Question

I have already solved the math portion (Expected cost = $2.2M and Expected Rev = $4.4M). I need someone to either check my drawing of the decision tree or post one so I can check it against mine. A risk-neutral firm is considering expanding output to supply an expected increase in demand. The cost of this initiative is expected to be $2 million (probability 0.8) or $3 million (probability 0.2). Revenues will be $5 million if demand is indeed strong (probability 0.7) but only $3 million if demand is weak (probability 0.3). Construct a decision tree to determine whether the firm should undertake the expansion.

Answer 1

Solution:

One important thing to note about decision trees is that it carries branches of decisions and uncertainties, and at any one time, only one chain of event shall be followed. Thus, decision trees do not include expected values, and the branches end at net profits or benefits or utility (expected values are calculated later on using these end values).

Correspondingly, we have the following decision tree for the given situation:

demand (ssmirbo- (ost Irm $2 rmilu Highlost (prに0.2) weak dd C3 expand $0 Expected profit 1.68 + 0.24 + 0.28 +。 - $2.2 m me nsk-naaral fYm Should undertake hu- ex pans expansim