Exercise 1 Miners at the Gopher Gold Mine in Siberia have put in a series of wage and condition demands that would cost $50m to the management and threaten to strike if the demands are not met. The management has to decide right away whether to increase short-term production to build up a stockpile of output to reduce the impact of a strike, a move that would cost $20m in overtime and other extra costs. If they build a stockpile they estimate that the probability that the strike goes ahead is 0.6, whereas if they don't build a stockpile the chance of a strike is put at 0.7. Once the workers decide to strike the management has to decide whether to accept the miners' demands or to take them on. If the management decides to fight, the chance that they win is estimated to be 0.75 if they have built a stockpile and 0.5 if they have not. Whether the management win or lose the cost of the strike to them will be $10m in lost production and geological problems. If management win the miners' demands will not be met, if they lose they will. If the miners do not strike their demands will not be met. (a) Draw a decision tree to advise the management of the company. (b) Show all the probabilities involved and how you obtained them. (C) After calculating the relevant expected values, what should be the right decision to make? (d) How sensitive are your recommendations to changes in the probability of the management winning if they have built a stockpile? Exercise 1 Miners at the Gopher Gold Mine in Siberia have put in a series of wage and condition demands that would cost $50m to the management and threaten to strike if the demands are not met. The management has to decide right away whether to increase short-term production to build up a stockpile of output to reduce the impact of a strike, a move that would cost $20m in overtime and other extra costs. If they build a stockpile they estimate that the probability that the strike goes ahead is 0.6, whereas if they don't build a stockpile the chance of a strike is put at 0.7. Once the workers decide to strike the management has to decide whether to accept the miners' demands or to take them on. If the management decides to fight, the chance that they win is estimated to be 0.75 if they have built a stockpile and 0.5 if they have not. Whether the management win or lose the cost of the strike to them will be $10m in lost production and geological problems. If management win the miners' demands will not be met, if they lose they will. If the miners do not strike their demands will not be met. (a) Draw a decision tree to advise the management of the company. (b) Show all the probabilities involved and how you obtained them. (C) After calculating the relevant expected values, what should be the right decision to make? (d) How sensitive are your recommendations to changes in the probability of the management winning if they have built a stockpile
