Expected Future Prices and Current Demand

Why Future Prices Can Affect Today’s Demand

A buyer deciding whether to purchase today may consider not only the current price, but also the price expected later. If a good can be stored or a purchase can be postponed, expected future prices can change the timing of purchases. Buyers who anticipate a price increase may bring purchases forward; those who anticipate a decrease may wait.

This is a change in current demand when buyers would choose a different current quantity at the same current price. It is not a movement along the current demand curve: that movement occurs when the good’s current price changes, with other demand determinants held fixed. The effect of expectations depends on the good and on the costs and benefits of changing purchase timing.

Definition: The expected future price is the price buyers anticipate paying in a later period. Holding the current price and other determinants fixed, a change in that expectation can shift current demand. For a storable good, a higher expected future price may shift current demand right; a lower expected future price may shift it left. Neither direction is automatic: storage, financing, waiting, and other costs matter.

A Simple Purchase-Timing Model

Consider a risk-neutral buyer choosing when to acquire a fixed quantity $Q$ of a storable good. The buyer can purchase $x$ units now and $Q-x$ units one year from now, where $0 \le x \le Q$. Assume the current price is $P_0$, storage costs $c$ dollars per unit purchased now, the expected future price is $E[P_1]$, and the effective annual interest rate is $i$. Assume there is no spoilage, no storage-capacity constraint, no change in quality, and no difference in the usefulness of acquiring a unit earlier rather than later. The future price is uncertain, and risk neutrality means the buyer evaluates the future payment using its expectation. The future payment is discounted by $v=1/(1+i)$.

The present-value cost of the purchase plan is current expenditure plus storage costs plus the discounted expected future expenditure:

$$ C(x)=(P_0+c)x+vE[P_1](Q-x). $$

The model has a simple implication because the cost is linear in $x$. The next derivation shows why the comparison of current and future costs determines purchase timing.

Find the cost of moving one unit to today.
Replacing one unit bought next year with one bought now changes present-value cost by $(P_0+c)-vE[P_1]$.

Compare the two costs.
If $P_0+c < vE[P_1]$, buying the unit now costs less in present-value terms, so the buyer prefers to bring purchases forward. If $P_0+c > vE[P_1]$, waiting costs less. If they are equal, the buyer is indifferent under the model’s assumptions.

Translate timing into current demand.
When buyers bring purchases forward, current purchases rise; when they wait, current purchases fall. The model describes a timing incentive, not a universal prediction that every expected price change must alter demand.

The inequality also explains why an expected price increase may not lead to stockpiling. The expected future price must be high enough to cover storage costs and the opportunity cost of paying earlier. For a nonstorable good, an advance purchase may be impossible; for a good with costly storage or a risk of spoilage, the threshold is higher.

Worked Examples

Worked Example: An Expected Increase Shifts Current Demand

A market analyst uses the following illustrative weekly demand schedule for a storable household supply, where $P_0$ and $E[P_1]$ are dollar prices per unit and quantity is measured in units per week:

$$ Q_0^d=150-4P_0+2E[P_1]. $$

At a current price of $20, calculate current demand when the expected future price rises from $25 to $29. State whether this is a movement along demand or a shift.

Method. Hold the current price fixed and substitute each expected future price into the schedule. The positive coefficient on the expected price means that a higher expectation raises current quantity in this illustrative relationship.

Before the expectation changes: $P_0=20$ and $E[P_1]=25$, so

$$ Q_0^d=150-4(20)+2(25)=150-80+50=120. $$

After the expectation changes: $P_0=20$ and $E[P_1]=29$, so

$$ Q_0^d=150-4(20)+2(29)=150-80+58=128. $$

Current quantity demanded rises by $128-120=8$ units per week at the same current price. The expectation change shifts current demand right; it is not a movement along demand. The method avoids the common mistake of treating the expected future price as if it were today’s price.

Worked Example: Checking Whether Stockpiling Pays

A retailer plans to use 10 units of a storable input over the next year and has none in inventory. It can buy units now for $40 each or buy them one year from now at an expected price of $50 each. Storage costs $2 per unit for the year. The effective annual interest rate is 4%, and storage capacity is limited to 6 units. Assume the retailer is risk-neutral and all other assumptions of the timing model hold. How many units should it buy now?

Method. Compare the current acquisition cost, including storage, with the present value of the expected future price. Here $P_0=40$, $c=2$, $E[P_1]=50$, and $i=0.04$. The discount factor is

v=\frac{1}{1+i}=\frac{1}{1.04}=0.961538\ldots

The present value of buying a unit next year is

vE[P_1]=\frac{50}{1.04}=48.076923\ldots \text{ dollars}.

The current purchase and storage cost is $P_0+c=40+2=42$ dollars per unit. Since $42<48.076923\ldots$, buying now is cheaper under the model. Without the capacity limit, the retailer would bring all 10 planned units forward. With capacity limited to 6, it should buy 6 units now and the remaining $10-6=4$ units next year.

Check. Six units bought now cost $6(42)=252$ dollars including storage. Four bought next year have present-value expected cost $4(48.076923\ldots)=192.307692\ldots$ dollars. Total present-value cost is $252+192.307692\ldots=444.307692\ldots$ dollars. The calculation avoids the trap of comparing $40 directly with $50 while ignoring storage and the time value of money.

Worked Example: An Expected Decrease Encourages Buyers to Wait

Three customers are considering the same one-use device. Each would buy it at the current price of $120 if there were no incentive to wait. The expected price next month is $100. Assume the effective interest rate for this one-month comparison is 0%, and treat each customer’s stated waiting cost as a dollar-equivalent loss of usefulness from postponing the purchase. The customers’ waiting costs are $5, $15, and $25, respectively. Determine how many buy now if the future price is expected to be $100, and compare that with the case where it is expected to remain $120.

Method. Compare the expected saving from waiting with each customer’s waiting cost. When the expected future price is $100, the saving relative to buying now is $120-100=20$ dollars per customer.

The first customer gives up $5 of usefulness by waiting, so the net gain from waiting is $20-5=15$ dollars. This customer waits. The second customer’s net gain is $20-15=5$ dollars, so this customer also waits. The third customer’s net gain is $20-25=-5$ dollars, so this customer buys now rather than incur the larger waiting cost.

Thus, 1 of the 3 customers buys now. If the expected future price instead remains $120, the saving from waiting is $120-120=0$ dollars. Each customer has a positive waiting cost, so all 3 buy now. An expected decrease therefore reduces current purchases from 3 to 1 in this scenario, shifting current demand left. The method avoids assuming that a future discount makes every buyer wait regardless of the cost of postponement.

Interpreting the Direction and Size of the Effect

An estimated demand schedule can summarize how current purchases respond to expectations. For example, a schedule of the form $Q_0^d=a-bP_0+\gamma E[P_1]$, with $b>0$ and $\gamma>0$, predicts that a higher expected future price raises current quantity at each current price. Holding $P_0$ fixed, an increase in expected price of $\Delta E[P_1]$ changes current quantity by $\gamma\Delta E[P_1]$. This is a convenient linear representation, not a universal law: the coefficient $\gamma$ depends on the good and the circumstances, and it may be zero or even differ in sign in a setting where the timing effect is different.

The usual stockpiling prediction is strongest when a good is storable, buyers can afford to purchase earlier, and storage costs are low. It may be weak when the good spoils quickly, storage is expensive, the buyer has limited space or cash, or consumption needs cannot be shifted between periods. For goods that cannot be stored, an expected price change can still affect purchase timing if buyers can postpone a durable purchase, but the relevant cost is then the value of waiting rather than a physical storage charge.

Expectations are not the only determinant of current demand. To isolate their effect, hold the current price and other relevant factors fixed. If the current price itself changes, buyers move along the current demand curve as well. If expectations and the current price both change, both effects can occur, so they should be identified separately rather than combined into a single direction-of-change claim.

Common Exam Trap

Suppose the schedule in the first example applies, the current price is $20, and the expected future price falls from $25 to $21. A common error is to substitute $21 as the current price, as though the future price expectation were today’s price. That incorrect calculation gives $150-4(21)+2(25)=116$, which changes the wrong variable.

The current price remains $20. Substituting the new expected future price gives $150-4(20)+2(21)=150-80+42=112$. Compared with the original quantity of 120, current demand falls by 8 units. The correct conclusion is a leftward shift caused by the lower expected future price, not a movement along the demand curve caused by a change in today’s price.

Key takeaway: Expected future prices can change current demand by changing when buyers purchase. Stockpiling is favored when the discounted expected future price exceeds the current price plus the cost of buying and holding the good; postponement is favored when waiting is cheaper. Always distinguish that timing response from a change in the current price.

Check Your Understanding

For each problem, hold other demand determinants fixed and identify the relevant timing or demand-schedule calculation.

A market’s illustrative weekly demand schedule is $Q_0^d=90-2P_0+E[P_1]$. At a current price of $15, the expected future price rises from $18 to $22. Find current quantity before and after, and state the direction of the shift. (Answer: 78 units before, 82 after; current demand shifts right by 4 units.)
A buyer faces a current price of $30, storage cost of $1.50 per unit, an expected price of $34 in one year, and an effective annual interest rate of 5%. Compare the current cost including storage with the discounted expected future price. (Answer: Current cost is $31; discounted expected future price is $34/1.05=$$32.38 to the nearest cent, so buying now is preferred.)
A buyer can purchase a device now for $75 or next month at an expected price of $68. The interest rate for the comparison is 0%, and the dollar-equivalent cost of waiting is $4. Should the buyer purchase now or wait? (Answer: Wait; the expected $7 saving exceeds the $4 waiting cost by $3.)
An illustrative demand schedule is $Q_0^d=200-5P_0+1.5E[P_1]$. At a current price of $12, the expected future price rises from $16 to $20. Calculate both current quantities and the change. (Answer: 164 units before and 170 after; current demand shifts right by 6 units.)
A firm faces a current price of $60, storage cost of $3 per unit, an expected future price of $68 in one year, and an effective annual interest rate of 10%. Should it stockpile under the simple timing model? Find the expected future price at which it would be indifferent. (Answer: No; the current cost is $63 and the discounted expected future price is $68/1.10=$$61.82 to the nearest cent. Indifference occurs when the expected future price is $63(1.10)=$$69.30.)

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