Gallagher
03/2010
The Effects of Demand Forecast Error
Consider a commodity market, like corn. The assumptions for our analysis are:
1. There are two production periods.
2. The present is at the beginning of the first period where farmers are deciding how
much corn to plant and produce, and buyers have not yet observed the price (P1) or
decided how much to consume.
3. Supply and demand curves for period 1 (S1 and D1) are the same as supply and
demand curves for the future period 2 (S2 and D2).
4. Period 2 demand consists of consumers who wait until observing the period 2 price
(P2) to decide on their corn consumption level.
5. Merchants carry (hedged) inventory from period 1 to period 2 (I12) on the basis of
profits obtained from buying at P1 and selling at Pf. Arbitrage and inventory
expansion occurs up to the point where profit opportunities are exhausted.
6. Market participants have accurate information about S1 and D1, but they rely on a
public forecast to establish the position of D2.
With a good Demand Forecast for D2,
0
𝐼12
= 0 in Figure 1 because ES = ED; That is, the future demand/supply balance is the
same as the present demand/supply balance. 𝑃10 is year 1 cash price. 𝑃20 is also year 2 cash
price. So there is no price variability.
𝑓
𝑓
𝑓
Suppose 𝐷2 is a mistaken forecast. Then inventory demand is defined by 𝐸𝐷12 . So 𝑃1 is year 1
𝑓
cash price, which is higher. 𝑃1 is also year 1 future price for year 2 delivery.
After actual Demand D2 is discovered in period 2, the market clears at price 𝑃21 . Now there is
𝑓
price variability – the price changes from 𝑃1 in period 1 to 𝑃21 in period 2.
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Figure 1. The Effect of a 2nd Period Demand Forecast Error, no Consumer Hedging.
𝐸𝑆12
𝑓
𝑆2 + 𝐼12
𝑆2
𝑆1
𝑓
𝑃1
𝑃10
𝑃20
𝑃21
𝐷1
𝐷2
0
𝐼12
=0
𝐸𝐷12
𝑓
𝐷2
𝑓
𝐸𝐷12
𝑓
𝐼12
Page 2|
Next replace Assumption 4 with the following:
4. period 2 demand is split equally between two groups: those who make their corn consumption decision for
period 2 on the basis of the futures price (for delivery in period 2) that prevails in period 1 (Pf), and those who
wait until observing the period 2 price (P2)to decide on their corn consumption level.
In the event that the demand forecast is accurate, the period 1 and period 2 price are still the same at 𝑃10 and 𝑃20 ,
𝑓
𝑓
𝑓
in figure 2. Similarly, the inaccurate demand forecast 𝐷2 still produces 𝐸𝐷12 and inventory 𝐼12 , as in figure 1.
However, the period 2 demand curve is steeper with respect to a decrease in the period 2 price. This occurs
𝑓
because the demand curve for hedged consumers becomes perfectly inelastic when the price falls below 𝑃2 .
Only the unhedged fraction of consumers increase demand when the price falls. (See Figure 3)
𝑓
Comparing to Figure 1, the price decrease in period 1, 𝑃21 − 𝑃20 is bigger than 𝑃2 − 𝑃20 , the period 1 price
increase. Why? Hedging and non-hedging consumers both reduce consumption when futures price increases in
figure 1. But committed consumers do not make adjustments when the price falls in period 2.
Now, compare the accurate and inaccurate demand forecast. From figure 2 producers gain area A + B in period
0 and lose area C in period 1 with an inaccurate forecast and price instability.
Figure 3 depicts the distribution of welfare change between unhedged and hedged buyers. The hedged
consumers lose area D with price instability. Meanwhile, the unhedged consumer gain area E.
In Figure 2, the net consumer gain from price stability in period 2 is Area C + F. Also the period 0 loss is area
A.
Page 3|
Figure 2. The Effect of a 2nd Period Demand Forecast Error, with Period 1 hedge.
𝐸𝑆12
S2 + I
S2
S1
𝑓
𝑃2
𝑓
𝑃1
𝑃10
A
B
𝑃20
C
𝑃21
F
D2
D1
0
𝐼12
=0
𝑓
𝐼12
𝐸𝐷12
𝑓
𝐷2
𝑓
𝐸𝐷12
𝐷2ℎ
Page 4|
Total Consumer Gain: +E-D
Figure 3: Distribution of Consumer Gain
Unhedged consumer
Hedged consumer
𝑓
𝑃2
D
E
𝑃20
𝑃21
𝑓
𝐷2
D2
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