8 where _PCC_ is the real quarterly CE cocoa price, P is the average observed real world price each quarter, _£_ is the iso-elastic short-run price elasticity of demand, a is the coefficient of variation of real quarterly world prices, and R is the relative risk aversion coefficient. The variable P is first calculated on a CIF basis from world market data (World Bank 1998) and then converted to a farm gate basis by subtracting maritime transport and direct domestic marketing costs. In terms of Table 1, P would then be 714 F/kg (i.e., the CIF price of 904 F/kg minus maritime transport of 75 F/kg minus direct domestic marketing costs of 115 F/kg). We refer henceforth to _P_ as the "farm gate FOB price".

We note, first, that output is affected by stabilization, even though stabilization is within seasons, given that there is some weak short-term supply response for tree crops. Second, it is assumed that R is unity, indicating that farmers are moderately risk averse (based on extensive empirical evidence launched by Binswanger, 1978). Third, in the absence of price stabilization, the volatility of domestic producer prices would be that of international cocoa prices. With those assumptions, we construct counter-factuals in which intra-annual producer price variability increases from zero (perfect stabilization) to world levels (perfect transmission of international prices) for each season from 1993/94 through 1997/98.

The within season coefficient of variation of monthly world prices had a maximum of 8.1 percent in 1993/94 and a minimum of 2.8 percent in 1994/95. The absolute value of the short-run price elasticity of demand is assumed to be 0.5. Counter-factual stabilization benefits expressed relative to the P from equation (1) would therefore have ranged from a maximum of 0.3 percent of P in 1993/94 to a minimum of zero in 1994/95. This range of benefits can be compared to the structure of export pricing from 1993/94 through 1997/98 expressed as a share of FOB: producer price, 49 percent; explicit export taxation, 22 percent; direct domestic marketing costs, 14 percent; CAISTAB's operating costs, 6 percent; and stabilization profits, 10 percent. Assuming for the moment that the average 22 percent of explicit export taxation was justified, farmers were further taxed some 16 percent of the world price (6 for CAISTAB costs and 10 for stabilization profits) and received stabilization benefits of less than 1 percent of world price. In the absence of stabilization, but with the same explicit export tax, farmers ought to have received a producer price at least 15 percent higher (in terms of the FOB price) or 125 F/kg in absolute terms.

The same result can be visualized over a longer period in Figure 3, which portrays the observed real official producer price of cocoa, the farm gate FOB price (_), and the certainty equivalent price _(Pce)_ by quarters from 1983 through 1997. The certainty equivalent price is close to _P_ given that quarterly prices vary little within crop seasons. The CE price is generally above the official minimum before 1989. A period of exceptionally low world prices occurred after 1989 and the CE price and the minimum were much closer then until 1993 or so when world prices rose again. In the 60 quarters observed from 1983 through 1997, in only nine did the producer price exceed the CE price.