pencils are produced in a perfectly competitive industry.The

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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

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
y=0,P

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