Example of Monopolistic Comp.
(Krugman & Obstfeld, International Economics, Ch.6)
industry sales S, firm output X, price P
Demand: X = S[1/n-b(P-P*)], if P=P*, X=S/n
Calculation of Marginal Revenue:
– inverse demand P-P*= 1/bS(S/n-X), dP/dX= -1/bS
– Marginal Revenue: P+XdP/dX = P - X/bS
Costs: TC = F + cX, AC = F/X + c, MC = c
Example, cont’d.
• SR Equilibrium: MR=MC:
– P - X/bS = c or P - c =μ = 1/bn.
– COMP curve: monopoly power and price fall with n.
• BE: P-MC = μ = F/X=nF/S, avg. costs rise with n
• Full Equilibrium: BE & COMP intersect
– 1/bn = nF/S
– n* = √(bF/S)
• As market size S increases
– BE shifts down
– n and X rise, μ falls
Example of Auto Market
(Krugman & Obstfeld, International Economics, Ch.6)
F = 750,000,000, c = 5,000
X = S[1/n - 1/30,000(P-P*)]
AC = 750 mil/X + 5000
France S=900,000, Germany S*=1.6 million
France Germany Combined
P=5000+30,000/n:
10,000 8,750
8,000
AC=5000+(F/S)n: 10,000 8,750
8,000
n*=(30,000S/F)½: 6
8
10
Example of Auto Market
Price
4 10
4
3 10
4
2 10
4
1 10
4
68
0
0
10
20
30
Number of Firms
COM P
BEFr
BEGer
BEFr&Ger
Comparison of Auto Markets
France
S 900K
n=6
X = 150K
F/X = 5000
P = 10000
Germany
S =1600K
n= 8
X =200K
F/X = 3750
P = 8750
Combined
S = 2500K
n = 10
X = 250K
F/X = 3000
P = 8000