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zoewong · 2022年04月21日

Q怎麼求出來

NO.PZ2018062003000067

问题如下:

For a market of perfect competition, the demand schedule is defined as P = 165– 3Q (for Q ≤ 55). For each company in the long-run, the total cost is given by: 125 + Q + 5Q2, the average cost is given by: 125/Q + 1 + 5Q, the marginal cost is given by: 1 + 10Q. At which of the following price, new competitors are most likely to enter?

选项:

A.

135.

B.

51.

C.

45.

解释:

B is correct

In a perfectly competitive market, for each company in the long-run, only when MC = AC = P, would the equilibrium be expected.

we can draw the equation:

MC=AC: 1 + 10Q = 125/Q + 1 + 5Q, Q=5.

At that time, P=MC= 1 + 10Q = 51

If the price is higher than 51, new competitors will enter for economic profits .

考点:完全竞争市场

解析:在完全竞争市场中,存在条件 MC = AC = P,

联立MC=AC: 1 + 10Q = 125/Q + 1 + 5Q, Q=5.,

解得:P=MC= 1 + 10Q = 51。

注意到,之所以不用需求函数 P = 165– 3Q参与联立是因为这里给的是整个市场的需求函数,而非单个厂商的 。但是题目给定的MC,AC都是单个厂商的关系式,所以整个市场的需求函数与它们并不匹配,不能参与联立。

老師,我知道原理但不會求q

1 个答案
已采纳答案

笛子_品职助教 · 2022年04月21日

嗨,努力学习的PZer你好:


Q就是用MR = MC联立之后,解方程。


计算Q等于多少,也就是解方程:1 + 10Q = 125/Q + 1 + 5Q。


以下是解二元一次方程的方法:


第一步,去除分母上的Q,等式两边同时乘以Q

Q+ 10Q^2 = 125 + Q + 5Q^2


第二部:把所有的Q转到一边

Q+ 10Q^2 - (125 - Q - 5Q^2) =0

5Q^2 -125 =0


第三步:计算出Q

Q^2 = 125/5

Q=5

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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