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## Monopoly, Sources of Monopoly and Short-Run Analysis

Monopoly::Sources of Monopolya) Control of Scarce Inputs (OPEC, DeBeers etc.)

b) Patents or Franchise / License Scheme (RN, MD, McDonald’s, Burger King etc.)

c) Government Enforced Barriers (NFL, MLB, NBA etc.)

d) Large Economies of Scale- Natural Monopoly

e) Merger and Acquisition (M&A)

f) Illegal ways to sustain monopoly power (Bribe, Lobby, Patent killing, etc.)

:Short-Run Analysisa) Derivation:

MR (Q)= dTR (Q)/dQ= (P+Q) (dP/dQ) and FOC of profit maximization is MR(Q) = MC(Q)

So, P= MRQ –Q(dP/dQ)> MC(Q)(dP/dQ <0)

Marginal cost and price elasticity of demand: Inverse Elasticity Pricing Rule (IEPR)At point M, MR(Q) = MC(Q). According to Amoroso-Robinson formula, we know:

The l.h.s. of above equation is the monopolist’s optimal markup of price over marginal cost, expressed as a percentage of the price.

For this reason, this equation is called the inverse elasticity pricing rule(IEPR). And l.h.s. is called Lerner Index of market power.

:Monopolist’s Demand for InputsIf the input market is competitive then this monopolist must take prices of inputs as given. We can simply derive the relationship using profit as a function of L and K not Q. Let TR(⋅) and TC(⋅) denote total revenue and total cost function, respectively. Then, we know:

TR = TR(Q) = TR( f (L, K)) and TC = wL + rK . Based upon these expressions, we can get

π = π (L, K) = TR(L, K) − TC(L, K)

(some textbooks are using MPP (marginal physical product) instead of MP) So, the final expression can be:

MRPL (L,K)= MR(Q). MPL (L, K) = w

MRP K(L,K)= MR(Q). MP K (L, K)= r

where MRP is marginal revenue product, which is similar to VMP (value of marginal product, P⋅ MP ) in perfectly competitive goods market.

Now, we need to think how equation (1) is related to MR(Q) = MC(Q) . We have total cost function TC(Q) = C( f (L,K)) ≡ wL + rK .

Differentiating this function w.r.t L and K,

2º: SOC would be MRP MRP LL KK < 0, < 0

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