解决这个问题King Julien rules the Madagascar island whose primary crop is coconuts. If the price of coconuts is P , then King Julien’s subjects will demand D(P ) = 1200 − 100P coconuts per week for their own use. The number of coconuts that will be supplied per week by the island’s coconut growers is S(p) = 100P. (a) (2 pts) Calculate the equilibrium price and quantity for coconuts. (b) (2 pts) One day, King Julien decided to tax his subjects in order to collect coconuts for the Royal Larder. The king required that every subject who consumed a coconut would have to pay a coconut to the king as a tax. Thus, if a subject wanted 5 coconuts for himself, he would have to purchase 10 coconuts and give 5 to the king. When the price that is received by the sellers is pS, how much does it cost one of the king’s subjects to get an extra coconut for himself? (c) (3 pts) When the price paid to suppliers is pS, how many coconuts will the king’s subjects demand for their own consumption (as a function of pS)? 2 (d) (2 pts) Under the above coconut tax policy, determine the total number of coconuts demanded per week by King Julien and his subjects as a function of pS. (e) (3 pts) Calculate the equilibrium value of pS, the equilibrium total number of coconuts produced, and the equilibrium total number of coconuts consumed by Julien’s subjects. (f) (5 pts) King Julien’s subjects resented paying the extra coconuts to the king, and whispers of revolution spread through the palace. Worried by the hostile atmosphere, the king changed the coconut tax. Now, the shopkeepers who sold the coconuts would be responsible for paying the tax. For every coconut sold to a consumer, the shopkeeper would have to pay one coconut to the king. For this new policy, calculate the number of coconuts being sold to the consumers, the value per coconuts that the shopkeepers got after paying their tax to the king, and the price payed by the consumers.

(a) 平衡价格为 P=6，平衡数量为 Q=600。
(b) 当价格为 pS=6 时，King Julien 的臣民为了自己获得额外的椰子，需要支付 12 个椰子。
(c) 当价格为 pS 时，King Julien 的臣民需要的椰子数量为 D(pS)=120-100pS。
(d) 在上述椰子税政策下，King Julien 和他的臣民总共需要的椰子数量为 120。
(e) 平衡价格为 P=6，平衡总共生产的椰子数量为 Q=600，平衡总共被 King Julien 的臣民消费的椰子数量为 600。
(f) 在新的政策下，卖椰子的商贩需要向国王支付一颗椰子的税。在这种情况下，被消费者购买的椰子数量为 600，商贩支付给国王的税后每颗椰子的价格为 3，消费者支付的价格为 6。