ABBREVIATIONS, ACRONYMS AND SYMBOLS USED

a:

the lower-range or minimum value of a random variable

A:

an annual payment amount which, continued over n years, constitutes an annuity with a terminal value A_n = A[(1+i)ⁿ-1]/i or which amortizes a PV where A = PV[i(1+i)ⁿ]/[(1+i)ⁿ-1]

A_n

a future amount to be received or paid in n years' time; it is equivalent to an annuity over n years of A = A_ni/[(1+i)ⁿ-1] and has a PV of A_n/(1+i)ⁿ

AB:

allocation budgeting

ac:

acre(s)

ac ft:

acre feet (of irrigation water)

AME:

adult male equivalent, a standardized unit of labour measurement

APP:

average physical product, equal to Y/X for Y = f(X)

AU:

animal unit, a standardized unit for aggregation or comparison of different types of animals

AVP:

average value product, equal to (APP)p_y

b:

the upper-range or maximum value of a random variable

B:

the resource pool available to the farmer or, in LP, the level of resource constraints or activities constituting the farm 'plan' at each iteration

B:

size of the available cash budget

B/C:

ratio of benefits to costs

B-1:

in AB and SP, the initial set of resource constraints

B-i:

in AB and SP, the balance of resource constraints after sequential introduction of the i-th activity into the plan, i = 1,2,...

C:

depending on context, cost or the coconut-to-copra conversion rate

CDF:

cumulative distribution function

CE:

a decision maker's certainty equivalent for a risky prospect

cm:

centimetre(s)

COP:

cost of production, calculated per unit of output as total cost divided by quantity of output, i.e., TC/Y

CV:

coefficient of variation, calculated as 100 to express the standard deviation of a variable as a percentage of its mean

CY:

crop-cycle year of a perennial crop

d:

the constant annual rate of depreciation under the declining-balance method

D:

the annual depreciation cost as measured by the straight-line method

D_t:

the annual depreciation cost in year t as measured by the declining-balance or sum-of-integers methods

DC:

direct cost of an enterprise (or activity), calculated as the sum of its VC plus its share of farm FC

DI:

Simpson's diversity index, equal to where S is the number of species or activities present; n_i is the number of individuals in the i-th species, or area devoted to the i-th species or activity, or income or value of the i-th species or activity; and N (=S n_i) is the total population of individuals across all species, or total area across all species or activities, or total farm income or value across all species or activities

dU/dX:

marginal utility of X for U = f(X)

dY/dX:

marginal product of X in Y = f(X) or the first derivative of Y with respect to X

E:

mean or expected value, calculated for a variable X as for a sample of observations X₁, X₂.... X_n

EMV:

the expected money value of a risky prospect

EU:

subjective expected utility of a risky prospect

EV:

expected value of a risky prospect

f_0.i:

the i-th fractile of a probability distribution; a proportion 0.i of the distribution of a random variable X will lie below the value X = f_0.i

FC:

fixed cost

F(PV):

CDF of PV

F(X):

the cumulative probability or CDF of a random variable X

G:

yield of grain

GAMS:

General Algebraic Modelling System

GM:

gross margin, calculated as gross return less variable cost

GR:

gross return or gross revenue

ha:

hectare(s)

HYV:

high-yielding variety

i:

real annual rate of interest after correcting for inflation or deflation, equal to [(1+i*)/(1+w)]-1, or, when used as a subscript, denotes the i-th member of a set

i*:

nominal annual rate of interest or rate of discount

IRR:

internal rate of return defined as the annual interest rate i at which the PV of an investment's costs is equal to the PV of its gross returns

K:

in LP, the maximum level of an activity permitted by a particular constraint

kg:

kilogram(s)

km:

kilometre(s)

L:

the expected total years of useful life of a capital item

LP:

linear programming

LU:

labour unit, a standardized unit for measuring labour

m:

metre(s)

m:

the modal value of a random variable

-M:

in LP, the notional high negative p value placed on Q_i

MC:

marginal cost or the change in TC as one more unit of a variable input factor is used

mds:

maunds, a volumetric measure used in Pakistan and India

MOTAD:

Minimization of Total Absolute Deviations, a form of linear risk programming

MPP:

marginal physical product, equal to dY/dX for Y = f(X)

mt:

metric tonne(s)

mths:

months

MVP:

marginal value product, equal to (MPP)p_y

n:

depending on context, the number of observations on a variable, or the size of a sample, or the number of input factors in a production process, or the number of equal intervals (usually years) in a period of time

n_i:

for a given farm system, the number of individuals in the i-th species, or area devoted to the i-th species or activity, or income from the i-th species or activity; used in calculating the DI of a farm system

N:

depending on context, quantity of nitrogen fertilizer or, for a given farm system, the total population of individuals across all species, or total area across all species or activities, or total farm income or value across all species or activities; used in calculating the DI of a farm system

no.:

number

NPK:

fertilizer containing nitrogen, phosphorous and potassium

NR:

net return or net revenue, calculated as TGR minus TC

Nu:

Ngultrum; Bhutanese unit of currency

OC:

overhead costs, defined as fixed costs accrued on a whole-farm basis

OGM:

operational gross margin of an enterprise (or activity), calculated as TGR minus DC of the enterprise (or activity)

O_i:

the i-th possible outcome of a particular risky decision

p:

in LP, the unit price or value of each real or disposal activity; it is equivalent to an activity's unit GM

p_g:

unit price of grain

p_i:

unit price of the i-th good

p_n:

unit price of N

p_x:

unit price of input factor X

p_y:

unit price of product Y

P:

quantity of phosphate fertilizer

pk:

patok(s), a Javanese land unit equal to about 0.1 ha

P(O_i):

the decision maker's subjective probability for the occurrence of O_i

P(R£ R*):

the probability that net return R will be less than or equal to any nominated value R*

PV:

the present value of a future lump sum or stream of payments or of an item; if A_n is to be received n years from now, its PV is A_n/(1+i)ⁿ assuming an annual interest rate of i

PV_t:

PV at time t

P(X):

probability of X

q:

number of times per year that compounding or discounting is to occur

Q_i:

in LP, the i-th minimum planning constraint or its corresponding artificial activity

r:

interest rate per period of length 1/q years, equal to an annual interest rate i of (1+r)^q - 1

R:

depending on context, rainfall, or net return, or an annual payment amount that continues in perpetuity and thus has a PV of R/i, or the income diversity ratio, equal to (S R_i)²/S R_i² where R_i (i = 1 to n) is the income from the i-th activity and 1 £ R £ n for R_i³ 0

R_i:

income from the i-th activity

R*:

any nominated value of net return R

RN:

random number

Rp:

Rupiah; Indonesian unit of currency

Rs:

Rupee; Indian, Pakistani and Sri Lankan unit of currency

RTC:

index of relative time-concentration of annual production or income of a product, calculated as the CV of the product's production or income pattern as a fraction of the corresponding CV for a perfectly concentrated product

RTD:

index of relative time-dispersion of production or income, calculated as 1 - RTC

S:

the number of species or activities in a farm system; used in calculating the DI of a farm system

SD:

standard deviation, calculated as the positive square root of variance

SP:

simplified programming

SV:

the salvage value of a capital item

t:

depending on context, ton(s) or tonne(s)

t:

time, e.g., year t, or the time-length of an activity

TC:

total cost, calculated as the sum of total variable cost and total fixed cost

TDN:

total digestible nutrients

TFC:

total fixed cost

TGM:

depending on context, the total gross margin of an activity, of an enterprise or of the whole-farm system; equal to TGR - TVC

TGR:

total gross return or total gross revenue

TPP:

total physical product, equal to Y for Y = f(X)

TVC:

total variable cost

TVP:

total value product, equal to (TPP)p_y

U:

a decision maker's utility function

U*:

the linear transformation of U, equal to aU + b with a > 0

UAE:

United Arab Emirates

U(X):

a decision maker's utility function specified in terms of the variable X

V:

variance, calculated for a variable for a sample of observations X₁, X₂,...X_n

Vt:

the depreciated value of an item at the end of year t under the declining-balance method

VC:

variable cost

vs:

versus

w:

annual rate of inflation (w > 0) or deflation (w < 0)

X:

a variable or an input factor

:

arithmetic mean of a set of sample observations {X_i}, i = 1 to n, on a variable X, calculated as

X₁ = h(X₂/Y*):

isoquant equation giving the locus of all combinations of two variable inputs X₁ and X₂ to produce a fixed level of output Y*

X_i:

depending on context, the i-th observation on a variable X, or the i-th input factor, or the level of the i-th input factor

Y:

depending on context, a product or the yield of product (or output) from a production process

Y*:

some fixed level of output Y

Y = f(X):

single-variable production or response function indicating output Y is a function of the variable input factor X

Y = f(X₁, X₂):

production or response function indicating output Y is a function of two variable inputs X₁ and X₂

Y = f(X₁, X₂,...X_n):

production or response function indicating output Y is a function of n variable inputs X₁, X₂,...X_n

Y = f(X₁/X₂,...X_n):

production or response function indicating output Y as a function of the variable input X₁ when inputs X are held constant

Z:

in LP, the TGM of a farm plan or the opportunity cost of including a unit of an activity in the plan

Z - p:

in LP, for an activity, when multiplied by minus one, indicates the net increase in plan TGM to be gained by adding one more unit of the activity to the plan

¶ Y/¶ X_i:

marginal product of X_i in Y = f(X₁, X₂,...X_n), i = 1 to n, or the first partial derivative of Y with respect to X_i

D (.):

a small incremental change in (.)

D X_i:

a small incremental change in the level of the variable input X_i

p

profit, equal to for the single product activity Y = /(X₁, X₂,...X_n); for multi-product situations, equal to TGR - TVC - TFC or, more simply, GR - VC - FC

for a variable X, the sum of the values X₁, X₂,...X_n

¥:

infinity

>:

greater than, i.e., a > b indicates a is greater than b

<:

less than, i.e., a < b indicates a is less than b

a:	the lower-range or minimum value of a random variable
A:	an annual payment amount which, continued over n years, constitutes an annuity with a terminal value A_n = A[(1+i)ⁿ-1]/i or which amortizes a PV where A = PV[i(1+i)ⁿ]/[(1+i)ⁿ-1]
A_n	a future amount to be received or paid in n years' time; it is equivalent to an annuity over n years of A = A_ni/[(1+i)ⁿ-1] and has a PV of A_n/(1+i)ⁿ
AB:	allocation budgeting
ac:	acre(s)
ac ft:	acre feet (of irrigation water)
AME:	adult male equivalent, a standardized unit of labour measurement
APP:	average physical product, equal to Y/X for Y = f(X)
AU:	animal unit, a standardized unit for aggregation or comparison of different types of animals
AVP:	average value product, equal to (APP)p_y
b:	the upper-range or maximum value of a random variable
B:	the resource pool available to the farmer or, in LP, the level of resource constraints or activities constituting the farm 'plan' at each iteration
B:	size of the available cash budget
B/C:	ratio of benefits to costs
B-1:	in AB and SP, the initial set of resource constraints
B-i:	in AB and SP, the balance of resource constraints after sequential introduction of the i-th activity into the plan, i = 1,2,...
C:	depending on context, cost or the coconut-to-copra conversion rate
CDF:	cumulative distribution function
CE:	a decision maker's certainty equivalent for a risky prospect
cm:	centimetre(s)
COP:	cost of production, calculated per unit of output as total cost divided by quantity of output, i.e., TC/Y
CV:	coefficient of variation, calculated as 100 to express the standard deviation of a variable as a percentage of its mean
CY:	crop-cycle year of a perennial crop
d:	the constant annual rate of depreciation under the declining-balance method
D:	the annual depreciation cost as measured by the straight-line method
D_t:	the annual depreciation cost in year t as measured by the declining-balance or sum-of-integers methods
DC:	direct cost of an enterprise (or activity), calculated as the sum of its VC plus its share of farm FC
DI:	Simpson's diversity index, equal to where S is the number of species or activities present; n_i is the number of individuals in the i-th species, or area devoted to the i-th species or activity, or income or value of the i-th species or activity; and N (=S n_i) is the total population of individuals across all species, or total area across all species or activities, or total farm income or value across all species or activities
dU/dX:	marginal utility of X for U = f(X)
dY/dX:	marginal product of X in Y = f(X) or the first derivative of Y with respect to X
E:	mean or expected value, calculated for a variable X as for a sample of observations X₁, X₂.... X_n
EMV:	the expected money value of a risky prospect
EU:	subjective expected utility of a risky prospect
EV:	expected value of a risky prospect
f_0.i:	the i-th fractile of a probability distribution; a proportion 0.i of the distribution of a random variable X will lie below the value X = f_0.i
FC:	fixed cost
F(PV):	CDF of PV
F(X):	the cumulative probability or CDF of a random variable X
G:	yield of grain
GAMS:	General Algebraic Modelling System
GM:	gross margin, calculated as gross return less variable cost
GR:	gross return or gross revenue
ha:	hectare(s)
HYV:	high-yielding variety
i:	real annual rate of interest after correcting for inflation or deflation, equal to [(1+i*)/(1+w)]-1, or, when used as a subscript, denotes the i-th member of a set
i:*	nominal annual rate of interest or rate of discount
IRR:	internal rate of return defined as the annual interest rate i at which the PV of an investment's costs is equal to the PV of its gross returns
K:	in LP, the maximum level of an activity permitted by a particular constraint
kg:	kilogram(s)
km:	kilometre(s)
L:	the expected total years of useful life of a capital item
LP:	linear programming
LU:	labour unit, a standardized unit for measuring labour
m:	metre(s)
m:	the modal value of a random variable
-M:	in LP, the notional high negative p value placed on Q_i
MC:	marginal cost or the change in TC as one more unit of a variable input factor is used
mds:	maunds, a volumetric measure used in Pakistan and India
MOTAD:	Minimization of Total Absolute Deviations, a form of linear risk programming
MPP:	marginal physical product, equal to dY/dX for Y = f(X)
mt:	metric tonne(s)
mths:	months
MVP:	marginal value product, equal to (MPP)p_y
n:	depending on context, the number of observations on a variable, or the size of a sample, or the number of input factors in a production process, or the number of equal intervals (usually years) in a period of time
n_i:	for a given farm system, the number of individuals in the i-th species, or area devoted to the i-th species or activity, or income from the i-th species or activity; used in calculating the DI of a farm system
N:	depending on context, quantity of nitrogen fertilizer or, for a given farm system, the total population of individuals across all species, or total area across all species or activities, or total farm income or value across all species or activities; used in calculating the DI of a farm system
no.:	number
NPK:	fertilizer containing nitrogen, phosphorous and potassium
NR:	net return or net revenue, calculated as TGR minus TC
Nu:	Ngultrum; Bhutanese unit of currency
OC:	overhead costs, defined as fixed costs accrued on a whole-farm basis
OGM:	operational gross margin of an enterprise (or activity), calculated as TGR minus DC of the enterprise (or activity)
O_i:	the i-th possible outcome of a particular risky decision
p:	in LP, the unit price or value of each real or disposal activity; it is equivalent to an activity's unit GM
p_g:	unit price of grain
p_i:	unit price of the i-th good
p_n:	unit price of N
p_x:	unit price of input factor X
p_y:	unit price of product Y
P:	quantity of phosphate fertilizer
pk:	patok(s), a Javanese land unit equal to about 0.1 ha
P(O_i):	the decision maker's subjective probability for the occurrence of O_i
P(R£ R):*	the probability that net return R will be less than or equal to any nominated value R*
PV:	the present value of a future lump sum or stream of payments or of an item; if A_n is to be received n years from now, its PV is A_n/(1+i)ⁿ assuming an annual interest rate of i
PV_t:	PV at time t
P(X):	probability of X
q:	number of times per year that compounding or discounting is to occur
Q_i:	in LP, the i-th minimum planning constraint or its corresponding artificial activity
r:	interest rate per period of length 1/q years, equal to an annual interest rate i of (1+r)^q - 1
R:	depending on context, rainfall, or net return, or an annual payment amount that continues in perpetuity and thus has a PV of R/i, or the income diversity ratio, equal to (S R_i)²/S R_i² where R_i (i = 1 to n) is the income from the i-th activity and 1 £ R £ n for R_i³ 0
R_i:	income from the i-th activity
R:*	any nominated value of net return R
RN:	random number
Rp:	Rupiah; Indonesian unit of currency
Rs:	Rupee; Indian, Pakistani and Sri Lankan unit of currency
RTC:	index of relative time-concentration of annual production or income of a product, calculated as the CV of the product's production or income pattern as a fraction of the corresponding CV for a perfectly concentrated product
RTD:	index of relative time-dispersion of production or income, calculated as 1 - RTC
S:	the number of species or activities in a farm system; used in calculating the DI of a farm system
SD:	standard deviation, calculated as the positive square root of variance
SP:	simplified programming
SV:	the salvage value of a capital item
t:	depending on context, ton(s) or tonne(s)
t:	time, e.g., year t, or the time-length of an activity
TC:	total cost, calculated as the sum of total variable cost and total fixed cost
TDN:	total digestible nutrients
TFC:	total fixed cost
TGM:	depending on context, the total gross margin of an activity, of an enterprise or of the whole-farm system; equal to TGR - TVC
TGR:	total gross return or total gross revenue
TPP:	total physical product, equal to Y for Y = f(X)
TVC:	total variable cost
TVP:	total value product, equal to (TPP)p_y
U:	a decision maker's utility function
U:*	the linear transformation of U, equal to aU + b with a > 0
UAE:	United Arab Emirates
U(X):	a decision maker's utility function specified in terms of the variable X
V:	variance, calculated for a variable for a sample of observations X₁, X₂,...X_n
Vt:	the depreciated value of an item at the end of year t under the declining-balance method
VC:	variable cost
vs:	versus
w:	annual rate of inflation (w > 0) or deflation (w < 0)
X:	a variable or an input factor
:	arithmetic mean of a set of sample observations {X_i}, i = 1 to n, on a variable X, calculated as
X₁ = h(X₂/Y):*	isoquant equation giving the locus of all combinations of two variable inputs X₁ and X₂ to produce a fixed level of output Y*
X_i:	depending on context, the i-th observation on a variable X, or the i-th input factor, or the level of the i-th input factor
Y:	depending on context, a product or the yield of product (or output) from a production process
Y:*	some fixed level of output Y
Y = f(X):	single-variable production or response function indicating output Y is a function of the variable input factor X
Y = f(X₁, X₂):	production or response function indicating output Y is a function of two variable inputs X₁ and X₂
Y = f(X₁, X₂,...X_n):	production or response function indicating output Y is a function of n variable inputs X₁, X₂,...X_n
Y = f(X₁/X₂,...X_n):	production or response function indicating output Y as a function of the variable input X₁ when inputs X are held constant
Z:	in LP, the TGM of a farm plan or the opportunity cost of including a unit of an activity in the plan
Z - p:	in LP, for an activity, when multiplied by minus one, indicates the net increase in plan TGM to be gained by adding one more unit of the activity to the plan
¶ Y/¶ X_i:	marginal product of X_i in Y = f(X₁, X₂,...X_n), i = 1 to n, or the first partial derivative of Y with respect to X_i
D (.):	a small incremental change in (.)
D X_i:	a small incremental change in the level of the variable input X_i
p	profit, equal to for the single product activity Y = /(X₁, X₂,...X_n); for multi-product situations, equal to TGR - TVC - TFC or, more simply, GR - VC - FC
	for a variable X, the sum of the values X₁, X₂,...X_n
¥:	infinity
>:	greater than, i.e., a > b indicates a is greater than b
<:	less than, i.e., a < b indicates a is less than b