Drastic innovation case

Similarly, we use the same idea to discuss the conditions in the drastic innovation case. Firstly, we discuss the means of fixed fee in exclusive licensing and non-exclusive licensing conditions. Second, we discuss the means of royalty in the same way.

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3.2.1 Fixed Fee

First of all, we consider that the outsider patentee decides to license the new technology to one of the firms by fixed fee licensing. The unit production cost of the licensee is , while the non-licensee drops out of the market. Therefore, we solve the monopoly problem, yielding the equilibrium quantity and the profit of the licensee:

Subsequently, the supplier sets the price of the intermediate good to maximize his profit:

It is obvious that the supplier will increase the price since the average of the production cost of the firm decrease. In other words, the supplier increases the price to compete with the outsider patentee.

In the first stage, the outsider patentee will set the fixed fee. For the drastic innovation, the licensee will accept the fee that is less than his profit. Hence, the outsider patentee will charge all the profit of the licensee:

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(ii)Non-Exclusive Licensing

Next, we consider that the patentee decides to license the new technology to the two firms by fixed fee licensing; therefore, their unit production costs equal . We substitute it into (5) and (6), yielding:

According to qualities of the firms, the supplier will set the price of the intermediate good to maximize his profit:

It also shows that the supplier increases the price contrast with . The total output also increases under both firms obtaining the innovation; thus, the supplier will receive more profit than . Comparing (36) and (41), we can find that the supplier will receive more revenue when the outsider patentee licenses the innovation to both firms. The reason is that the firm produces less output as monopoly; that is, the total output increases when the outsider patentee licenses the innovation to both firms.

Besides, the supplier sets the same price in both exclusive and non-exclusive licensing cases. As a result, the supplier obtains more revenue when the both downstream

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firms acquire the innovation.

Similarly, the outsider patentee will charge all of the profits from both firms:

Comparing (37) and (42), it shows that is larger than . The reason is that the revenue of the outsider patentee equals the profit of the firms. It is obvious that the monopoly can obtain most revenue; thus, the outsider patentee chooses to license the drastic innovation to one firm. Therefore, we have the following proposition:

Proposition 4. Under the fixed-fee licensing and a drastic innovation case, the

outsider patentee will license to only one firm.

3.2.2 Royalty

(i) Exclusive Licensing

Firstly, we consider the case that the outsider patentee chooses to license the new technology to one firm under royalty ( ) per unit of production. The unit production cost of licensee equals , while the non-licensee drops out of the market. We can solve it as a monopoly problem, yielding the quantities and the profits of the licensee:

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In the stage 2, the supplier sets the price of the intermediate good to maximize his profit:

In the stage 1, the outsider patentee sets the royalty rate in order to maximize the revenue:

Since the royalty rate is restricted, , the maximum is attained at

The outsider will choose when . We substitute it into (43) and (44), yielding:

Subsequently, we substitute r = ε into (45) to yield the price of the intermediate goods and obtain the profit of the supplier:

We can find that the suppler obtains less profit than since the total output

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decreases when the firm is monopoly and he keeps the same price of the intermediate good.

Consequently, the outsider patentee will obtain the revenue:

On the other hand, the outsider will choose when . We substitute it into (43) and (44), yielding:

We then substitute into (45) to yield the price of the intermediate goods and obtain the profit of the supplier:

Consequently, the outsider patentee will obtain the revenue:

(ii) Non-Exclusive Licensing

Next, we consider the outsider patentee chooses to license two firms under a royalty ( ); hence, the both firms‟ unit production costs equal . We substitute it into (5) and (6), yielding the quantities and the profits of the both firms:

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In the stage 2, the supplier sets the price of the intermediate good to maximize his profit:

In the stage 1, the outsider patentee sets the royalty rate to maximize the revenue, solving:

Since the royalty rate is restricted, , the maximum is attained at

The outsider will choose when . We then

substitute it into (58) and (59), yielding:

Next, we substitute r = ε into (60) to yield the price of the intermediate goods and obtain the profit of the supplier:

Similarly, since the royalty equals the product-reducing cost, the supplier will

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keep the same price. As a result, the qualities of output remain the same and the supplier receives the same revenue.

Finally, the outsider patentee will obtain the revenue:

On the other hand, the outsider patentee will set when . We substitute into (58) and (59), yielding:

Subsequently, the supplier also decides the price and his profit by :

Consequently, the outsider patentee will obtain the revenue:

The above results show that is larger than . The supplier will choose the same price in the same royalty no matter in exclusive or non-exclusive licensing conditions. Besides, the output increases when the outsider patentee licenses the innovation to both firms. As a result, the outsider patentee receives more revenue in the non-exclusive licensing condition. Thus, we have the proposition:

Proposition 5. Under the royalty licensing and a drastic innovation, the outsider

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patentee can receive more revenues if he licenses to both downstream firms.

Comparing the revenues of the outsider patentee in drastic innovation case, it is demonstrated that is also the best. Consequently, we can obtain the following proposition.

Proposition 6. Under the drastic innovation case, for the outsider patentee licensing

to both downstream firms by royalties is superior to the fixed fee.

Similarly, the outsider patentee can weaken the supplier‟s advantage when he licenses by means of royalty. The royalty affects the production cost and the price strategy of the supplier. As a result, the outsider patentee can obtain more the benefits caused by the innovation when he licenses by royalty.

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