一道微观经济学的题目，很急，谢谢~~~~~

来源：百度知道 编辑：UC知道 时间：2024/06/04 02:04:44
pencils are produced in a perfectly competitive industry. The demand function for pencils is given by D(p)=100-p. The average cost of producing y units is given by AC(y)=4+(2-y)^2
问：Determine the individual supply curve of each firm and find the long run industry supply curve under the assumption of free-entry

你好楼主，解答如下。
For each firm, its goal is to maximize the profit. In a market of free entry ,
it requires P=MC.
TC=AC*y=4y+y*(2-y)^2
MC=d(TC)/dy=3*y^2-8*y+8
Solve this second-oder equation 3*y^2-8*y+8-P=0,we get
y=4/3+((3P-8)^0.5)/3 or y=4/3-((3P-8)^0.5)/3(This does not make sense,for higher P results in higher y for supplier)
and P must greater than min(AC)=4
So supply function for each firm is
y=4/3+((3P-8)^0.5)/3,P>=4,
y=0 P<=4
For long turn ,because market is of free_entry,so the equilbrium must be achieved at the min(AC)=4
So the long run supply curve is y=infinity,P>=4
y=0, P<=4
先有MC=P 求供给线。
由AC=4+(2-y)^2 求得TC，再求得MC=d(TC)/dy=3*y^2-8*y+8
P=MC，移项德二次方程3*y^2-8*y+8-P=0，解得
y=4/3+((3P-8)^0.5)/3 or y=4/3-((3P-8)^0.5)/3（舍去）
再求关门条件，P》=min(AC)=4
供给曲线为y=4/3+((3P-8)^0.5)/3 P》=