King Kanuta rules a small tropical island, Nutting Atoll, whose primary crop is coconuts. If the price of coconuts is P, then King Kanuta’s subjects will demand D (P) = 1, 200 − 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) The equilibrium price of coconuts will be ________ and the equilibrium quantity supplied will be ________.
(b) One day, King Kanuta 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) When the price paid to suppliers is pS, how many coconuts will the king’s subjects demand for their own consumption? (Hint: Express pD in terms of pS and substitute into the demand function.).
(d) Since the king consumes a coconut for every coconut consumed by the subjects, the total amount demanded by the king and his subjects is twice the amount demanded by the subjects. Therefore, when the price received by suppliers is pS, the total number of coconuts demanded per week by Kanuta and his subjects is ________.
(e) Solve for the equilibrium value of pS ________, the equilibrium total number of coconuts produced ________, and the equilibrium total number of coconuts consumed by Kanuta’s subjects. ________.
(f) King Kanuta’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. This plan resulted in ________coconuts being sold to the consumers. The shopkeepers got ________per coconut after paying their tax to the king, and the consumers paid a price of ________ per coconut.