(c) It seems realistic to assume that the game could continue indenitelyafter all, the world will need otters 50 years from now just as badly as it does today. But time is money, so a dollar of prot a year from now is only valued as much as $d received today, where d {the discount rate) is some amount less than $1. Assume that you adopt a grim trigger strategy whereby your country pledges to produce 1,000 otters as long as the other country produces 1,000 otters. But should the other country ever produce 2,000 otters, you will respond by producing 2,000 otters, forever and ever. After you announce your strategy, the other country pledges to abide by the grim trigger strategy. a \"That stream of prots will you generate if both countries adopt such a grim strategy? {Dont forget to discount each years future profits by the appropriate multiple of d.) Express your answer as a sum. o Suppose your country decides to take advantage of the other countrys pledge to reduce output by ex panding your own output in the rst year. 'What stream of prots can you expect to generate? Again, he sure to discount appropriately. and express your answer as a sum. o At what level of d are you indifferent between cheating on or abiding by the agreement? If d is greater than this value, should you cheat? Other Country Produce 1,000 Otters Produce 2,000 Otters Your Country Produce 1,000 Otters $500 $500 $250 $700 Produce 2,000 Otters $700 $250 $400 $400