Additional Decision Theory Problem

Product development. A small firm has developed a new machine to manufacture

printed circuit boards. The machine is a considerable improvement over machines

currently on the market. If management decides to manufacture this new machine, it

is almost certain that the larger firms in the industry will copy the design and take the

majority of the market through price competition. Therefore, management feels that

the decision of whether or not to manufacture depends solely on expected profit in the

first year of production. The costs of setting up the production lines and marketing the

new machine are estimated to be $$250,000.$ The variable cost of the machine is about

$$10,000$ per machine, and the firm plans to sell the machine for $$15,000.$ To simplify

the problem, let us assume that the market demand will be either $50$ or $75$ machines,

that is$,$ there is a $50/50$ chance of either prior to obtaining additional information.

Assume that demand and production are evenly distributed throughout the year.

Management believes that these two levels of demand are equally likely. Market

research can be done at a cost of $$10,000.$ In the past, this market research has

successfully predicted demand level $75$ percent of the time; that is$,$ P $($research

indicated demand will be $50$ machines given the demand is for $50$ machines$)=\mathrm{.}75.$

a$.$ Draw and label the decision tree.

b$.$ Evaluate the decision tree.

c$.$ What is the optimal EMVer strategy?