Economic forecasting

profileMick Green
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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.

a. What is the profit equation for the monopolist? b. 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

a. Construct point and normal 90% interval forecasts for the next four quarters (third quarter 2019 to second quarter 2020).

b. 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.

3. In the trend model Tt = 0 + 1*Timet, suppose that 1 > 0.

a. Is the series expected to grow or decline in future periods?

b. Does this mean that the series grow or decline with certainty in every period?