Question

Question 2. A risk neutral decision maker is trying to decide whether to expand its product line by manufacturing and marketing a new product, which is “backyard storage sheds.”. The courses of action that may be chosen are: (1) building a large plant to manufacture storage sheds, (2) building a small plant to manufacture storage sheds, (3) building no plant at all. Resulting payoffs of these actions under different states of nature are as follows: (1) building a large plant to manufacture storage sheds: 200 000 TL if the market is favorable, -180 000 TL if the market is unfavorable (2) building a small plant to manufacture storage sheds: 100 000 TL if the market is favorable, -20 000 TL if the market is unfavorable (3) building no plant at all: 0 TL Probability of favorable market is same as probability of unfavorable market. (i.e., each state of nature has a 0.50 probability.)

a) Represent the decision maker’s problem by using a decision tree.
b) Determinethebeststrategythatmaximizestheexpectedpayoff.Showyourwork.(Show

your calculations for the expected value of uncertain events, show the eliminated decisions etc.)

WE SHOULD DO DECISION TREE ANALYSIS

Answer 1

The square (or rhombus) nodes represent the decision nodes and the round (or circle) nodes represent the chance (states of nature) nodes. The decision tree is shown below

Folding from the right, we see that the expected payoff is

Large plant = 0.5*200000 + 0.5*(-180000) = 10000

Small plant = 0.5*100000 + 0.5*(-20000) = 40000

No plant = 0

Given this, the best option is to build a small plant because that provides the highest expected value of 40000.