A monopolist sells a product at price P and has no cost of production. The demand…

  1. A monopolist sells a product at price P and has no cost of production. The demand equation is Q = 2a – P, where Q is quantity and a is a demand shifter.
    1. What is the profit equation for the monopolist?
      What is the profit-maximizing price as a function of a? Denote the profit- maximizing price as P*.
      c. What profit is earned as a function of a? Denote the optimal profit at π*.
      d. Now suppose that a is unknown, and the firm must forecast it. The firm sets its price based upon this forecasted value of a,. The forecast error is a – â. What is the expression for the loss, π* – π(â)? Note that this expression will include both a and . What relationship does this bear to a quadratic loss function?
  2. f yt =b0 +b1*Timet +et
    And Timen = 100 for n = 100, which is the second quarter of 2019 (quarterly data). Suppose the estimated model is

𝛽0 = 0.51 𝛽1 = 0.02 𝜎2 = 16

  1. Construct point and normal 90% interval forecasts for the next four quarters (third quarter 2019 to second quarter 2020).
  2. Suppose that the yt in the previous part was yt = ln(Yt). Construct point and interval forecasts for Yt for the four quarters following 2019q2.
  1. In the trend model Tt = b0 + b1*Timet, suppose that b1 > 0.
    1. Is the series expected to grow or decline in future periods?
    2. Does this mean that the series grow or decline with certainty in every period?

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