2.7.7)

Private Consumption versus Government Income

1 ,4 If consumption benefits in the hands of the private sector are as valuable as those in the hands of the government, there is no need to make a distinction, and benefits for the two entities can be added together without adjustments. However, many governments, because they are unable to tax private income to the "optimal" extmt, feel that projects which increase government revenues are more valuable socially than those which do not. Therefore to bias projects towards the former, a premium is placed on income in the hands of the government. Where benefits are initially measured in terms of private consumption, the approach used is to discount private consumption benefits by dividing these by the social value of public income (v), (see paras. 7.1 - 7.6)

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The Choice of Numeraire and the Associated Choice of Discount Rate

1 .5 It is necessary to have a common unit of account -- a numeraire -- in terms of which everything is measured. The choice of the numeraire does not make any real difference provided one uses the appropriate discount rate. As has been indicated implicitly in the last paragraph, the numeraire used in this paper is the present value of uncommitted government income measured in foreign exchange. Th.is is natural enough for this method since it is the optimal allocation of public revenue which forms the purpose of public sector project selection. To render this numeraire comparable to other values in the system it needs to be denominated in world prices. Hence the unit of account is "foreign exchange at the disposal of the government".

1 .6 Using uncommitted government income as the numeraire implies that the discount rate should be the rate at which the value of public savings (v) falls over time. This is referred to as the accounting rate of interest (ARI) ( see paras. 8. 1 - 8. 3) . It is different from the consumption rate of interest (CRI), which is the rate of fall of the value of consumption. (see paras. 5.1 - 5.2)

The Income-Distribution Weights

1 .7 The difference in the social value of an additional unit of consumption in the hands of the rich and the poor is due to the higher marginal utility associated with the poor, i.e., an additional unit of consumption to the poor man will have greater social value .than an additional unit to the rich man. Income-specific distribution weights (di) may be obtained for the additional unit of consumption going to a person in the ith income group relative to a person in the average income group. Benefits going to the ith income group are then multiplied by di· If that group's pre-project income is less than that of the average income group, d;iis greater than one and vice-versa.· Hence di is a project-specific parameter.(see paras. 7.7.8 - 7.7.10)

1 .8 There is also a national or summary distribution measure, D, which expresses a general additional unit of consumption in terns of an additional unit of consumption at the average income level. This parameter will have values greater than one when income in the hands of the rich is less valuable than that in the hands of the poor (see paras. 6.1 - 6.3).

Sunnnary of the Values of the Shadow Prices

1 .9 The table below lists the values calculated for the various parameters and shadow prices. Since, in several instances in the text, ranges of each values were computed, it was decided to present only the -":;nost likely" values which would be considered useful in any economic analysis and they exclude income-distributional effects (see

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para. 10.2.1 ). The presentation below is not meant to suggest their mechanical application. It is suggested that the user go through the text to verify whether the assumptions used coincide with his present knowledge of the situation, and to make a judicious interpretation of the values if they do not. References to the relevant paragraph are provided in the third column in order to facilitate any changes.

A SUMMARY OF THE CALCULATIONS

1.

2.

3.

4,

5.

6.

7.

8.

9.

Symbol

The Standard Conversion Factor SCF

The Shadow Exchange Rate SER

The Consumption Goods Conversion Factor ~

The Capital Goods Conversion F~t~ ~k

The Intermediate Goods Conversion Factor ~I

The Conversion Factor for Construction CFC

The Conversion Factor for Electricity and Water Supply CFP

The Conversion Factor for Transportation CFt

The Marginal Product Capital q

10. The Marginal Propensity to Save s

11. The Elasticity of the Marginal Utility of Consumption n

12. The Pure Rate of Time Preference p

13. The Consumption Rate of Interest CRI I

Value Paragraph

0,77 2.3.3

9.28 sh/$ 2.3.3

o.656 2.4

0.9523 2.5

0.8179 2.6

0.8507 2.7.5

0.819 2.7.5

O. 7801 2. 7. 5

15% 3.7

0.2 4. 1

14. The Summary Distribution Measure D

15. The Social Value of Public Income v

16. The Accounting Rate of Interest ARI

17. The Shadow Wage Conversion Factor SWR w

1 .25

1 .%

4.9%

1.109

3 .167

8.78%

0.45

5.4

5,4

5.5

6.2

7.9

8.6.2

9.3

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II. Conversion Factors

2.1 This section develops the conversion factors required to change domestic market prices into border or traded prices. The reason for this conversion is that the value of a traded commodity expressed in terms of its domestic market price, is usually overstated in comparison with its true social value. Since the trading opportunity cost reveals the social value of traded goods, domestic market prices must be converted into border prices.

The following conversion factors are calculated:

( 1 ) The Standard Conversion Factor (SCF)

(2) The Conversion Factor for Consumption Goods ( ~ )

(3) The Conversion Factor for Capital Goods(~)

(4) The Conversion Factor for Intennediate Goods (~)

(5) The Conversion Factor for the following three non- traded goods

(a) Construction (CFC) (b) Electricity & Water Supply (CFP) (c) Transportation (CFt)

The conversion factor for labour, or the shadow wage rate is developed in another section. (see para. 9,1)

2.2 The simple formula for the calculation of conversion factors is given below. It should be noted that the same formula may be applied for the SCF or the conversion factors for consumption, capital or intermediate goods where the values of imports, tariffs, duties, etc. refer to the goods in question or to all goods for the SCF.

M + X M(1+tm) + X(1-tx)

( 1 )

where Mis the c.i.f. value of imports Xis the f.o.b. value of exports tm is the average tax on imports tx is the average tax on exports\

This fonn of the equation is useful when there are constraints on information and/or time. However the following assumptions underlie the equation:

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(1) Export demand and import supply are infinitely elastic.

(2) Marginal changes in expenditure on non-tradeables can be neglected.

(3) All income elasticities are unity.

If the assumptions are abandoned then ~ is given by / 1 /.

~ =

(2)

where Ej, j = m, xis the income elasticity

APCj, j = m, xis the average propensity to spend on the jth connnodity.

m, x refer to importables and exportables, respectively.

2.3 The Standard Conversion Factor (SCF)

2 .3 .1 The SCF is particularly useful in (a) the calculation of otner basic parameters where national values that are not project­ specific are needed and (b) the revaluation of non-traded goods for which specific conversion factors are not available. Equation (1) is used to estimate the SCF. Here the Mand X refer to total imports and exports. The SCF is the reciprocal of the shadow exchange ratio, which when multiplied by the market exchange rate, would give the shadow exchange rate (SIB).

i.e., SER = 0.1!.:R be.I:<'

where 01:!lt = 01'ficial exchange rate.

2.3.2 The SCJ:t' was calculated from the data available from 1966 - 1970. They are tabulated in Table 1. It should be noted that there were no major quantitative restrictions (QRs) during that period, nence these were not reflected in the tm tenn (the average import tari:r'f). It is assumed that post 1970 values for SCF would be smaller due to the advent of substantial QRs and an estimate of an average figure is given below. The average SCF for 1965-1970 was calculated as shown, using the data from Table 1.

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SCF = M + X M(1+tm) + (1-tx)

= 1754.8 + 1710.8 (17Sh,8)(1+0.1943)+(1710)(1-0.0207)

SCF = 0.9191

The conversion factor for foreign exchange= 1 0. 9191

SER= 1 .09 x OER = 1 ,09 x 714 = 7,78 Sh/$

1.09

This appears to be a reasonable estimate of the overvaluation of the official exchange rate over the period under consideration.

2.3.3 For post-1970 it is estimated by the country economist that the overvaluation is 30%. This yields

SCF = O. 77

and SER= 1 .3 x 7,14 = 9,28 Sh/$

2,4 The Conversion Factor for Consumption Goods ( ~ )

is calculated from the data presented in Table 2

663.5 (1+0.J.5) + 171,1 (1-0.m)

= 0.7835

f i for the post~1970 period is estimated to be 16.22% l1less than 0.7~35, Hence r = 0,656 .

663 .5 + 171 • 1

.1/ This figure is the percentage change of the SCF from the pre-1970 average to the post 1970 average. i.e. 0,9191 - 0,77 x 100 = 16.22%.

0 .9191

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The Conversion Factor for Capital Goods (fk)

t\= M + X M(1+tm) + X (1-tx)

Since Tanzania exports no capital goods X = o

1=-1 - P 1+tm

tm = 5% (an estimate obtained from the country economist)

~ - -1 +-~-- 0-5 2.6 The Conversion Factor for Intermediate Goods cP1)

h was calculated for the sake of completeness and in the faint hope that some project economist might need it sometime. Table 2 presents the relevant data.

rz,_ = .....,..,..,._......,.., _ _,,6 ...... 64,._ • ..,..8_+__,...1 5~3..,...9 -,;· 7,._.,..,--,-~~ \~i (664.8)(1+0.1313) + 1>39-7 (1-0.0218)

= 0.9762

For post-1970 (\ is estimated to be= 0.8179 Y 2.7

2. 7. 1

The Conversion Factors for Non-Tradeables (CFnt)

These conversion factors are given by

CFnt = value at social prices value at domestic prices

The non-tradeables that were considered were construction, electricity and water supply, and transportation.

y This post-1970 is assumed to be 16.22% less than 0,9~2. The assumption that the proportionate changes in Ac and are each equal to the proportionate change in the SCF cannot e rigorously defended. They should be considered to be reasonable first­ approximations only.

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2.7.2. Each non-traded good was broken dqwn into traded and non­ traded components by means of an input-output table .2/ Domestic indirect taxes/subsidies and depreciation were omitted. The former because they are transfers in the economy and do not constitute a real cost, the latter because they are accounting costs and not real costs to the economy. The breakdown of non-traded elements was not repeated because it was not considered necessary or practical. However, theoretically this process could be repeated several times into traded elementss labour and residual non-traded elements.

2.7.3 The traded elements were then valued at social prices by multiplying the domestic value by the relevant conversion factor. The latter was approximated by 1/1+tm where tm is the average import tariff.

2.7.4 The non-traded elements were converted to their respective social values by using the SCF. For wages and salaries a conversion factor of 0.8 was used as an approximation. For operating surplus the conversion factor for consumption goods was used.

2.7.5. The conversion factor was then obtained by taking the ratio of the value at border (social) prices and that at domestic prices.

a) Construction (CFc)

The data are tabulated in Table 3.

1012.6 "'0.8507 1190. 2

b) Electricity and Water Supply (CFp)

The data are in Table 4.

CFp = 92.6h 1131. 1

0.8190

JI This is strictly correct only in the presence of constant production costs. This will then ensure that the average costs implicit in input-output will be equal to the required marginal costs of production.

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It should be noted that construction is one of the non-traded elements in this calculation and the conversion factor Cl<cwas used to obtain its border value.

c) Transport (CFt)

The data are in Table S.

CFt = zs2.61 1003.2

= 0.7801

Both construction and electricity and water supply are non-tradeables in this section and CFc and CFp were used as their respective conversion factors.

2.7.6. It is clear that the process is an iterative one, and one may recalculate,CFc (construction) by using the calculated values of the conversion factors (CFc, CFp, CFt) instead of the SCF. This process may be repeated for each of the above non-traded good several times. Assuming that this iterative process converges (it has not been proved, nor has it been shown to do so in any study), then one may establish a tolerance limit and stop when

(k-1) (k) CFnt - CFnt ~ e

where e is a small number, say 10-4, and the superscript (k) refers to the kth step.

2.7.7 This iterative process was not performed due to time constraints. In all three cases the SCF used was 0.9191 and not 0.77 (post-1970 XF) as the input-output table used was that of 1970, the latest one available. It was not possible to break down transport into road and rail, electric power into peak and non-peak use and construction into two or more categories as the data was not available. It is also not clear whether this extra sophistication is worth the cost.

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III. The Marginal Product of Capital (q)

3.1 The marginal product as the return from a marginal in terms of foreign exchange. below.

of capital in the public sector is defined investment in the public sector expressed It may be evaluated from the equation

q = (k - mnl) SCF (3k

(4)

where k is the incremental output/capital ratio ran is the marginal ~roduct of all labour in the national economy.

1 is the incremental employment/capital ratio.

~ converts the marginal product of capital from domestic

rk currency terms to foreign currency.

Equation (4) is derived from a traditional two factor production function. Let the production function be given by

Y = f(K,L) K = capital, L == labour, Y = output

then dY dY dK+ iJY dL ';,K n 6Y dY ?)y dL D K dK t>L. dK

In terms of equation (id

q = 6Y, k = dY, mn = 6Y, 1 = dL ok dK oL dK

The estimation of q requires an estimation of, Illn, and 1 . National data is employed since such data does not exist for the public sector.

3.2 The Incremental Output/Capital Ratio (k)

The data obtained is shown in Table 6. Two incremental ratios were obtained, one with capital lagged by one year, and another, capital lagged by two years.

k = k =

0.293 0.353

1 year lag 2 year lag

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3.3 The Marginal Product of Labour (mn)

3.3.1 In the formal sector the real annual average wage was found to be 3680 Sh (1966) (see Table 7). In the informal sector the rea,l annual average wage over the same period (1966-71) was estimated k/ to be 1500 Sh (1966).

3.3.2 Employment in the informal sector over the same period was estimated to be a third of total employment.

3.3.3 An estimate of the marginal product of labour was approximated by the weighted average of the above figures. The method is highly questionable but a sophisticated technique was not attempted for the reasons that will become apparent at the end of this section (para.3.6)

Hence

3.4

mn = 1/3 x 1500 + 2/3 x 3680

2953 Sh

The Incremental Employment/Capital Ratio (1)

The data and calculation are presented in Table 8. Two ratios were again calculated, one with a one-year lag in capital and the other with a two-year lag.

1 = 8.57 x 10-6 : 1 year lag

1 = 10,05 x 10-6: 2 year lag

3.5 The marginal product of capital may now be calculated.

Case I (using 1 year lags)

k 0.293, 1 = 8,57 X 10-6

q = ( k - mnl ) SCF

0k = ffi • 29 3 '.'" 295 3 X 8 • 57 X 1 0-5' X 2.:.2..l2l.

0~ = 0.258

!!/ By the country economist

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Case II (using 2 year lags)

k = 0.353,] = 10.05 X 10-6

q = ffi.353 - 2953 X 10.05 X 10-§7 X 2..:.2l2l. 0.9523

0.311

3.6 Given these two values for q and making allowances for approximations and margins of error, a reasonable range for q might be

0.20 ~ q ~ 0.30

viz. the marginal product of capital is between 20% and 30% in Tanzania. This ia considered to be too high and the reason becomes apparent from the fact that equation (4) is based on a two-factor production function, rather than a general n- factor production function which would incorporate various classes of skilled and unskilled labour, human capital (disaggregated into managerial and technical skills), raw materials availability, land, etc. Clearly equation (4) overestimates the marginal product of capital. Also, the use of aggregate employment figures (Table 8) tends to overestimate the marginal productivity of capital. This is so because of the drama.tic fall of employment in estate agriculture in the middle-sixties due to the collapse of the international sisal market. Sisal was (and to a lesser extent still is) an important enclave type industry and chanees in employment in that industry should be included for the purpose of calculating q. Hence it was not considered practical to obtain a more accurate estimate of the marginal product of labour in para 3.3.

3.7 One alternative procedure would be to look at the rates of return obtained from past projects, where all prices for inputs and outputs in these projects are measured in terms of foreign exchange. The time constraint prevented such an analysis.

3.8 The estimate used is that obtained by Devplan/2/. This valu~ of q is hence 15.54% in domestic currency terms or 15% in foreign currency terms.

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IV. The Marginal Propensity to Reinvest (s)

4.1 The calculation of sis based on a macro approach. It is based on the assumption that both public and private investment have, on the average, the same impact on private consumption. Given this assumption, one may calculate the change in private consumption as a proportion of the change in NNP. (Depreciation is netted out of GNP as the use of sis directed towards project analysis and not for macroeconomic policy purposes). Tables 9 and 10 indicate the data and the calculations. The 8-year average value of s was found to be 0.376 whereas the last three-year average value was 0.317. CPP calculations indicate a value of 0.155, hence a value of 0.20 was chosen for further work.

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V. The Consumption Rate of Interest (CRI)

5 .1 The CRI is a discount rate with consumption as the numeraire and is defined as the rate of fall over time in the value of the marginal utility of consumption at the average level of consumption. (In theory one may define the CRI at any level of consumption.) It measures how much less valuable a unit of consumption received a year from now is than a unit received today [il. This depends upon the rate of pure time preference and the dimiQished marginal utility of an additional unit of consumption received in a year's time. At that time, the person's income will be higher due to the growth of per capita income and the marginal utility added by a unit of consumption will be less than that which would be added by the. same additional unit today. This, of course assumes that the elasticity 01 marginal utility is not zero. The CRI underlies the intertemporal weighting system, and its purpose in project selection, is to ensure that the government's preferences concerning future consumption (growth) and current consumption are adequately reflected in shadow prices.

5,2 The CRI is calculated according to the equation below

CRI "' i = ng + p ( 5) where

n = elasticity of marginal utility of consumption with respect to changes in per capita consumption. Intuitively the higher the value of n the more egalitarian the government objectives. Generally o -<. n ~ 2 • fJi.l

g = growth rate of average per capita consumption.

p = pure discount rate of time preference. Generally 0% < p !:: 3%. /Ji1

The parameter n is a subjective one and is based on perceived value judgments of the Tanzanian Government regarding the trade-off between intra-temporal and intertemporal consumption groups. Hence this parameter is a value judgment of the Government's set of value judgments. The value of n would be between 0.5 and 1 .5. The most realistic one is assumed to be 1 .25.

5.3 The value of the pure rate or time preference is also subjectively set. Two values were chosen, that of p = 1% and p = 2%.

5.4 Table 11 would be

I The growth rate of per capita consumption is determined from and is found to be equal to 3.13%. A suitable range for g 2.5% ~g ~3-5%.

Using n = 1 .25, p = 1% and g = 3.13% and equation (5). CRI = i = 1 .25 x 3.13 + 1 = 4,91%.

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5.5 Using different values of n and g, with p 1, we get the results shown in the Tabie below:

Table 12

Values of GRl

~ 0.5 1.5

2.5 2.25 4,'f5

3 .1 J 2.57 5.'(

3.5 2,7S 6.2.,

u~.1 . .ng p = 2~ alters each value by 1%. A range of the CRI may be taken as

2. 57% $ i ~ 5. 7%

The value considered to be most realistic is 4.91%.

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VI . The Distribution Summary Measure. D

6.1 The distribution summa ry measure is a global or national measure. It is not project-specific and is defined as the increase in total welfare generated when an increment in consumption is distributed among the population in the same way as is current aggregate consumption. It is calculated by using equation (6),[5].

D = o-n ( er -1 ) 1 -n n I o (n+u-1)

where n = the elasticity of marginal utility with respect to per capita consumption.

o= the distribution of consumption parameter (see below)

if n = 1 or o, then D = 1. if o- = o0 one would have a perfectly egalitarian distribution of consumption and as er tends to one, the distribution becomes increasingly inegalitarian. 0- may be derived from equation (7),

v = 1 + A (7) 2X

where A= the Gini Coefficient. Its value for Tanzania is taken to be 0.48. This is an approximate measure obtained from the DRC.

= 1 ,48 0.96

6.2 Using equation (6) and n = 1 .25

D = 1,541 ,25 (1,.25 + 1 ,54 -1 )(1 ,.54 -1 )0.2.5

1 • 1 09

6.3 For other values of n, we have Din Table 13.

TABLE 13

n D

0.5 0.877 \

1.25 1 .109

1.5 1 . 274

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VII. The Social Value of Public Income (v)

7.1 The value of public income is considered to be one of the most difficult variables to estimate. It is used for many different purposes such as education, defense, administration costs, investments, etc. Hence v may be interpreted as a weighted average of the values of different types of public expenditure, the weights beine the proportion of each in the marginal unit of expenditure. At the margin, a perfectly rational government would ensure that ·all·types of expenditures were equally valuable. Hence the assll!!!E,tion of perfect allocation of public resources would then be assumed f!:/ 7,2 The social value of public income may be considered to be the accounting (shadow) price of public income expressed in terms of the welfare value of a marginal increase in consumption at the average level of consumption. It may be viewed as the relative value of public savings (i.e., uncommitted government income) to consumption. If the national income distribution is considered to be inoptimal, then money in the hands of the government may be worth more than money in the hands of the private consumer. At the margin, this may be so either because public investment is more valuable than general consumption or because public money is better spent subsidizing people poorer than those at some (i.e., say average) level of consumption. In either case, if one then supposes that extra government revenue is worth v times extra money in the hands of the consumer at the average level of consumption, then v will be greater than unity. Hence v may be viewed as a weighting function.

7.3 This has implications for the treatment of indirect taxes in valuing social costs & benefits.§ Consider benefits first. Let

(C+T) be the private costs at market prices, wherP. C is the cost at producer prices and Tis the indirect tax component. Assume a project that lowers these costs by A(C+T). Then, the net social benefit of this change can be calculated as the weighted sum of its impact on the private sector and government. The following table shows the income changes and weights, with government income as the numeraire:

Income Change

Private Consumption:

Government:

Income Weight

1/v

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Therefore the Net Social Benefit (NSB)

= 1 .fl( C + T) -AT V

= .M. +llf ["2. - 2.7 V V

A9_ -AT [i - ! J .l/ V V

7.4 The NSB is equal to /1 C if and o~ly if v = 1. In that case one is indifferent to the distribution of marginal income between the private consumer and the government and then taxes may be ignored. If however v) 1, then the reduced tax revenue imposes a distributional cost on society. Hence if income distribution is in optimal ( v > 1 ) , ignoring the taxes would over-estimate the benefits.

7.5 In considering the treatment of taxes in valuing social costs one must be aware of the asymmetry between benefits and costs which will permit the ignoring of taxes on the cost side. While the benefits of a project accrue mainly to the non-government elements, the (construction) costs are borne entirely by the government. For this reason the exclusion of taxes from costs does give their correct social valuation. The tax component is merely a transfer from the right hand of the government to the left (i.e., say from Ministry A to Ministry B). Hence it will not affect the overall distribution of income. On the benefit side, the transfer was from the government to the private sector. This asymmetry is a cause of the private-benefit versus public­ nature of most projects, and omitting taxes from the benefit side would therefore over-estimate the true social rate of return, if income distribution were inoptimal. Hence it becomes essential to obtain an accurate value for v.

7,6 There are three approaches used to calculate the value of public income. The first one is the method suggested in the Revised Draft /87 and involves the use of critical consumption levels and the income".:specific distribution parameter. The second one involves an actual calculation of the rate of fall of public income !§7 and the third one involves an explicit evaluation of the value of public income /10/.

1/ One could use general consumption as the numeraire in which case the weight for private consumption would be 1 and for government, v. Then NSB = AC - (v-1) AT.

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7.7 Method I

7.7.1 Since public investment is a major component of marginal public expenditure, an attempt is made to estimate its value, which is then equated to the value of public income under the assumption of perfect allocation of resources. The equation below is considered to be the upper limit of v.

v = q - sq D i - sq ~

(8)

where q = the marginal product of capital.

s = the public sector's ITBrginal propensity to reinvest out of q.

i = the consumption rate of interest.

~=the conversion factor for consumption.

D distribution summary measure.

All the variables relate to the immediate future, i.e., 5 to 10 years from the date of appraisal. The numerator reflects that part of the marginal product that is consumed, weighted by the summary distribution factor. This is converted to border prices by~ and discounted to the present rate, which is the CRI minus the proportion of the marginal product saved /11/.

7.7.2 The use of equation (8) assumes

(1) that the government and the private sector save and reinvest some of the returns from public investment.

(2) all the aprameters remain unchanged over time. This will lead to an over-estimate of v because the divergence between q and i may decrease over time. Hence this value of v should1be treated as an upper bound.

(3) all public income is equally1valuable and that private savings are as valuable as public investment.

7.7.3 To offset the tendency to overestimate an attempt is made to estimate a minimum value by assuming no reinvestment i.e., s = o. Then equation (8) becomes

v = ~ D i ;;

(9)

- 20 -

7.7.4 This approach could still involve an overestimate of v if the constancy of q and i over time has a greater influence than the elimina­ tion of reinvestment.

7.7.5 In both equations the use of Dis justified by the assumption that the consumption benefits of the project are distributed in the same way as is aggregated consumption, so that public investment neither improves nor worsens the income distribution. If Dis close to one, this adjustment will not be too important. ·

7,7.6 The tables below (14 & 15) give the values of public income under different assumptions about the underlying parameters.

TABLE 14

Value of Public Income: Simple Case - The Lower Bound I

V = q a= 0.7835 ?i ~-

~ % 2 .57 4.91 5.7

0.15 7,45 3.89 3.36

0.20 9,9 5.54 4,47

0.258 12.78 6.69 5.76

0.311 15.43 8.09 6.95

TABLE 15 Value of Public Income: With Reinvestment. The Upper Bound

V = q - Sq 1 i - sq T (3, = o. 7835

s = 0.2

~ 2.57 4.91 5-7 %

0.15 * 8.021 5.674

0.20 * 22.52 12.0

0.258 -lr "h- 52.8

0.311 -l~ * -lr

* i ~ sq. Under this condition the value of v will be very large and in the limit tend to infinity. This is not a plausible result because it implies a zero value for consumption. It should be noted that the

- 21 -

values of v are not multiplied by the Swnmary distribution parameter. We will return to this later (see para. 7,7,14).

7,7,7 The Critical Consumption Level (CCL)

Having computed the range of values for v, its plausibility may be checked by relating it to estimates of the critical consumption level. This is defined as the level of consumption at which a unit of public income (measured in tenns of foreign exchange) is considered as valuable as a unit of private sector consumption (measured at domestic prices). Hence an estimate of v implies an estimate of the CCL and vice versa. If the CCL turns out to be equal to half the average consumption level, then the public income is as valuable as private consumption at that (critical) level of consumption. If the CCL is below some minimum consumption level, then it implies that the Government is indifferent between additions to its own income and additions to the consumption of those who are currently at that (critical) level. Under those circumstances that estimate of v should be eliminated because it is clearly an overestimate Lii/. The estimation of the CCL requires a knowledge of another parameter, the consumption distribution weight (d).

7.7.8 The Consumption Distribution Weight (d)

Unlike the national distribution parameter D, the consumption (income-specific) distribution parameter d, is used to weight project benefits and costs when the recipient or payer can be identified. Hence this parameter is project-specific. If one has knowledge of the income distribution a different d can be calculated for each of the ith income groups that can be identified,til7.

7,7.9 The basic assumption underlying the derivation of distribution weights is a specific utility function with diminishing marginal utility of consumption, for n greater than zero and a constant marginal utility of consumption, for n equal to zero. The higher then the higher the weight.

7.7.10 The utility function used is

U(c) = 1 1-n for n ~ 1 ,;: 1 - n

and (10)

U(c) = log C for n = 1 e

For marginal changes in consumption d may be calculated as

d = ( C )n (~)

(11)

Where c is the average per capita consumption level.

- 22 -

For non-marginal discrete changes, as will often be the case, d may be calculated from

d = U(c2) - U(c1)

(c2 - c1) en when consumption increases from an initial (pre-project) level of cl to a final (post-project) one of c2·

(12)

/U(c1) i = 1,27 is the utility level, at consumption Ci, which may be computed from-equation (10).

For n I 1 this reduces to

d = xn (1-yl-n) (1 - n)(l - y)

and for n = 1

-1 d = loge y

_L(l - y) X

(13)

(14)

where X: c/c2 and Y = Cl/c2.

Tables are available for some values of n'in the references cited at the end. But it may be necessary to compute a value ford at a particular level of n.

7.7.11 The CCL Revisited

The CCL (c*) is obtained from equation (11) which is reproduced below.

d· [+T . * _ 1/n i.e., c = c/d

(11)

(15)

c is obtained from Table 10, i.e., c 675. This is the average value of consumption.

The definition of CCL requires that d = vf. LW•

- 23 -

Two values of v will be chosen,

Case I: with reinvestment: v = 8.021

Case II: the simple case: v = 3.89

Case I represents the upper limit of v and Case II the lower limit. The implied value of n in each case is 1.25 (see Tables 14, 15).

Case I. V = 8.021, n = 1.25

d = 8.021 X 0.7835 = 6.284

* C = 155.17

Case II. v = s.89, n = 1.25

d = 3.89 X 0.7835 = 3.048

c~- • 276.64

7.7.12 In the first case the estimate of v implies that the Government is indifferent between additions to its own income and additions to consumption of those who are cuITently enjoying slightly less than one-fourth ( ,:;,r, 155.17/675) of the average consumption level. For Case II the indifference is with those enjoying just over two-fifths ( ~ 276.64/675) of the average consumption level. However, since information on the distribution of consumption was not available it was difficult to state which case (if either) was closer to the "true" situation.

The Value of Public Income Revisited

An acceptable value of v may be chosen after a careful assess­ ment of relevant government policies. Since the objective is to derive a set of d's (which are project-specific) and a value for v (which is a national parameter) which will provide the correct signals for the selection of projects an iterative cross-checking procedure should be performed for the projects .6JJ.7. · 7.7.14 For illustrative purposes the values of v chosen are 3.89 and 8.021. Since the distribution factor D was omitted earlier:

v1 = J.89 x D ~ 3.89 x 1.109 = 4.31

Vu= 8.021 X 1.109 = 8.89

i.e., 4,31 ~v ~ 8.89

i.e., the premium on public income ranges between 331% and 789%. The latter does appear to be rather high.

- 24 -

7,8 Method II

7.b.l An alternative method has been suggested ["9J which yields the value of the percentage rate of change _of public income. This is given

by i = q/q - pl~ - CRI/CRI V

where xis the percentage change in x X

and q/q = k - lllnl

k - 11\-il

7.8.2 The percentage change in the marginal product of capital (q/q) is calculated in Table 16 and is founn to be -1.08%. The percentage change in the CRI is shown in Table 17 and is equal to -11.5%. However, this figure is based on the assumption that n and pare constant over time. This need not be the case and for Tanzania the figure chosen was -9.0%. The percentage change in the conversion factor for consumption is -2.7% (= -16.22/6).

7 .8 -3 Hence

V = -1.082 + 2.7 + 9,0 = 10.62% V

This is thought to be a rather high figure and could be due to the fact that there were wide fluctuations from year to year in the values of q/q and CltI/CRI (see Tables 16 and 17), Therefore, any value, including an average value, cannot be too meaningful. This method may be more effective fo;r countries that have "smoother" changes in these parameters.

7,9 ~thod III

7. 9 A third method f_IQl yields an est :imate ( an "exact-approximation") of v without the use of the critical consumption level or the income-specific distribution weight. The value of vis given by

v = (~- s ) q t - exp L:(i-sq)j}7+ (1- s ) q exp f_:(i-sq)!/ (17) ( J. - sq) (s J (1 +i-sq) 7f

where t is the time that it will take for the value of v to reach its11optimal" level. Using s = 0.2, q = 0.15, 0 = 0.656, i = 0,0491 and t = 20

V = J.045 + 0.122

Le., V = 3.167

It is felt that this method best reflects the "true" value of v.

- 25 -

VIII. The Accounting Rate of Interest (ARI)

8.1 The accounting rate of interest arid the conswnption rate of interest are both discount rates. The choice of the discount rate depends on the numeraire in which benefits and costs are expressed. The choice of the numeraire does not make any difference, so long as one is consistent. The numeraire used !J.r£7 is 11the present value of uncommitted government income measured in foreign exchange." Foreign exchange prices (border prices) are used rather than domestic prices because foreign aid and loans account for a large part of new fixed public investment.

8.2 Under these circumstances, the appropriate discount rate is the rate of fall over time in the value of uncommitted public income measured in terns of foreign exchange, and is referred to as the accounting rate of interest. This makes the ARI directly comparabie with interest on loans payable in foreign currency or with lending abroad. Since consumption is not neutral, the CRI was not used as the discount rate. In addition the use of consumption as a nwneraire would have necessitated its specification in terns of some average ( e . g • as the CRI does) or some particular group of individuals.

8.3 The purpose of a discount rate, in this case the ARI, is to allocate public investment funds among competing uses in a socially desirable __ w~y. If the ARI is too high, few projects will pass the test of having a positive net present value (NPV); if too low, several projects will have a positive NPV. Hence the ARI may be regarded as a social rate of return on the marginal project in the public sector.

8.4

8.4.1

Method I

One method of estimating the ARI is with the equation below iI£7 ARI = sq + (1-s) q/v~ • (18)

All the parameters have been previously defined. Two values for the ARI are calculated for the following values of the parameters:

Case I:

q = 0.15, s = 0.2, 0 = 0.7835

V = 4.Jl (= 3.89 X D)

ARI = 0 • 2 X O .15 + 0. 8 X O • lg - . 4,31 X 0.7 35

= 0.0?6

= 6.6%

- 26 -

Case II: V = 8.89 (= 8.021 X D)

ARI = 0.2 X 0.1_5 +

= 0.047

=~

0.8 X 0.1~ 8.89 X 0.7 35

8.4.2 It is possible to test further for different values of s, and q. The following points should be noted; the ARI increases if:

(i) s decreases (i.e.,

often holds)

(ii) v decreases (i.e.,

(iii) q increases (i.e.,

d ARI <. o if vr > 1. This condition oS

d ARI ?) V

oARI

4. 0)

-;:, o) ~q

Hence if one feels that the ARI is too low or too high one may make the appropriate adjustment in the relevant parameters.

8.4.J In this case the ARI of 6.6% is felt to be on the low side for Tanzania. This is due to the high value of v, which as stated earlier is a very difficult parameter to estimate.

8.5 Method II

Another method for the calculation of the ARI is shown below /YJJ. ARI= CRI + v

V

Since;= 10.62%5./ V

(19)

Hence

ARI= 4.91 + 10.62

15.53%

2/ See para. 7.8.3 for a criticism of this high value. This value of y leads to the high value of the ARI.

V

- 27 -

8.6 Method III

8.6.1 A third method is based on Method III for the calculation of v (para. 7.6) !J.Q].

ARI = sq + ( 1 - s) q/v ~ ( 18)

using s = 0.2, q = 0,15, v = 3.167 x 1.109 3.12.

~ ~ o.656

ARI= 0.03 + 0.051

"'0.081

8.6.2 Without incorporating the summary distribution measure (D) the value of ARI= 8.78%. This value of the ARI is considered to be the most reasonable one for Tanzania.

IX. The Shadow Wage Rate for Rural Workers (SWR)

9.1 The SWR is project-specific LIJJ and is given by:

SWR = l_;t..m + r (w - m) - (w - m) siJ V

where

w = market wage rate

(20)

m = foregone marginal product of labour at domestic prices

ii...= conversion factor form valued as output ( = r' if unknown)

conversion factor form viewed as consumption goods bought with the income represented by m

d = income-specific distribution weight applied to an increase in wages

v ~ social price of public income

o(m is the domestic market value of the marginal product of labour (m) which is lost by employing labour in a project. It is valued at border prices by multiplying by the conversion factor (p(.) the value of the marginal product. This is its direct opportunity cost.

- 28 -

p (w - m) is the difference between the project wage rate (w) and the foregone marginal product (m) multiplied by r to convert to border prices. (w - m) d/v is included because additional consumption is not only a cost (in terms of foreign exchange lost to the government) but also a benefit. So this additional consumption has to be valued at border prices and weighted by the income distribution parameter (d) and converted to its value in terms of public income by dividing by v.

The SWR may be divided by w to give the conversion factor for labour.

9,2 A calculation is presented below only to serve as an example and does not refer to any specific project. This calculation would have to be performed for every specific project.

The average consumption level is denoted by c and is equal to 675 sh.

o<m = 0.45 (from the Devplan Study) L-2.J w

Let m = 175 w = 340

,<:.ill = 0,45 340

,/.._ = 0,45 X J40 0.874 17.5

Let d = 2.65, V = 3,167

SWR = 0.874 X 175 + 0,7835 (340 - 175) Ll - h65 __ J . J.lb7

= 1s2.95 + 129.2s co.17)

174,93

Conversion factor: SWR = ~ = ~ w 340

9.3 The conversion factor, ignoring all income distribution effects is given by:

~=Jm=.QdQ w w

- 29 -

X. Conclusions

10.1 Data Constraints

Data and time constraints were felt to be the most severe. In particular, most recent data do not tend.to be available, subsequently estimations of some conversion factors or shadow prices may refer to a period which may not be representative of one during which project appraisal is being undertaken. Further it should be noted that ill, shadow prices are averages, because they are based on parameters which are themselves averaged over a number of years. Hence a pre-1970 average need not be equal to the post-1970 average. Therefore, unless a project economist feels that the values presented hold for the period under con­ sideration, he will have to make an intelligent guestimate of the change. Using the basic equations,as presented,may be of some help under those circumstances.

10.2 The Use of Distribution Weights

10.2.l The use of distribution weights (di) in project evaluation is to ensure a more equitable distribution of income. However, since the Government of Tanzania is committed to balanced regional growth and it ensures this growth through locational policy, this makes the use of weights redundant. In other words, if the Government feels that the south-west region of Tanzania is economically depressed and wishes to achieve a more equitable distribution of income, it would make a deci­ sion that would ensure that project A would be located in that (south­ west) region so that it may benefit the people of that area. Such an action (referred to as locational policy above) negates the use of distribution weights in project evaluation, since the income distribution aspect of the project has been determined through its location. Hence the recommended values of the shadow prices given in the introduction bl are those which do not take the income distribution aspect into account.­ The main bpdy of thetext, however, does use them.

10.2.2 A justification for the use of these weights is that the government is fiscally constrained and is therefore unable to redistribute income. These constraints may be due to the fact that the administrative costs are too high and the political power wielded by the rich is too great. Whatever the cause, fiscal constraints exist. Now, say a financial analysis indicates that the (financial) rate of return is unacceptable, i.e., it is negative. A decision

£1 A case however may be made for the use of distribution weights if the government wishes to redistribute income within the region determined by the locational policy.

- 30 -

to implement that project would imply that it be subsidized, either at a constant rate (if the divergence between market and accounting prices remains constant), or at a declining rate (if this divergence diminishes). But assume that using distribution weights, a project is "acceptable", i.e., the (internal) economic rate of return is greater than (or equal to) the accounting rate of interest. If the economic analysis reached this conclusion by assuming that the government~ capable of subsidizing the project, then that situation presents an internal contradiction, because the use of distribution weights was justified on the assumption that the government was fiscally constrained. It is unlikely that this constraint is asymm etric, i.e., the government is able to disburse funds even though it could not tax the public effectively.II This asymm etry could be possible if the government had an outside source of funds, e.g., another country or a development bank. But in that case income redistribution would be more effectively brought about (i.e., at zero welfare costs) by using those same funds to effectuate a lump-sum transfer to the poor, rather than by the indirect route through the project. However, the indirect route might be justified under two conditions: (1) for political reasons the govern­ ment cannot make this transfer; (2) the project-subsidy element is very small compared to the subsidy required for the desired income redistribution.

10.3 The Choice of the Utility Function

10.3.1 The value of the income-specific distribution parameter (d) and that of the elasticity of the marginal utility of consumption, with respect to per capita consumption (n), are both dependent upon the particular form of the utility function (see para. T:f: 10). Considering d, first, the value of d being dependent upon the form of the utility function implies that different values of d may be obtained for every different form of the utility function. This in turn implies that every benefit or cost (e.g., the SWR , para. 9.1) that depended on d, would be dependent upon the choice of the utility function. Since there is no a priori reason for the function chosen, those who believe that the utility function is perhaps a different (more complicated?) function of consumption would come up with a different set of weights and hence different shadow prices. Under such a situation, it is not possible to choose one set in preference to another. The same statement may be made ~bout n, because it is (arbitrarily) chosen, its value (of 1.25 in Tanzania) is only meaningful when one assumes that particular form of the utility function given (see para. 7.7.10). Altering the fora of the utility function would alter the value of this elasticity) and all shadow priQes that depend on it (e.g., CRI, v, ARI ) •

]j The government may choose to restrain expenditure in some direction in order to subsidize the project, but thi's would then violate the assumption made in the calculation of v, viz. that the government is a rational one which ensures that at the margin, additional expenditure has the same value in all uses [:6J.

- 31 -

10.3.2 The above paragraph highlights the subjec~ive nature of d and n which derive from the subjective nature of the utility function. To determine the choice of a utility function on the basis of simplicity or ease of mathematical manipulation would suffice in a theoretical framework, which elucidates a possible methodology. To justify its use, in empirical work, on the basis of the~ criteria, appears to be rather tenuous at best, and could well provide all the wrong signals for project selection at worst.

10.3.3 It is also questionable that governments of various developing countries, should have the same utility function, the only difference being in the value of n, which is a subjective estimation of the govern­ ments' desire for income redistribution. If that subjective estimation is the same, then the utility function is identical. The only common bond between LDCs is the fact that they~ LDCs. In several other characteristics such as size, population, growth rates, etc., they may be different. Hence the use of "universal" social welfare function for all LDCs does not appear to be justified.

10.3.4 From the preceding paragraphs, the crux of the problem is the choice of the utility function. A possible suggestion would be the formulation of a utility function of the Von Neuman-Morgenstern (VNM) type for each country. This would be a major project, difficult to imple­ ment and its success would depend largely on the formulation of the proper questions, and on the accuracy of the responses from various government officials. Assumin g that the formulation of a "perfect" VNM function is impossible, an "imperfect" one would still be a better first-approximation to the 't.rue"function than one chosen arbitrarily.

10.3.5 The elasticity of marginal utility with respect to changes in per capita consumption and the income-specific distribution weights may then be calculated.

10,4 The Pure Rate of Time Preference

10,4.1 The arbitrary choice of the pure rate of time preference (p) needs to be mentioned. Its effect on the CRI (and subsequently on v, and the ARI) is not significant if pis assumed to vary within a narrow band , of approximately 1 percentage point from the chosen value. However, variations of p from 4 to 5 percentage points (i.e., 1% ~ p ~ 5%) could cause significant changes in the value of CRI.

10,4,2 In the. ca'se of Tanzania p was chosen to be 1%. If, however, the "true" p were closer to 5% then for n = 1.25,the value of CRI would change from 4.91% to 8.91% with subsequent repercussions in later calculations.

Annex

List of Tables Referred to in The Main Text

Table 1:

Table 2:

Table 3:

Table 4:

Table 5:

Table 6:

Table 7:

Table 8:

Table 9:

Table 10:

Table 11:

Table 12:

Table 13:

Table 14:

Table 15:

Table 16:

Table 17:

Total Exports and Imports

Imports and Exports of Consumption Goods, Intermediate Goods and. Capital Goods

Calculation of the Conversion Factor for Construction

Calculation of the Conversion Factor for Electricity and Water Supply

Calculation of the Conversion Factor for Transportation

Calculation of the Incremental Output/Capital Ratio (k)

Country-Wide Real Average Wage

Calculation of the Incremental Employment/Capital Ratio (1)

Current and Real Values of GNP, NNP, Pnivate Consumption, Total Consumption and Savings

Calculation of MPS (s)

Growth Rate of Per Capita Consumption (g)

Values of CRI (in the main text)

Values of D (in the main text)

Value of Public Income: Simple Case--The Lower Bound (in the main text)

Value of Public Income: With Reinvestment--The Upper Bound (in the main text)

Calculation of the Percentage Change in the Marginal Product of Capital

Calculation of the Percentage Change in the CRI

- 1 - !ABIE 1

Total Exports & Imports U (Data for the Calculation of the standard Conversion Factor - SCF)

1965 1966 1967 1968 1969 1970 Average - -- - Total J.h88 1766 1728 1676 1771 1836 1710.8 Exports Y

(Sh x 106)

Total 1h05 1691 1625 1834 1710 2264 1754.8 Imports l/

6 (Sh X 10 )

Export 29.J 12.3 37.9 33.5 53.0 47 .4 Duties!±/ 6 (Sh x 10 )

Import 245-3 259.7 296.6 355.3 530.2 343.9 Duties l±/ Average Export Duty% 1.95 .69 2.19 1.99 2.99 2.58 2.07

- Average

19.43 Import 17 .45 . 15 .35 18.25 19.J7 31.0 15.18 Tariff ( %)

11 From IBRD "The Economic Development and prospects of Tanzania 11 (EDP). Volume I.

V EDP, Volume II, Table 15

ll EDP, Volume II, Table 18

l±/ EDP, Volume II, Table 20

- 2 - TABLE 2

Imports and Exports of Consumption Goods, Intermediate Goods and Capital Goods

1965 1966 1967 1968 1969 1970 Average Average l/

Duty/Tariff

Exports lJ Consumption Goods (Sh x 106) J..48.8 176.6 172.8 167.6 177.1 183.6 171.1 1%

Imports of Consumption Goods Y (Sh x 106) 548 Boo 578 731 642 682 663.5 35%

Exports of Intermediate Goods k/ (Sh X 106) 1339.2 1589.4 1555.2 1508.4 1593.9 1652.4 1539.7 2.18%

Imports of Intermediate Goods Y 4€:4 567 662 682 695 919 664.8 13.13%

Imports of Capital Goods Y 393 324 385 421 373 673 428.2 5%

y 10% of total exports

g/ Economic Survey Table 9 and the country economist for 1965.

lf · From the country economist.

k/ 90% of total exports

- 3 -

TABLE 3

Calculation of the Conversion Factor for Construction

Domestic/ Conversio~/ Border Value 1. Factor - Value

Sh. mill

Other Crops 50.7 0.7]1 36.2 Forestry & Hunting 61.5 0.9191 56.52 Other Mining 21.7 0.909 19.73 Textiles o.8 0.769 0.62 Sa~lling & Carpentr~ 30.9 0.769 23.76 Printing & Paper 3.8 0.833 3.17 Chemicals & Petroleum 0.7 0.769 0.54 Metallic & Non-Metallic Products 78.1 0.909 71.0 Auto Assembly & Repairs 9.7 0.833 8.08 Other Manufacturing 11.1 0.833 9.25 Electricity & Water Supply 4.6 0.9191 4.23 Construction 0.3 0.9191 0.28 Connnerce 155 .9 0.9191 ili 3.23 Hotels & Restaurant 5.7 0.9191 5.24 Transport 91.8 0.9191 84-37 Communications 3.5 0.9191 3.22 Banking & Insurance 4.8 0.9191 4.41 Business Services 5.4 0.9191 4.96 Health 0.4 0.9191 0.37 Other Services o.6 0.9191 0.55 Imports 246.3 0.9191 226.37 Custom Duties 17.2 0 0 Wages & Salaries 316.1 o.8olf 252.8 Operating Surplus 68.6 o.783sW 53.7

Total 1190.2 1012.6

Conversion Factor 0.8507

V From Input/Output Tables for Tanzania 1970 g/ Conversion Factor for Tradeables = 1/1 + tm where tm is the average

import tariff from "EA Customs & Excise Tariff". For non-tradeables SCF is used.

'JI This is an approximation.

k/ This is equal to ~ •

- 4 -

TABLE 4

Calculation of the Conversion Factor for Electricity and Water Supply

Domestic11 Value - (Sh mill)

Conversi~? Factor -

Border Value

Printing & Paper Chemicals & Petroleum Auto Assembly & Repair Other Manufacturing Electricity & Water Supply Construction Commerce Transport Communications Banking & Insurance Business Services Education Imports Custom Duties Wages & Salaries Operating Surplus

Total

Conversion Factor

0.4 8.o 3.0 3.6 0.3 4.0 4.5 4.0 0.5 0.3 1.2 1.1

11.5 0.2

30.7 39.8

113.1

0.8190

0.833 0.769 0.833 0.833 0.9191 o.8567 0.9191 0.9191 0.9191 0.9191 0.9191 0.9191 0.9191

0 . 0.80 0.7835

0.33 6.15 2.50 3.0 0.28 3.4 4.14 3.68 o.46 0.28 1.10 1.01

10.57 0

24-56 31.18

92.64

Y From Input/Output Tables, Tanzania 1970. Y Conversion Factor for Tradeables = 1/1 + tm where

tm = average import tariff. For non-tradeable SCF1is used. For construction, the value obtained in Table 3 was used. It affected the trial conversion factor in the 3rd decimal place only. The value to two significant deqimal places is unaffected.

\

TABLE 5

Calculation of the Conversion Factor for Transport

Domestic Valuel/ Conversion Factor Border Value (Sh. mill)

Textiles 0.5 0.769 0.39 Sawmilling & Carpentry 0.4 0.769 0.31 Printing & Paper 2.6 0.833 2.17 Chemicals & Petroleum 13.7 0.769 10.54 Metallic & Non-Metallic Products 4.0 0.909 0.36 Railway Workshop 19.2 0.833 15.99 Auto Assembly & Repair 33.2 0.833 27.66 other Manufacturing 3.7 0.833 3.08 Electricity & Water Supply 4.2 0.8189 3.44 Construction 15.3 0.8507 13.02 Commerce 34.3 0.9191 31.53 Hotels & Restaurant 1.8 0.9191 1.65 Transport 45.3 0.9191 41.64 Connnunications 3.4 0.9191 3.12 Banking & Insurance 11.8 0.9191 10.84 Business Services 3.0 0.9191 2.76 Health 0.1 0.9191 0.09 other Services 0.4 0.9191 0.37 Imports 19.55 0.9191 179.68 CUstoms Duties 64.6 0 0 Wages & Salaries 365.0 0.80 292.0 Operating Surplus 181.2 0.7835 141.97

Total 1003.2 782.61

Conversion Factor 0.7801

1/ From Input-Output Tables of Tanzania 1970.

Y For tradeables 1/l+ tm was used where tm = average import tariff. For non-tradeables SCF was used. For electricity and water supply and construction, the values obtained in previous tables were used.

- 6 -

TABLE 6

Calculation of the Incremental output/Capital Ratio (k)

Real Real Capital 6. 60Utput L\.OUteut output l/ Formation V output CaJ2• For. Cap. For.

t-1 t-2

1964 5619 807 154 0.19

1965 5773 935 741 0.782 0.918

1966 6511 1092 263 0.24 0.281

1967 6777 1252 351 0.28 0.321

1968 7128 1352 131 0.096 0.104

1969 7259 1216 421 0.346 0.311

1970 7680 1821 325 0.178 0.267

1971 8005· 2168 498 0.229 0.273

1972 8503 1835

Average 0.293 0.353

V

Real GDP at factor cost in 1966 TSh from the National Accounts of Tanzania, 1964-1972. Table 1.

Real Gross Capital Formation in 1966 TSh. This is taken to define investment which is the change in capital stock. From the National Accountsof Tanzania, 1964-1972. Table 3.

- 7 -

TABLE 7

Country-Wide Real Avera~e Wage

Average Wage 1/ Real Average Wa~e Sh. 1966 ShJj

1966 3487 3487

1967 3599 3621 .45

1968 3738 3710.17

1969 3763 3661.93

1970 3994 3734.12

1971 4195 3796.72

Average 3680.45

Y Economic Survey 1971/72, Table 36 - Averaged over workers.

Y GDP Price Deflector used. See Table 9

- 8 -

TABLE 8

Calculation of the Incremental .Employment/Capital Ratio (1)

Real Total Wage21

/l Total Ll Employment LI Employment Capital 1/ Employment::. Wage Cap. Fgr• Cap. Fgr·

Formation (Thousands) Employment xlO- t-l x10- t-2

1965 935

1966 1092 336 11000 10.07 11.76

1967 1252 347 5000 3.99 4.58

1968 1352 352 16000 11.83 12.78

1969 1216 368 8000 6.58 5.92

1970 1821 376 16000 8.79 13.16

1971 2168 392 22000 10.15 12.06

1972 1835 414

Average 10.05

];/ Real Gross Capital Formation in 1966 TSH mill from Table 6.

'ij Figures for 197i and 1972 from the Economic Survey 1972-J. Table 28.

,:;_.:;

- 9 - TABLE 9

Current and Real Va Lue s of c;-;p, XNP, Private Cmsumption, Total Consumption and Sav i r.g s Si1 1i 11

GDP Price l/ GNP atl/ Real c:,p Private 1/ RE:a~ Private fetal 2/ Real ,.'ot2l- 1/ Real ~'"NP at Re a I :S.'NP Year Index ti96-6=100)- MKT. l: at MKT. P "Con sumo t i on " Corisur-o ~ ior. C)n,:rnotion- Coris u-no t i.on Savings Savini;;s XKT. P a t 1-'c,a. p

lS1:4 99.55 5954 5980.9 4353 4352. 72 4951 4973.4 6S5 693.14 505'S sc::.z :scs 98.23 6C66 6175.3 4452 4533.3 51.00 519:i.. 9 '5% ~·05. 7 4 57.!i.4 ':'"< IQ, .)v~u

i 9•j6 100.0 6905 6905 5288 5288 6013 6013 691 691.0 6560 6540

1967 99.38 7249 7294.2 5225 5257.6 5028 6055.6 379 884.48 6837 6880

196B 100.7_5 7841 7782. 6 5674 5631.76 6558 6509.2 790 78~.12 7383 7333

1969 102. 76 8232 8010.9 5829 5S72.44 6824 6.\i4C. 7 878 854. !,.l 7763 7554 ~ 197C 106.96 9148 8552.7 6396 5979.81 7604 7 i09. 2 1215 1135. 94 8636 8074

1971 110. 49 9749 8823.4 6742 6101. 91 8107 7337.3 1153 1043.53 9139 8317

19, z· 118. 02 11034 9349.3 7785 6597.19 9173 7772.!+ 1270 1076.S9 10426 83 3 ~~

1/ ?r0:c :·a::ional Accoun t s of Tanzania, 1964-1972, Summa r y Table 1.

'l_/ Fr om :,c:tional Accounts of Tanzania. Table 1.

·:,\!'l·\l

- 10-

TABLE 10 Calculation of MPS (s)

6. AREAL REAJ,1/ PRIV.1/

~RIV. CONS NNP CONS (Sh. mill) (Sh. mill) 6NNP

1964 166 155.6 0.937

1965 692 750 1.084

1966 340 -30.4 -0.089

1Y67 453 374,2 0.826

1968 221 40.68 0.184

1969 520 307.37 0.591

1970 243 1 21 .5 0.5

1971 517 495.3 0.958

1972

Average 0.624 mps ~ 0.376 ( 164 - '72)

Average . 0.683 mps = 0.317 (l70 - t 72)

11 From Table 9.

. - 11 - TABLE 11

Growth Rate of Per Capita Consumption (g) (Data For the Calculation of the CRI)

1964 1965 1966 _ 1967_ ~- 1968 ~-1969 --~.1970 1971 _ 1972

Private Trial Consumption Expendi~ure Sh x 10 !/ 4363 4458 5288 5225 5674 5829 6396 6742 7786

Government Final Consumption Expendi59:7-

.588 e+2 725 803 884 995 1208 1365 1387 Sh X 10 - -

Total Congumption 4951 5100 6013 6028 6558 6824 7604 8107 5:73 Sh x 10

Population/ 11.06 11.34 11.62 12.56 13.25 13.60 (x 10 ) f. 11.91 12.23 12 .91

Per Capita Consumption 447.65 449. 74 517 .47 5o6.13 536.22 543 .31 589.0 611.85 674-49

GDP Price Index (1966 = 100) .Y 99.55 98.23 100.00 99.38 100. 75 · 102.76 106.96 110.49 118.02 -

Real Per Capita Consumption (1966 T. Sh) 449.67 457.84 517.47 509.29 532.23 528.72 550.67 553.76 571.5

Change in Real Per Capita Consumption

. (1966 T. Sh) 8.17 59.63 -8.18 22.94 -3.51 21.95 3.09 17.74

Growth in Real Per Capita Consumption (%) 1.81 13.02 -1.58 4.5 -o.65 4.15 o.56 3.2 3.13

(Average)

17 National-Acccunts of Tanzania 1964-1972: Table 1 2/ National Accounts of Tanzania 1964-1972: Summary Table I, Economic Survey 1971-72, Table 36 II Thi.s is t.he GDF price index. Calculated from the Summary Table I.

- 12 -

TABLE 16

Calculation of the Percentage Change in the Marginal Product of Capital

LiOutput Li:&npl't t.Capy-1 1/ ti.Cap!gl

x 10- (1)V (k -

1967 0.24 10.07

1968 0.28 3.99

1969 0.096 11.83

1970 0.346 6.58

1971 0.178 8.79

1972 0.229 10.15

l'.\.(k - ml)

0.21 0.06

0.27 -0.209

0.061 0.266

0-327 -0.174

0.153 0.046

0.199

0.2033 -0.0022

% Change in the marginal product of capital= -0.0022 x 100 0.2033

= -1.082%

1./ From Table 6

g/ From Table 8

2/ m = 2953 Sh.

- 13 - TABLE 17

Calculation of the Percentage Change in the CRI

Ee~G~~:~a~~~s~p!f~~ !/ mil ~CIU (g)

1968 4-5 6.63 -8.W+

-0.65 -1.81 8.o

1969

4.15 6.19 -4-49

1970

o.56 1.7 3.30

1971

3.2 5.0 1972

Average 3.542 -0.408

% change in CRI -0.40 8 X 100 3 .542

= -11.52% ·

y From Table 10

y CRI = ng + p "Where n = 1.25 & p = 1

References

In .:i.11 tho rflferences below 11::AP11 refer:: to the "Econom i.c A.nalyr:i:._; of Pro ject.s " by J. Linn, L • .Squire, II. v.ui der T:1k. Juno 1"111.

1. EAP. Appendix III. para. 19,

2. "Project Appraisal for the Long-Term Industrial Strategy" by M. Roemer and D. Williams. January 1973.

3. EAP. Appendix II. para. 15.

4. EAP. Annex. para. 22.

5. EAP. Annex. para. 21.

6. EAP. Annex. para. ~2.

7. "A Comparison of the IBRD and Little-Mirrlees Apprvri s a L of a Highw.::;r Project in Malaysia" by s. Anand, March 1973.

8. EAP. Appendix II. paras. 9-lJ.

9. "Economic Analysis of Pro,iects: The Estimation of the Accounting Rate of Interest." A Memo to L. Squire from A. M. Choks i.. October JO~ +97L •.

10. "Ec.onomic Analysis of Projects: The Estimation of the Accounting Rate of Interest II." A Memo to L. Squire from A. M. Choksi. November 7, 1974.

11. EAP. Appendix II. para. 10.

l" EAP. Appendix n. para. 12. ;:_ •

13. EAP. Annex. para. 16.

14. EAP. Appendix II, para. 13.

15. EAP. para. 30.

16. EAP. Appendix II. para. 23.

17. EAP. Annex. para. 44.