A firm is considering whether to market a new type of computer game during the upcoming Christmas season. The profit contribution of this computer game will depend on the extent of the demand θ. where θ denotes the number of thousands of copies of the computer game to be sold. It is estimated that the net profit of marketing the computer game will be approximately 2θ² — 500,000 dollars. Assume that the firm’s initial prediction of demand distribution on θ is a uniform density on the interval 0 ≤ 0 ≤ M. in terms of M determine the following.
a. For what value of the demand θ should the firm market the new type of toy?
b. What is the expected value of θ?
c. How much should the firm be willing to pay to find out exactly what the demand θ will be?