Storable Goods and Expected Future Prices

Why Future Prices Can Affect Current Supply

A seller who can store a good chooses not only whether to produce it, but also when to sell it. If the seller expects a higher price later, holding inventory may be more attractive than selling today. The decision depends on more than the price forecast: the seller must also consider the return available from selling now and storage costs. This is why expectations can change the amount offered for sale today even when current production has not changed.

The distinction matters for storable goods such as grain, metals, or durable materials. For a good that cannot be stored, a seller generally cannot shift its sale from one period to another. For a storable good, some current output may be retained as inventory, reducing the quantity supplied to the current market. This treatment of expectations is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.

Definition: Inventory is a stock of goods held for sale or use in a later period. For a storable good, the seller's current quantity supplied can include goods released from inventory as well as goods produced for current sale. Withholding inventory means retaining goods rather than offering them for sale now.

A useful way to analyze a storage decision is to compare two alternatives for one unit: sell it now and invest the proceeds, or store it and sell it later. For a clear one-period model, suppose there is no spoilage, the effective annual interest rate is $i$, storage cost $c$ is paid at the end of the period, and the expected future price is $E[P_{t+1}]$. Assume either certainty about the future price or a risk-neutral seller who compares expected monetary values. There are no taxes or other costs, and the seller can store the unit.

The Storage Decision

Let $P_t$ be the current price. Selling now produces $P_t$, which can grow to $(1+i)P_t$ by the end of the period. Storing instead produces expected sale revenue $E[P_{t+1}]$, less the end-of-period storage cost $c$. Thus, the seller compares the future value of selling now with the expected net revenue from storing.

\begin{aligned} \text{Future value of selling now} &= (1+i)P_t,\\ \text{Expected net revenue from storing} &= E[P_{t+1}]-c. \end{aligned}

Decision rule: Under the one-period assumptions above, storing is more attractive than selling now when $E[P_{t+1}]-c>(1+i)P_t$. Selling now is more attractive when $E[P_{t+1}]-c<(1+i)P_t$. The seller is indifferent when the two amounts are equal.

The rule gives a useful threshold current price. Rearranging the inequality, storing is attractive when the current price is below $\frac{E[P_{t+1}]-c}{1+i}$, and selling now is attractive when it is above that threshold. A higher expected future price raises the threshold, making storage worthwhile at a wider range of current prices. A higher interest rate or storage cost lowers the threshold, making storage less attractive.

Why the Comparison Works

The comparison is based on opportunity cost: a seller who stores gives up the proceeds that could have been earned by selling immediately. Because those proceeds could earn interest, the forgone amount must be measured at the end of the period, not just as the current price. The derivation is simply to put both choices on the same time basis.

Value the sell-now option at the future date.
Selling today yields $P_t$. Investing that amount for one period at effective annual rate $i$ yields $(1+i)P_t$.

Value the storage option at the same date.
The expected sale price is $E[P_{t+1}]$. After the storage cost $c$, expected net revenue is $E[P_{t+1}]-c$.

Choose the larger value.
Store if $E[P_{t+1}]-c>(1+i)P_t$; sell now if the inequality is reversed. Equality means neither option has a higher value under this model.

The model is deliberately limited. If the good deteriorates, storage capacity is constrained, future prices are risky and sellers are not risk-neutral, or there are additional costs, the simple comparison needs adjustment. In particular, a forecast of a higher future price is not enough by itself to show that storage is worthwhile: the expected price increase must cover both the return sacrificed by not selling now and the storage cost.

Worked Example: A Modest Price Increase and a Storage Decision

A seller has one unit of a durable material that can be sold today for $50. The effective annual interest rate is 4%. If the seller stores the unit for one year, storage costs $1, paid at the end of the year. The seller expects the price in one year to be $54 with certainty. Should the seller store it or sell it today? Use the one-period model, with no spoilage or other costs.

Method. Compare the end-of-year value of selling now and investing the proceeds with the expected net revenue from storing.

Sell now and invest. The end-of-year value is $50(1.04)=\$52.00$.

Store and sell later. Expected sale revenue after storage cost is $54-1=\$53.00$.

Decision. Since $\$53.00>\$52.00$, storing has an expected advantage of $\$53.00-\$52.00=\$1.00$ per unit. Equivalently, the threshold current price is $(54-1)/1.04=\$50.9615\ldots$, which is above the current price of $50. The seller should store under the stated assumptions.

Check. The two alternatives have both been valued at the end of the year, and the storage cost is subtracted from the later sale price. The result agrees with the threshold test. A common mistake would be to ignore interest and compare $53 directly with $50; that comparison uses different time values. Here it happens to point to storage too, but it does not measure the correct advantage.

Worked Example: A Higher Future Price Does Not Always Justify Storage

A seller can sell a durable unit today for $80. The effective annual interest rate is 5%, and one year of storage costs $2 at the end of the year. The expected price in one year is $84. Assume no spoilage, no other costs, and certainty about the future price. Should the seller hold the unit?

Method. Compare both choices at the end of the year rather than comparing the two sale prices alone.

Sell now and invest. The proceeds grow to $80(1.05)=\$84.00$.

Store and sell later. Net sale revenue is $84-2=\$82.00$.

Decision. Because $\$82.00<\$84.00$, selling now is better by $\$84.00-\$82.00=\$2.00$ per unit. The threshold current price is $(84-2)/1.05=82/1.05=\$78.0952\ldots$. Since the actual current price of $80 is above this threshold, the seller should sell now.

Check and trap. The expected future price, $84, is greater than the current price, $80, but that is not the correct comparison. A mistaken calculation would conclude “store because $84>80$.” The corrected comparison includes both the $4.00 return from investing the $80 for a year and the $2.00 storage cost; together they make selling now more attractive.

From an Individual Choice to Current Market Supply

When many sellers make this decision, their inventory choices affect how much is offered to the current market. Hold other conditions fixed, including current demand, current production, and storage capacity. If expectations of future prices rise, some sellers may withhold storable goods that they would otherwise sell today. Current quantity supplied then falls. If expected future prices fall, sellers may release inventory sooner, increasing the amount offered now.

This is a change in current supply associated with inventory decisions; it does not necessarily mean that producers have changed their production plans. The distinction between production and quantity offered for current sale is essential. The effect is conditional: if the good cannot be stored, storage is already at capacity, or the expected future price is not high enough to cover carrying costs, a higher price expectation may not reduce current sales.

Worked Example: How Price News Changes Current Sales of Inventory

A group of sellers has 100 units of a durable product available today. At most 60 units can be stored until next year; the other 40 units must be sold today. The current price is $100 per unit, the effective annual interest rate is 4%, and storing a unit costs $2 at the end of the year. First, sellers expect next year's price to be $108. Then new information changes their expectation to $105. Assume the forecasts are certain, storage capacity is available for all 60 storable units, and the 100 units are the only units being allocated between current sale and inventory. How does the change affect current quantity supplied?

Method. Apply the storage rule at the same current price under each forecast, then account for the 40 units that cannot be stored.

First forecast: $108. Selling now and investing yields $100(1.04)=\$104$ at the end of the year. Storage yields $108-2=\$106$. Since $\$106>\$104$, sellers store as many units as capacity permits: 60 units. The remaining $100-60=40$ units are sold now, so current quantity supplied is 40 units.

Revised forecast: $105. Selling now and investing still yields $104. Storage now yields $105-2=\$103$. Since $\$103<\$104$, sellers prefer selling now to storing. They sell all 100 available units, so current quantity supplied is 100 units.

Conclusion and check. The lower expected future price raises current sales from 40 to 100 units, an increase of $100-40=60$ units. That is exactly the amount previously withheld in storage. The example holds production and current price fixed, isolating the inventory response to changed expectations. It does not imply that the underlying production capacity changed.

Common Mistakes and Practical Limits

Comparing future and current prices without adjusting for time. A seller gives up the opportunity to earn interest by holding the good. Compare values at a common date.
Ignoring storage costs. The later selling price is not the storage payoff if storage uses resources. Subtract the stated cost at the date it is paid.
Assuming any expected increase means withholding. Storage is attractive only when expected net revenue exceeds the future value of selling now.
Confusing a change in current sales with a change in production. Inventory can shift the timing of sales even when the amount produced is unchanged.
Applying the model when storage is impossible. A good that cannot be stored cannot be shifted from current sale to future sale by this mechanism.

Key takeaway: For a storable good in the one-period model, compare $E[P_{t+1}]-c$ with $(1+i)P_t$. A sufficiently high expected future price encourages withholding inventory and reduces current quantity supplied; a sufficiently low expectation encourages current sales. Interest, storage cost, and the ability to store determine whether the expectation is strong enough to change the decision.

Check Your Understanding

For each problem, use the one-period storage model. Unless stated otherwise, assume no spoilage, no costs other than those given, and certainty about the future price.

A unit sells today for $40. The effective annual interest rate is 5%, storage costs $1 at the end of the year, and the expected future price is $44. Should the seller store or sell now, and by how much does the preferred option exceed the other at the end of the year? (Answer: Store; $44-1=\$43$ versus $40(1.05)=\$42$, so storage is better by $1.00.)
A durable unit sells today for $60. The effective annual interest rate is 10%, end-of-year storage cost is $2, and the expected future price is $68. What is the decision? (Answer: Indifferent; $68-2=\$66$ and $60(1.10)=\$66$.)
A material sells today for $25. The effective annual interest rate is 4%, storage costs $0.50 at year-end, and the expected future price is $26. Calculate both end-of-year values and state the decision. (Answer: Sell now; $25(1.04)=\$26.00$, while $26-0.50=\$25.50$, so selling now is better by $0.50.)
The current price is $50, the effective annual interest rate is 2%, and end-of-year storage cost is $1. What expected future price makes the seller exactly indifferent between storing and selling now? (Answer: $52; $E[P_{t+1}]-1=50(1.02)=51$, so $E[P_{t+1}]=\$52$.)
A market has 80 units available today, of which at most 30 can be stored. The current price is $20, the effective annual interest rate is 5%, and storage costs $0.50 at the end of the year. The expected future price is $22. If all sellers who can store choose to do so whenever it is strictly better than selling now, how many units are supplied today? (Answer: 50 units; storage yields $22-0.50=\$21.50$, compared with $20(1.05)=\$21.00$, so 30 units are stored and $80-30=50$ are sold.)

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