Externalities Example

Edgeworth box example

-> Given:

-> If there is not an authority defining if in the house we can smoke the agents will fight.

The Market Signal for Merging:

-> Steel mill & Fishery: price takers.

SCENARIO A: separate

Steel mill: max π (S, x) = psS – Cs (S, x) Suppose  Cs (S, x) = S2 + (x-4)2 and ps=12. F.O.C1 (∂π/∂s) =0; S* = 6 F.O.C2 (∂π/∂x) =0; x* = 4 πS = 36

Fishery: max π (f, x) = pFf – CF (f, x) Suppose  CF (f, x) = f2 + xf and pF=10. F.O.C (∂π/∂f) =0; 10 -2f*- x = 0; f* = 5 – (1/2)x Given the choice of x*=4 by Steel mill, f* = 3. πF = 9

π_S + π_F = 36 + 9 = 45.

SCENARIO B: Merged

Merger: Steel mill + fishery: max π (S, f, x) = 12S + 10f – S² – (x-4)² – f² – xf

F.O.C₁ (∂π/∂s) =0; S^M = 6

F.O.C₂ (∂π/∂f) =0; 10 -2f*- x = 0; x^M = 10 – 2f^M

F.O.C₃ (∂π/∂x) =0; -2(x^M-4) – f^M = 0

Substituting F.O.C₂ in F.O.C₃: x^M = 2 and f^M = 4

π_M = 48 while in scenario A it was π_S + π_F = 36 + 9 = 45.

=> Intuition: When there are signal profit => the market should provide incentives to merging.

• The firms would also care of social cost of steel production making everybody better off.
• Scenario A: S* = 6; x* = 4, f* = 3, π_S + π_F = 45
• Scenario B: S^M = 6; x^M = 2, f^M = 4 , π_M = 48

The Steel mill now cares about the damage provoked on the fishery:

• In scenario A, Steel mill F.O.C₂ (∂π/∂x) =0          (∂C_s(S, x)/∂x) =0
• In scenario B, Steel mill F.O.C₃ (∂π/∂x) =0         (∂C_s(S, x)/∂x) +(∂C_F(f, x)/∂x) =0