# 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 An = A[(1+i)n-1]/i or which amortizes a PV where A = PV[i(1+i)n]/[(1+i)n-1] An a future amount to be received or paid in n years' time; it is equivalent to an annuity over n years of A = Ani/[(1+i)n-1] and has a PV of An/(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)py 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 Dt: 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; ni 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 ni) 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.... Xn EMV: the expected money value of a risky prospect EU: subjective expected utility of a risky prospect EV: expected value of a risky prospect f0.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 = f0.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 Qi 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)py 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 ni: 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) Oi: 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 pg: unit price of grain pi: unit price of the i-th good pn: unit price of N px: unit price of input factor X py: unit price of product Y P: quantity of phosphate fertilizer pk: patok(s), a Javanese land unit equal to about 0.1 ha P(Oi): the decision maker's subjective probability for the occurrence of Oi 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 An is to be received n years from now, its PV is An/(1+i)n assuming an annual interest rate of i PVt: PV at time t P(X): probability of X q: number of times per year that compounding or discounting is to occur Qi: 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 Ri)²/S Ri² where Ri (i = 1 to n) is the income from the i-th activity and 1 £ R £ n for Ri³ 0 Ri: 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)py 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,...Xn 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 {Xi}, 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* Xi: 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,...Xn): production or response function indicating output Y is a function of n variable inputs X1, X2,...Xn Y = f(X1/X2,...Xn): 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/¶ Xi: marginal product of Xi in Y = f(X1, X2,...Xn), i = 1 to n, or the first partial derivative of Y with respect to Xi D (.): a small incremental change in (.) D Xi: a small incremental change in the level of the variable input Xi p profit, equal to for the single product activity Y = /(X1, X2,...Xn); 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,...Xn ¥: 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