There are two consumers  1 and 2  in an endowment economy with a single good (cookies). Person 1's utility is u1 = c1 and person 2's utility is u2 = 2c2 where c1 and c2 are each person's cookie consumption. The total supply of cookies is 48. 

a. Explain briefly why any allocation of cookies must be Pareto efficient, so long as all cookies are consumed. 

b. Find and draw the utilities possibility frontier, assuming that the gov- ernment can make lump-sum transfers. Find the cookie allocation that will result if the government is (i) Utilitarian and (ii) Rawlsian, and show the utility distri- bution on your diagram. 

c. Assume that person 1 starts with all the cookies, and that 25% of cookies break when they are transferred. Find and draw the new (second-best) utilities possibility frontier. Find the cookie allocation that will result if the government is (i) Utilitarian and (ii) Rawlsian, and show the utility distribution on your diagram. 

d. Assume that each person starts with 24 cookies, and that 25% of cookies break when they are transferred. Find and draw the new (second-best) utilities possibility frontier. Find the cookie allocation that will result if the government is (i) Utilitarian and (ii) Rawlsian, and show the utility distribution on your diagram. 

e. Explain briefly why the second theorem of welfare economics is satisfied if no cookies break when transferred.