Please solve it with step-by-step explanations. Thank you.

6. Suppose the Fed pursues a policy with a (geometric) average inflation target of 2% over a three-year period (that is, from f to t + 1, from # + 1 to t + 2, and from t + 2 to t + 3). However, imagine now that the first year's inflation rate (the inflation rate from t to t + 1) ends up being below target, at 0%. What will the next two years' inflation rates have to be for the Fed to live up to its inflation policy? 7. Suppose the quantity theory holds at all points in time so that there is an immediate and full response of the price level (and no response of either velocity or output) of a change in the total stock of money in the economy. Assume that velocity is equal to 1. Andy, Martha, and Chris make up the whole population in this economy; their holdings of money are $70, $40, and $90, respectively. Assume that the government's holdings of money are zero (the total stock of money is the amount of money held by both consumers and the government). (a) If output in this economy is 100 apples, what is the price of an apple? (b) Calculate the purchasing power of Andy, Martha, and Chris' money holdings (expressed in apples)? (c) Suppose now that, as a statement of protest against his former employer-the Council of Economic Advisers (Andy used to be an economist there)-and on live TV, Andy burns all his money. What is the purchasing power of Andy, Martha, and Chris' money holdings now? Who will gain the most from the money burning: the most money-rich or the least money-rich? (d) If Andy's fire was observed by Chair Powell and, as a result, he instructed his New York Fed crew to issue $70 to fully sterilize Andy's money fire (i.e., so that the total money stock remained at $200), what will be the purchasing power (in terms of apples) of Andy, Martha, and Chris now? You may assume that the new money issue is a purchase of a $70 government bond directly from the government. 8. Suppose that an increase in robberies induces consumers to hold less money. How does this event affect the real value of money? Briefly,| defend your