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Chapter 11: Monopoly (Monopoly Profit Maximization (Elasticity of demand…

- - - - MR = ∂R/∂Q
        MR = Marginal revenue
        ∂R or ∂R(Q) = Change in revenue
        ∂Q = Change in market quantity
      - R = pQ
        R = Revenue
        p = Price
        Q = Market quantity
    - - MR = p + (∆p/∆Q)Q
        MR = Marginal revenue
        p = price
        (∆p/∆Q) = Slope of demand line
        Q = Market quantity
      - MR = p(1 + 1/𝜺)
        From: MR = p + p(∆p/∆Q)(Q/p) where p/p = 1 added
    - - 𝜺 = (∂Q/∂p)(p/Q)
        From: 𝜺 = (∂Q/Q)/(∂p/p)
        𝜺 = Market/Price elasticity of demand
        (∂Q/Q) = percent change in quantity
        (∂p/p) = percent change in price
  - - - Marginal revenue always below demand curve
      - Marginal revenue and demand curve are both downward sloping.
    - - Marginal revenue and demand curve are both horizontal for an individual firm. (Demand curve for market is downward sloping)
      - Marginal revenue is equal to the demand curve.
  - - - Find Q
        
        MR = MC
        
        To find MR
        R = pQ
        MR = derivative of R
        
        To find MC
        C = FC + VC
        MC = derivative of C
      - Find p
        
        Sub Q into p(Q) to find p
      - Shutdown?
        
        Short run AVC = VC/Q. If AVC > p, shutdown
        
        Long run, AC = C/Q. If AC > p, shutdown.
        Or, π = R - C. If π < 0, shutdown.
        
        If you only have pQ, MC, and FC
        Find Q via MR = MC
        π = (MR - MC) * Q - FC. If π < 0, shutdown.
  - - - A given Q can correspond to more than one monopoly optimal price.
      - Shift in demand curve may cause price and/or quantity to change.
      - Supply is not independent of demand.
  - - - 𝜺 = -1, MR = 0
      - 𝜺 = 0, perfectly inelastic
      - 𝜺 > -1, elastic, MR is positive
      - -1 < 𝜺 <= 0, inelastic, MR is negative
      - 𝜺 → -∞, elastic, MR = p, Q = 0
- - - - In other words: what percentage of price is due to markup?
      - Markup: what firm with market power charges above price of a competitive firm
  - - - Find Qc of competitive market
        MC = p
      - DWL = height *base /2
        DWL = ((p(Qm) - p(Qc))*(Qc - Qm)) /2 + ((p(Qc) - MC(Qm))*(Qc-Qm))/2
        DWL = ((p(Qm) - MC(Qm))*(Qc - Qm)) /2
        DWL = deadweight loss
        p(Qm) = price of monopoly quantity on the demand curve
        p(Qc) = price of competitive quantity on the demand curve
        MC(Qm) = price of monopoly quantity on the MR = MC intersect
        Qc = competitive quantity
        Qm = monopoly quantity
      - Find Qm of monopoly
        MC = MR
- - - - aka incumbent effect: market profitably supports only one firm
      - Condition for natural monopoly:
        C(Q) < C(q1) + C(q2) + ... + C(qn), where Q = q1 + q2 + ... + qn
        Or simplified for this course:
        C(Q) < C(Q/2) + C(Q/2)
      - Natural monopoly has strictly declining average cost (AC)