Question

Remember King Kanuta and his tropical island? The demand function for coconuts by his subjects on the island is D(p)1,200100p and the supply function is S(p)100p. The law used to be that any subject who consumed a coconut had to pay another coconut to the king. King Kanuta then ate all the coconuts he got. But now the king, apparently fed up with coconuts, decides to sell the coconuts that he collects in the local market at the going selling price, ps. In equilibrium, what is the number of coconuts that will now be produced?

Answer 1

Consider the following problem here the demand and the supply curves are given by.

=> “Qd = 1200 - 100*P” and “Qs = 100*P”, => at the equilibrium “Qd” must be equal to “Qs”.

=> Qd = Qs, => 1200 - 100*P = 100*P, => P = 1200/200 = 6. Now, the quantity demanded is given by “Qs=100*P = 600 = Qd”.

Now, here each people have to consume twice what they want to consume, => the new demand is given by.

=> Qd’ = 2*Qd = 2*(1200-100*P) = 2400 - 200*P, => Qd’ = 2400 – 200*P. Now, because “King” already have ate all the coconut and will supply what they get, => the new supply curve is given by.

=> Qs’ = Qs+Qd = 100*P + 1200 – 100*P = 1200. So, at the equilibrium “Qs’=Qd’, => 2400 – 200*P = 1200”.

=> P = 1200/200 = 6” and the equilibrium quantity traded is given by “Qs = Qd = 1200”. So, here the equilibrium quantity is given by “1200”.