Two Year Transactions
Let the demand curve for wool in year t (t = 0, 1,2 ... s) be of the form:
q,
= k,p,", (C. 1 )where k, i s a constant, specific to year t, which determines the level o f the demand curve in that year.
Thus if ITo is the price in the year ° when stocks are acquired, then:
But by (C. 1),
(q,jk,//IIO
=Po;
hence:
Ito
=po{1-r ,
//"0 (C.2)From equation 2.6 trading profits, To, are given by:
(C.3)
To find the minimum
Itl"
which must be realised if the Wool Authority is to avoid trading losses, the right-hand side of the equation (C.3) is set to zero, and solved forItl, thus obtaining:
Itj•
=ItoCl
+B) + g + a +2F/(r�oJ
(C.4)In year 1, the price would.have been PI if'stocks roqo had not been liquidated. Under the simplifying assumption that the wool clips qu and ql are of the same size, then
Itl
is given by:But by (C l ),
(q/k/I"I
=PI '
so that: Thus if:PI
=IT/(
1 +r 0/1"1
• •lIn
PI
=ITI
/ (1 +r
oJI
(C5) (C6)PI"
can be interpreted as the minimum free-market price which would have to prevail in year 1 in the absence of the scheme to ensure that a trading loss is avoided on the purchase of stocks in year O. For a specified set of assumptions aboutq()
IT() r()
floalld Ill' the hidden returns
(
Ko- Ho -
Lo)
can be computed on the assumption that the. break-even price IT," is actually realised.
Six-Year Transaction
Let qo be the production of wool in each of the six years, ITo be the price realised during year 0 in which the stocks
r �o
are purchased, and � be the price in each of the years 1 through 5, during which one-fifth of the stocks is disposed of annually.""
In this case trading profits for the six year cycle, To will be given by:
(=1 j= 1 j= 1
where the fourth and fifth terms on the right-hand side are variable costs, and the last term represents the sum of interest charges calculated separately on each one fifth of the stocks. The last term reduces to - « 1 + 8)[(1 + 8)5 - 1] / (58)
-
1)1tr�o
J
Thus substituting
fir�J5
for D, and simplifying:It"
= )"[0 (1 + B)[ (1 + B)5 - 1 ]/ (5B) + 3g + a + 6F/(roqo)(e.8)
/'
The net returns No to the scheme for the six-year cycle will be:
/'
No = R' t + I5 R \ + Ko - Ro - I5 Rt + To
1 = 1 1= 1
where p = )"[ (1 + rcl5) · 1/il would have been the free market price in each of the
years 1 through 5 if there had been no liquidation of stocks, with jz the elasticity
/'
of demand in each of these years. Substituting for To [rom (e.7) and simplifying:
A
No = qo[)"[o { 1 - ro(1 +B)((1 +B)5 - 1)/(5B) - (l-ro)1/·no}
+ n {5 (1 - (1 + rcl5)""') + ro} - ro (3g+a)] - 6F (C.9)
The above formulae can be generalised to the case where stocks are bought in an initial year 0, and disposed of in equal annual quantities over s years of stable demand. It is only necessary to substitute s [or 5, (s + 1 ) for 6, and (s + 1)/2 for 3 in equations (C8) and (C9) above.
Table C 1 gives some idea of the effect of a longer disposal period. The gains and losses shown in the table occur on the assumption that stocks of wool are liquidated at a steady rate over a five-year period during which time the demand curve does not change. The only other difference from the assumptions made for Tables 2.3 and 2.4 is that the selling price is substantially higher (65.5 pence cf. 57.0 pence) to compensate for the increased interest charges arising from the longer storage period.
Epd during selling period -0.5 -0. 7 -0.9 -1.0 -1. 1 -1.5 -3.0 -10.0 Notation: TABLE C. l:
Hidden Gains and Losses from the Floor-Price Scheme
(expressed in millions of Australian £)
Six-Year Transactions Cycle: 5 % of the clip acquired
Elasticity of Demand (Epd) during the Purchase Period
-0.5 -0. 7 -0.9 -1.0 -1.1 -1.5 -3.0 - 1 1 .0 -19.6 -24.S -26.2 -27.6 -3 1 .S -36.8 - 1 .2 -7.4 - 1 2.3 - 14.0 - IS.S - 19.3 -24.7 7.9 -0.7 -S.6 -7.3 -8.8 - 12.6 - 17.9 10.3 1 .7 -3.2 -S.O -6.4 - 10.2 - 1S.6 12.2 3.6 - 1 .3 -3. 1 -4.S -8.3 - 13.7 17.3 8.7 3.8 2. 1 0.6 -3.2 -8.6 24.3 IS.7 10.8 9. 1 7.6 3.8 - 1 .S 29.2 20.6 IS.7 14.0 12.S 8.7 3.4 -10.0 -40.6 -28.4 -2 1 .7 - 19.4 - 17.S - 12.4 -S.3 -0.5
Pt Average price of Australian wool in year t, in the absence of a buffer-stock scheme, i.e. the free-market price.
1tt Average price of wool in any year t during which the Wool Authority operates on the open market. If the year t is one during which stocks are accumulated, 1t/ is the floor price.
qt Output of wool in year t.
rt The proportion of the clip acquired
b
y the Wool Authority in the year t; defined for years in which stocks are acquired.Rt Revenue accruing from the sale of wool under free market conditions in year t:
R'I Revenue realised on commercial sales of wool in year t:
R ',
=rt,( l-rJq,
in a year of stock accumulation,= rtfl, in a year of stock disposal.
01 Revenue realised on the sale of stocks by the Wool Authority In year t;
defined only for those years in which such sales occur:
KI Money paid out by the Wool Authority in year t to acquire stocks; defined
only for those years of stock accumulation:
TI Trading profit associated wiLh the purchase of stocks in year t; defined only for years of stock accumulation.
HI Loss of revenue from commercial sales of the current year's clip in year t; defined only for those years which stocks are acquired:
lI, = (R, -
R 'J
A
negative value ofHI
implies a gain.LI Loss of revenue on the wool clip in year t+ 1 due to the depressing effect of disposal operations on the price during that year; defined for years immediately antecedent to disposal operations:
nl Price elasticity of demand for Australian wool in year t.
B Rate of interest charged on the working capital used in the buffer-stock scheme.
ml Interest charged on the capital invested in wool stocks:
nI, = Br fl,It,
F Fixed handling and administrative costs per annum.
g Handling costs per lb. of wool per annum. These mainly represent charges for insurance and storage.
a Handling costs per lb. which are independent of the period of storage. They mainly represent freight charges and commission on the resale of stocks.
VI Variable handling costs incurred on stocks acquired in year t: VI = (g + a)r,ql
in the case of two year transactions.
Nt Net returns from the scheme, associated with the purchase of stocks of greasy wool in the year t; defined only for years in which purchases are made.
wt Physical volume of stocks sold in year t: WI = rl.] ql.]
Source: Powell, A. & Campbell,K.O. Revenue of a Buffer-Stock Scheme With An Uncertain Demand Schedule. Economic Record, September,