Consider an industry with n firms with outputs y¹,..y", facing an input price vector W= (W1₁,..wn). The total industry output is Y = 19. The firms' cost functions are Ci(w, y) = a(w) + 0¹ (w) [y] (to avoid confusion, note that [y] is y to the power 3), j = 1..n, where a (w) and (w) are functions of input prices. The industry aggregate costs are C = -1 C (w, y). When can the aggregate costs be written as some function of input prices and total industry output (namely, when can it be written as C = a(w) + 0(w)Y)? (a) when a; (w) = 0 for all firms (b) when (w) is the same (0 (w) = 0(w)) for all firms (c) when 3 = 1 for all firms (d) when 3 = 1 and 0¹ (w) = 0(w) for all firms

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter12: The Partial Equilibrium Competitive Model
Section: Chapter Questions
Problem 12.2P
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16. Consider an industry with n firms with outputs y¹,..y", facing an input price vector
W = (w₁,..wn). The total industry output is Y =
1. The firms' cost functions
are Ci(w, y¹) a(w) +0¹ (w) [y] (to avoid confusion, note that [y] is y to the
power 3), j = 1..n, where a (w) and (w) are functions of input prices. The industry
E-1 C (w, y). When can the aggregate costs be written as
some function of input prices and total industry output (namely, when can it be written
as C = a(w) + 0(w)Y)?
aggregate costs are C
(a) when a, (w) = 0 for all firms
(b) when 0¹ (w) is the same (0¹ (w) = 0(w)) for all firms
(c) when 3 = 1 for all firms
(d) when 3 = 1 and 0¹ (w) = 0(w) for all firms
=
=
Transcribed Image Text:16. Consider an industry with n firms with outputs y¹,..y", facing an input price vector W = (w₁,..wn). The total industry output is Y = 1. The firms' cost functions are Ci(w, y¹) a(w) +0¹ (w) [y] (to avoid confusion, note that [y] is y to the power 3), j = 1..n, where a (w) and (w) are functions of input prices. The industry E-1 C (w, y). When can the aggregate costs be written as some function of input prices and total industry output (namely, when can it be written as C = a(w) + 0(w)Y)? aggregate costs are C (a) when a, (w) = 0 for all firms (b) when 0¹ (w) is the same (0¹ (w) = 0(w)) for all firms (c) when 3 = 1 for all firms (d) when 3 = 1 and 0¹ (w) = 0(w) for all firms = =
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