INTROD. TO DECISION-MAKING 2021-22 ASSIGNMENT DECISION TREES GROUP- F6 DEADLINE- May 13, 2022 SUBSIDENCES1 An entrepreneur can acquire two pieces of land to build houses in an area where there is a possibility of subsidence (or sinking). If the land does not show subsidence, the entrepreneur expects to make a prot of 200,000 per piece of land. By contrast, if the land shows subsidence, the entrepreneur expects to incur a loss of E1 80,000 per piece of land. The entrepreneur believes that the probability that both pieces of land will sink is 0.2, the probability that only one of them will sink is 0.3. and the probability that neither will sink is 0.5. The entrepreneur has to decide whether to buy two pieces of land, none or, initially, buy one piece of land, do a test (we assume that this test determines with certainty whether that piece of land can suffer subsidence or not) and in View of the test, decide whether or not to buy the other piece of land. In this use, the entrepreneur's prot or loss will depend on how many pieces of land slhe acquired and whether such lands show subsidence. The cost of the test is 2,000. We assume that the entrepreneur's preferences are represented by expected monetary value and therefore she is risk neutral. SUGGESTED NOMENCLATURE _ 1 1 sinking 2 2 sinkings m First land does not sink 15 First land sinks We also assume that if only one piece of land sinks, then the probability that the rst land is the one which will sink is the same as the probability that the second land is the one which will sink. That is: P(1H |1)= P(1NH |1)=0.5. Note also that: P(1NSl'l0)=P(0)=O.5 and P(1Sl'lZ)=P(2)=0.2 Draw the decision tree and apply backward induction to determine the optimal action. 1 Inspirado en anch,S (1986) Decision Theory: An lntmducbn to the Mathematics of Rationality. Chlchester: Ellis Homod Lid