Suppose that an oil field is discovered and that the price of a barrel of oil (determined exogenously by OPEC) is £10. This oil can be extracted using pumps, which have a fixed cost of £1000 per pump. Total production (in barrels) from the oil field depends on the total number of pumps used (N) and is given by B = 500N - N2. Each pump receives an equal share of the total oil.
a. Suppose that each firm may only place one pump, and there is free entry into the market. Each firm is small, hence a new firm decides whether to enter the market by considering the revenue they would earn from their new pump (given the number of firms already in the market) against the cost of buying the pump. How many firms would enter the market?
b. Suppose instead that a central government controls the oil field and can decide how many pumps it wishes to place, in order to maximise total profits. How many pumps would they place? Is this different from the answer in part (a), and, if so, why?
c. The central government, for political reasons, now decides that it does not want to own and control the pumps, but hand it back to the private sector, whilst ensuring that the competitive marketplace still maximises aggregate profits for society. describe why holding an auction, for the right to have total control over the oil field (including the number of pumps which are placed) could achieve this. Why is this conceptually similar to the idea of all the small firms, in part (a), looking to merge together? d. Suppose, at the auction, that each bidding firm does not know the true production function of the oil field, but instead believes it to be B = ΛN - N2
, where Λ could be a number greater than, or less than, the true value of 500. Λ is given to the firm by their Research Team, who believe their number to be 100% correct, but the firm will only find out that the true value of Λ=500 if they win the auction and have the opportunity to conduct test drilling. Show why the amount each firm would be willing to bid up to for the oil field is increasing in Λ, so long as they believe Λ>100. Why do you think this type of scenario might be known as the "Winner's Curse"?