Cash Prices, Future Prices, and Inventory Equilibrium
In June of the corn marketing year, supply is given by the inventory carry in from earlier in the crop year (. The demand curve (D(Pt)) indicates the amount that will be consumed in the present, which ends when the new harvest becomes available. The inventory supply curve, ES12, in panel b defines the amount that speculators must pay to carry grain (store inventory) into the next production period; it is defined as the difference between supply and demand at a given price.
Anticipated demand and supply in the post-harvest period are shown in panel c. the demand curve De(Pe) is a downward sloping function of the anticipated price in the post-harvest period; the anticipated price, Pe, is the futures market price in the period after the crop has been planted and before the harvest is known. The demand curve represents speculators’ assessment of the amount that consumers will be willing to buy next year; speculators place the position of anticipated demand based on their assessment of upcoming livestock market populations and upcoming conditions of foreign markets. Similarly, the position of the anticipated corn supply is defined by speculators’ collective assessment of the production for the upcoming crop. Anticipated production is indicated by the vertical line, Qa. Anticipated supply does not respond to the futures price because producers have already planted; they cannot adjust input use or output if market conditions change.
The inventory demand curve in panel b, Eda, is the difference between anticipated demand and anticipated supply at a given future price. It indicated the amount that speculators expect to receive when they sell stored inventory in the post-harvest period.
Equilibrium for inventory is and price is given by the intersection of the inventory supply and inventory demand schedule in panel b. The cash and futures price are equal in equilibrium; the inventory supply curve indicates the marginal cost of diverting the last unit from current consumption. Meanwhile, the inventory demand curve indicates the expected benefit from the incremental unit of future consumption. The equilibrium condition says that the two values are balanced. Finally, the futures price for the post-harvest period is what the actual cash price in the post harvest period will be IF speculators’ assessment of the position of the supply and demand schedule is accurate.
The Effect of Inaccurate Production Forecasts
First, imagine that market participants believed the production forecast Qa was accurate. Then the springtime price and the post-harvest price would be the same, at . This would happen because the inventory carryover, Io, would be the right amount to clear the post-harvest market at .
Second, suppose that our estimate of production was too high; after the harvest, we find out that Qb is the amount that is actually produced even though the government announced the production forecast, Qa. The pre-harvest price is still because everyone expected the output forecast Qa. Similarly, Io is still the inventory carry-out because they believed the production forecast.
An improved production forecast would change the inventory decision and improve welfare. In figure 2, the best possible production forecast is Qb instead of Qa. If market participants know that Qb will occur, Edb defines the expected gain from carrying inventory, and the inventory equilibrium is I1.
Clearly, more accurate production reports would bring Pt+1 and closer together. In fact, a perfect production forecast, at Qb, would result in the same price () in the present period and the future period.
Comparing the production forecast, Qa, to the perfect production forecast, Qb, the welfare changes are as follows:
Period O:Period 1:
Consumers: - CoConsumers: +B1+D1+C1+A1
Producers:+Co+BoProducers: -B1
NetBoNetD1+C1+A1
Total Welfare Gain: Bo+D1+C1+A1
Figure 1. Cash and futures Price formation with inaccurate production information (Qa) and accurate production information (Qb)
Welfare change with perfect production forecast:
Period O:Period 1:
Consumers: - CoConsumers: +B1+D1+C1+A1
Producers:+Co+BoProducers: -B1
NetBoNetD1+C1+A1
Total Welfare Gain: Bo+D1+C1+A1