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Consider a coffee industry made up of 100 firms with the long-run cost curve c(q) =...

Consider a coffee industry made up of 100 firms with the long-run cost curve c(q) = 2 + q^2 /2 and 120 firms with the long-run cost curve c(q) = q^2 /4. Assume that no new firms can enter the industry. Derive the long-run industry supply curve. (Don’t worry about the constant in one of the long-run cost curves.)

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Answer #1
  • 100 firms have a long run cost function C = 2 + 0.5q^2 and 120 firms have a long run cost function C = 0.25q^2. Hence the individual supply functions are P = MC or p = 2*0.5q and p = 0.25*2q for two types of firms. This becomes q = p and q = 2p for single firms. For 100 firms, market supply is Qs = 100q = 100p and for 120 firms, market supply is Qs = 120q = 240p. Aggregate market supply is Qs = 100p + 240p = 340p.

Hence long run industry supply curve is Qs = 340p

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