Firm X Is Currently Selling a Consumer Good at a Standard

Firm X is currently selling a consumer good at a standard price, but is also considering cutting its price. The main risk facing the firm concerns the course of the economy in the near-term: whether the economy will grow at a steady pace (G) or whether it will experience a recession (R). The table below shows the firm's possible profit results (in $ millions). Finally, the firm judges that there is a 70% chance of growth and a 30% chance of a recession.
$\begin{array} { | l | c | c | } \hline & \text { Growth } & \text { Recession } \\\hline \text { Standard Price } & 20 & - 10 \\\hline \text { Cut Price } & 15 & 0 \\\hline\end{array}$ (a) Firm X must make its decision now (before knowing the future course of the economy). Which pricing policy maximizes its expected profit?
(b) Now suppose that Firm X can wait and decide its pricing decision after it knows the course of the economy. Determine its best pricing decisions and its overall expected profit.
(c) Firm X has hired a macroeconomic forecaster. The macro forecast is either positive (+) or negative (–). In the past, the forecaster has made positive forecasts prior to 4 of 7 periods of economic growth: Pr(+|G) = 4/7. In turn, he has made negative forecasts prior to 2 of 3 recessions: Pr(–|R) = 2/3. Compute Pr(G|+) and Pr(G|–)
(d) Suppose the forecasting report can be purchased for $.2 million. Should Firm X buy the report? Explain your answer.