California Mining Co must decide whether or not to start a project for a gold mi

Question

California Mining Co must decide whether or not to start a project for a gold mine in South Africa. The drilling at the start of a project costs $100,000, and if gold is found, the value is estimated to be $600,000. At present, California Mining Co thinks there is a 45% chance that the field contains gold. Before drilling, California Mining Co can pay $10,000 to a geologist to obtain more information about the likelihood that the field will contain gold. There is a 50% chance that the geologist will issue a favorable report and a 50% chance of an unfavorable report. Given a favorable report, there is an 80% chance that the field contains gold. Given an unfavorable report, there is a 10% chance that the field contains gold. Determine California Mining Co's optimal course of action. Also determine EVSI.

Explanation / Answer

Ans:G=Gold

NG=not Gold

F=favourable

UF=unfavourable

P(G/F)=0.8

P(NG/F)=0.2

P(G/UF)=0.1

P(NG/UF)=0.9

P(F)=P(UF)=0.5

Calculate posterior probabilities for sample information:

P(F/G)=P(G/F)*P(F)/[P(G/F)*P(F)+P(G/UF)*P(UF)]=0.8*0.5[0.8*0.5+0.1*0.5]=0.4/0.45=0.89

P(UF/G)=1-0.89=0.11

P(F/NG)=P(NG/F)*P(F)/[P(NG/F)*P(F)+P(NG/UF)*P(UF)]=0.2*0.5/[0.2*0.5+0.9*0.5]=0.1/0.55=0.18

P(UF/NG)=1-0.18=0.82

EVSI=Expected value with sample information-Expected value without sample information

Expected value with sample information=0.45(500000*0.89-500000*0.11)+0.55(0.18*(-100000)-0)=165600

Expected value without sample information=0.45*500000-0.55*100000=170000

EVSI=165600-170000=-4400

EVSI is -ve i.e there is no worth of hiring a geologist.Hence, they should not hire geologist and directly go for drilling.

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