最新钱报（七）|两种产品的需求函数求解

马二哥

2021/11/05

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今天小编为大家带来最新钱报（七）
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本期推文阅读时长大约6分钟，请您耐心阅读。
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Today, the editor brings you the latest money report (7)
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注：建议阅读此文时可下载该篇文献，以便于更好学习需求函数如何求得。
Note: It is recommended to read this article when you read this article so that you can better learn this document.

01
疑问：两种商品竞争的需求函数如何求解？
问题

小编最近各种学术问题困扰，其中之一就是知网大佬的论文里面的需求函数是如何根据效用函数得来的呢？您的科研道路上是否也有过我这样问题呢？经过小编的努力思考，这个问题终于迎刃而解啦！
02
问题还是要多琢磨，我们先来分析吧！
解决
关于如何求解的问题，我们从例子中开始看吧！
We start looking at how to solve the problem!



我们首先来看这篇文章如何根据效用函数求需求函数的呢？
前提：两种产品，一种新产品，一种再制造产品，研究它们的需求函数如何求得？
Let's first see how this article is based on the utility function to demand a demand function?
Prerequisites: Two products, a new product, a re-manufacturing product, how to study their needs functions?
1.红线框着的是新产品与再制造产品的效用函数。然后我们根据：
1.The red line frame is the utility function of new products and re-manufacturing products. Then we according to:



2.根据这个式子我们就可以求出来三个临界支付点Vi(i=1,2,3)啦！
2. If we can ask for three critical payment points Vi (i = 1, 2, 3)!




编辑搜图

由于原文中的V3看不清，小编在此重新编辑了。
Due to the V3 in the original text, Xiaobian re-edited it.
3.求得临界支付点我们就可以得出购买两种产品的最低支付意愿啦！
我们可以看到v1和v3是消费者购买两种产品分别的最低支付意愿，当V小于V1和V2中的最小值时，消费者不会购买任何产品，消费者需要购买新产品的效用，其必须大于V1和V2中的较大值。而购买再制造品的充要条件是V3<V<V2。购买哪一种产品的具体情况也可以看上述图片呢。
3. We can get the lowest payment of the two products!
We can see that V1 and V3 are consumers to buy two products, the minimum payment will, when V is smaller than the minimum of V1 and V2, consumers will not purchase any products, consumers need to purchase new products, Must be larger than the larger value in V1 and V2. The charging condition for purchasing re-made products is V3<v <v2.You can also see the above pictures on the specific situation of purchasing which product.
4.为了得出制造品和新产品的市场竞争策略。我们要在此对V1,V2,V3的大小进行讨论。
4. In order to obtain market competition strategies for manufacturing products and new products. We want to discuss this on the size of V1, V2, V3.
1）先假设V1<V3。
1) Assume the V1


当V1>V3时，比较V2与V1的大小，通过做差比较出V2<V1。
When V1> V3, the size of V2 and V1 is compared, V2



所以V2<V1<V3,这种情况下，根据上面购买再制造品的充要条件可知消费者这种情况不会购买再制造产品。此时市场需求只有新产品，新产品的条件为V>V1即可。这个时候新产品的效用就是1-V1。
2)假设V1>V3
Therefore, in this case, it is known that consumers will not purchase re-manufacturing products according to the charging conditions of the re-manufacturing products above. At this time, market demand is only new products, and the conditions for new products are V> V1. At this time, the utility of new products is 1-V1.
2) Assumption V1> V3


当V1>V3时，比较V2与V1的大小，通过做差比较出V2>V1，所以V2>V1>V3,这种情况的话再制造产品就会参与竞争。此时购买新产品的V>V2,为购买新产品的充要条件。
此时新产品的需求就为：
When V1> V3, the size of V2 and V1 is compared, and V2> V1 is compared by doing the difference, the product of V2> V1> V3, this situation will participate in the competition. At this point, V> V2 of the new product is purchased to purchase a new product.

The demand for new products at this time is:



再制造产品的需求就为：



您读到者可能会思考需求怎么来的，需求函数的求解用了积分，这里的积分就相当于纸老虎，不要被吓着了。小编给大家技巧：
根据新产品的积分，新产品的需求直接就为：1-V2
根据再制造品的积分，再制造品的需求就等于V2-V3。这样就可以分别求出彼此的需求啦！
When you read, you may still think about the demand, the demand function is solved, the points here are equivalent to paper tigers, don't be scared. Xiaobian is tip:

According to the integral of new products, the demand for new products is directly: 1-V2

According to the integral of the reminder, the demand for remanding products is equal to V2-V3. This will ask each other's demand!

03
求解技巧总结
总结
1.算出三个临界支付值Vi（i=1,2,3)，其计算式子为U1=0,U1=U2,U2=0，算出Vi
2.V1,V3为两种情况的最低支付意愿。V2为两种临界支付意愿。
3.一种情况V>max(V1,V2),另一种情况，V<min(V1,V2)。分析情况。
4.分情况讨论
1)V1>V3.
2)V1<V3.
1. Calculate three critical payment values vi (i = 1, 2, 3), which calculates U1 = 0, U1 = U2, U2 = 0, calculates VI
2.v1, v3 is the lowest payment of two situations. V2 is a willingness to pay for two crities.
3. One case V> max (V1, V2), another case, V<min (v1,="" v2).="" analysis.<="" div="">
4. Discussion
1) V1> v3.
2) V1<v3.

04
练习
两个产品的效用函数:
Effective functions for two products:



根据小编前面所讲求出各自分别的需求函数:
According to the front of the small series, the respective demand functions are obtained.







具体求解过程和条件范围读者自己去计算呢，求出了V1,V2,V3之后如果还是实在不会，小编也总结出的两种需求函数分别为：
The specific solution process and condition range readers should calculate itself. If you find V1, V2, V3, if it is still not, the two demand functions that have been summed up separately.



这是小编自己总结出来的简单技巧，具体的分段条件范围还需要读者自己去计算呢，在算出Vi后就可以求出分段的条件范围啦！此方法只用于大家不理解怎么求的情况，如果想要为什么这样求解以及含义，请读者自己在求解中揣摩吧！
This is a simple skill that Xiaobian summed up. The specific segmentation condition range needs to be reader to calculate it. After calculating VI, you can find a segmentation range! This method is only for everyone to seek how to ask, if you want to solve this and meaning, readers yourself try to figure it out!

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参考资料：Google翻译
参考文献：2018+消费者后悔预期对IR市场进入策略的影响_高鹏
本文由LearningYard学苑整理并发出，如有侵权请在后台留言！

文案 | Qian
排版 | Qian
审核 | Tian