Question

5. 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?

Please explain why(containing the solving process).

Thank you

Answer 1

In equilibrium, the number of coconuts produced are determined by forces of demand and supply. King produces the number of coconuts for which demand equals supply so that there is no shortage or surplus of coconuts in the market. Thus, at equilibrium, demand = supply. That is, D(p) = S(p)
So, 1200 - 100p = 100p
So, 100p + 100p = 1200
So, 200p = 1200
So, p =1200/200 = 6

And, number of coconuts = S(p) = 100p = 100(6) = 600

Thus, 600 coconuts will be produced in equilibrium.