Nonrival Knowledge and Its Economic Properties

Why Knowledge Has Distinctive Economic Properties

A machine can usually be used in only one production process at a time. A written design, mathematical method, or software routine can often be used by many producers at once. That contrast matters for economic growth: knowledge can support additional production without being used up, even though the people and physical resources needed to apply it remain limited.

The key is to separate two questions. Does one person’s use reduce the amount available to others? That is the question of rivalry. Can an owner prevent others from using it? That is the question of excludability. Treating the questions separately helps explain why knowledge may be easy to reuse but still controlled by a patent, license, trade secret, or access rule.

Definition: A good or input is nonrival when one user’s use does not reduce the amount available to another user. It is excludable when someone can prevent a person who has not obtained permission from using it. Knowledge is often nonrival, while its excludability varies with its form and the institutions governing access.

A pure public good is both nonrival and nonexcludable. Knowledge should not automatically be called a pure public good: a technical manual may be nonrival once copied, yet access to the manual can be restricted. Conversely, some knowledge is hard to keep exclusive, particularly after it has been widely disclosed. “Partly excludable” describes this range rather than a single fixed property.

Reusing Knowledge Does Not Divide It

Consider a production relationship in which firm $i$ uses capital $K_i$, labor $L_i$, and knowledge level $A$:

Y_i=A\sqrt{K_iL_i}.

For this illustration, assume $A$ is a codified production method that each firm can apply, firms have separate capital and labor, and using the method does not congest it or reduce its effectiveness. The function is a simplified example, not a claim that all technologies have this form. Under these assumptions, each firm can use the same $A$; the knowledge input is not allocated by dividing it among firms.

Worked Example: One Production Method, Two Firms

Two hypothetical workshops use the same production method, with $A=2$. Each workshop has $K_i=100$ units of capital and $L_i=25$ units of labor. Use $Y_i=A\sqrt{K_iL_i}$ to calculate output for each workshop and total output. Then compare with the mistaken calculation that divides $A$ equally between them.

Method. Apply the production function separately to each workshop because their capital and labor are distinct, while the method is available to both.

For either workshop, $K_iL_i=100\times25=2{,}500$, and $\sqrt{2{,}500}=50$. Thus its output is $Y_i=2\times50=100$ units. The two workshops together produce $100+100=200$ units.

The mistaken calculation gives each workshop half the knowledge level, $A/2=1$. It then calculates output as $1\times50=50$ per workshop, or $100$ in total. This incorrectly treats knowledge like a fixed stock of rival input that must be split. Under the stated assumptions, each workshop uses $A=2$, so the correct total is 200 units.

Check. Each workshop’s capital and labor are unchanged, and both use the same method. Adding the second workshop therefore adds another 100 units of output without reducing the first workshop’s output.

This example also shows why nonrivality does not mean that production uses no scarce resources. The method can be reused, but capital and labor cannot be assumed unlimited. A scarce specialist may need to train each user; adapting a design may require engineering time; and production may require additional equipment. These are constraints on applying knowledge, not evidence that the underlying codified method is necessarily rival.

Fixed Development Cost and the Cost of Reuse

Knowledge is often costly to create but inexpensive to reproduce or apply to an additional user. A basic cost model separates a fixed development cost $F$ from a per-user access or reproduction cost $c$. If $N$ users each receive one copy, total cost is $C(N)=F+cN$, and average cost per user is $C(N)/N=F/N+c$. This model assumes the fixed development cost is incurred once, each user requires the same variable-cost access, and there are no capacity costs or other changing costs.

As $N$ increases, the fixed-cost component $F/N$ falls. That arithmetic can create substantial scale economies in distributing knowledge. It does not imply that the marginal cost is always zero: copying, delivery, customer support, or permission management can have a positive cost. Nor does a low reproduction cost eliminate the original cost of developing the knowledge.

Worked Example: Spreading a Software Development Cost

A hypothetical firm spends $180,000 developing a training program. Each user’s account and delivery cost $6, and the program is provided to 3,000 users in the first year. Assuming no other costs, calculate total cost, average cost per user, and the change in average cost if the program instead serves 9,000 users.

Method. Use $C(N)=F+cN$, then divide total cost by the number of users. The assumptions mean that the development cost remains fixed and that the $6 cost applies to each user.

At 3,000 users, variable cost is $6\times3{,}000=\$18{,}000$. Total cost is $\$180{,}000+\$18{,}000=\$198{,}000$. Average cost is $\$198{,}000/3{,}000=\$66$ per user.

At 9,000 users, variable cost is $6\times9{,}000=\$54{,}000$. Total cost is $\$180{,}000+\$54{,}000=\$234{,}000$. Average cost is $\$234{,}000/9{,}000=\$26$ per user.

Check. The development cost per user falls from $\$180{,}000/3{,}000=\$60$ to $\$180{,}000/9{,}000=\$20$. Adding the unchanged $\$6$ per-user cost gives the calculated averages of $66 and $26. The additional users do not make the development cost disappear; they spread it across more users.

Excludability Depends on Access and Institutions

The practical ability to exclude users varies. A firm may keep a process secret, limit access to a database, or require a license to use a design. Patent rights can grant legal control over specified uses, while copyright can protect particular expressions of knowledge. These arrangements can make knowledge more excludable, but they do not turn it into a rival input: one firm’s authorized use of a design need not prevent another authorized firm from using it at the same time.

Exclusion is rarely perfect in every respect. A patent has a defined legal scope and duration; a license may permit some uses but not others; and a secret can lose its protection if disclosed. Some knowledge is tacit, meaning that using it effectively depends on experience or skill that is difficult to write down and transmit. In that case, the constraint may be the time of people who possess the skill, rather than the rivalry of a codified formula.

A useful way to analyze a case is to ask what exactly is being reused and what exactly is scarce. A digital file may be copied without reducing the original, but server capacity and support staff can be congestible. A production technique may be available to several firms, but specialist equipment may not be. Describing both the knowledge and the complementary resources prevents the error of calling an entire activity “nonrival” when only one input has that property.

Identify the knowledge.
Specify whether it is a design, formula, software routine, skill, or another form of know-how.

Test for rivalry.
Ask whether one user’s use directly reduces what is available to other users, holding other resources and capacity fixed.

Test for exclusion.
Identify legal rights, secrecy, technical controls, or contracts that can restrict access, and note their limits.

Separate complementary inputs.
Check whether labor, equipment, delivery, or adaptation is scarce even if the knowledge itself is reusable.

Why Private and Total Returns Can Differ

A creator may capture value through its own use of an invention, sales, licensing fees, or another enforceable right. Other users may also benefit if they gain access or apply the idea in a different setting. The creator’s private return counts benefits and costs that the creator bears or receives. A broader accounting of total value includes benefits to all users and real resource costs, but does not count a payment from one party to another as an additional resource benefit: the payment is a transfer between them.

This distinction identifies a possible gap without assuming that every invention creates one. If the creator can capture nearly all the value and access is costly, the gap may be small. If other users gain substantial value that the creator cannot charge for, total value can exceed the creator’s private return. Measuring that difference in a real setting requires evidence about benefits, costs, access, and rights.

Worked Example: Private Return and Total Value

A hypothetical research firm spends $110,000 developing a production method. During one year, using it in its own operation gives the firm $90,000 in additional operating surplus. A license brings in $10,000 from another producer, whose gross benefit from using the method is $36,000. The license and adaptation require $2,000 in real resources. Calculate the firm’s private net return and the total net value across the two producers for this year. Assume the stated amounts are all relevant benefits and costs, and ignore any benefits beyond this year.

Method. First calculate the creator’s receipts and subtract its development cost. Then calculate total benefits across users and subtract real resource costs. Treat the license payment as a transfer, not as a separate addition to total value.

The research firm’s private receipts are $\$90{,}000+\$10{,}000=\$100{,}000$. Its private net return is $\$100{,}000-\$110{,}000=-\$10{,}000$.

Across both producers, the stated operating benefits total $\$90{,}000+\$36{,}000=\$126{,}000$. Subtract the $110,000 development cost and the $2,000 real licensing and adaptation cost: total net value is $\$126{,}000-\$110{,}000-\$2{,}000=\$14{,}000$.

The $10,000 license receipt is income to the creator and a payment by the user. It is not added again to the $126,000 of operating benefits. Check. The creator’s net return is negative $10,000, while the stated total net value is positive $14,000, a difference of $24,000. That difference equals the other producer’s $36,000 gross benefit less the $10,000 transfer and $2,000 real access cost.

Deriving the Nonrival Reuse Result

The arithmetic behind reuse is simple, but its assumptions matter. Suppose each of $n$ firms uses the same knowledge level $A$ and has its own capital and labor. Assume knowledge use by one firm does not change $A$ for any other firm. With firm-level output $Y_i=f(A,K_i,L_i)$, total output is the sum of the firms’ outputs:

Y_{\mathrm{total}}=\sum_{i=1}^{n} f(A,K_i,L_i).

Adding another firm with inputs $K_{n+1}$ and $L_{n+1}$ gives:

Y_{\mathrm{total,new}} = Y_{\mathrm{total,old}}+f(A,K_{n+1},L_{n+1}).

The existing firms retain the same $A$, so their outputs do not fall merely because another firm uses the knowledge. The new firm’s output is added, subject to its own resources and the model’s assumptions. Replacing $A$ with $A/n$ would describe a different technology in which knowledge is rival and divided; it does not follow from the nonrival model.

The result is limited to the stated case. Congestion, scarce expert time, restricted access, or differences in users’ ability to apply the method can reduce the benefits of adding users. Nonrivality is a property of the knowledge input under specified conditions, not a guarantee that every user can obtain equal output at no cost.

Common Mistakes and Economic Significance

Equating nonrival with nonexcludable. A method can be usable by several firms without depletion and still be protected by a license or secrecy.
Equating nonrival with costless. Creating knowledge can require substantial resources, and distributing or applying it may also cost money.
Dividing knowledge among users. If the model says each user can apply the same knowledge, do not replace $A$ with $A/n$ without a specific assumption that makes the input rival.
Ignoring complementary inputs. Reusable knowledge does not make labor, capital, capacity, or specialist time unlimited.
Counting a transfer twice. A license fee affects who receives income, but it is not an additional social benefit on top of the user’s underlying gain.

These properties help explain why knowledge can support repeated production and why access rules can matter for who benefits from it. They also clarify why a creator’s return may not match the total value created: control can be incomplete, and some benefits may accrue to other users. The detailed analysis of how those benefits spread and how research incentives respond requires additional tools.

Key takeaway: Knowledge is often nonrival because one user can apply it without reducing its availability to others, but it may still be partly excludable through law, secrecy, technology, or contract. Reuse can spread fixed development costs, while the creator’s privately captured return may differ from the total value generated.

Check Your Understanding

Work through each problem by stating the relevant assumptions and keeping knowledge distinct from rival inputs.

A process manual is used simultaneously by four independent plants. Each plant has its own staff and machinery, and one plant’s use does not affect the others. Is the manual rival under these assumptions? Are the staff and machinery necessarily nonrival? (Answer: The manual is nonrival; staff and machinery are separate rival inputs and are not made nonrival by the manual’s properties.)
A hypothetical design costs $96,000 to develop and $3 per user to distribute. For 4,000 users, calculate total cost and average cost per user. (Answer: Total cost is $108,000; average cost is $27 per user.)
A software routine has a fixed development cost of $150,000 and a per-user support cost of $5. Calculate average cost for 5,000 users and for 15,000 users, assuming no other costs. (Answer: $35 per user at 5,000 users; $15 per user at 15,000 users.)
A creator spends $70,000 developing a method and receives $55,000 in operating benefits plus $8,000 in license fees. Another user gains $20,000 in gross operating benefit and incurs $3,000 in real adaptation costs. Calculate the creator’s private net return and total net value, treating the license fee as a transfer. (Answer: Creator’s private net return is $-\$7,000$; total net value is $55,000+20,000-70,000-3,000=\$2,000$.)
A firm owns a patent on a production technique, while several licensees can use the same technique at once. The technique does not become less effective with additional users, but each licensee needs a scarce specialist for one week of training. Identify the rivalry and excludability properties. (Answer: The technique is nonrival under the stated assumptions and partly or substantially excludable through the patent and licensing; specialist training time is rival because it is scarce.)

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