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mc
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atc
1.
Suppose there are 100 identical demanders in the widget market and that each demander’s demand function
is: x = 10P.
The production function for any firm is x = min{S, T} and the market prices for S and T are Ps
and Pt respectively.
a.
Just add horizontally to get market demand:
X
D
= 1000100P.
b.
Note that with this production function you will always want S=T and so S* = x
and T* = x, so that if lrtc=PsS*(x) + PtT*(x) then lrtc(x) = (Ps+Pt)x
c.
Plugging in the factor prices you get: lrtc = 2x, so that lratc = 2.
So long run price must be $2.
Now,
plugging P*=2 into market demand you X*=800.
d.
S*=T*=700.
e.
NO.
It’s an increasing cost industry now.
f.
No.
Since the lratc curve is horizontal, you can not determine a unique value for the number of units
produced by the firm in longrun equilibrium. If you were TOLD the number of firms, then you could
backout the number produced by each firm.
But there are many possibilities here, so the answer is
indeterminate.
All we can conclude uniquely is that P*=2 and X*=800.
2.
A competitive firm has the following shortrun cost function: srtc(x) = x
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 Fall '06
 MASSON
 Economics, MC AVC ATC, X*=800. d. S*=T*=700.

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