Smith can produce with or without a filter on his smokestack. Production$$without a filter results in greater smoke damage to Jones. The relevant gains$$and losses for the two individuals are listed in the table below: $($LO$3)$With i lter Without i lter$$Gains to Smith $$200/$wk $$245/$wk$$Damage to Jones $$35/$wk $$85/$wk$$a$.$ If Smith is not liable for smoke damage and there are no negotiation costs,$$will he install a filter? Explain carefully.$$b$.$ How, if at all, would the outcome be different if Smith were liable for all$$smoke damage and the cost of the filter were $$10/$wk higher than indicated$$in the table? Explain carefully