Ben and Jerry drill oil in Texas and operate in the same oil deposit. The quantity of oil pulled from the deposit is determined by the joint total amount of capital in the deposit: q=50015K where q is the amount of oil pulled out per unit of capital and K is the total amount of capital in the deposit. The price of each unit of capital is 100 dollars and oil can be sold at 25 dollars per unit. (a) Ben and Jerry have a good friendship and manage to operate as just one to maximise their joint profits. Compute the amount of oil that each of them drills and the profits each of them obtains if everything is split in half. (b) Ben and Jerry have a dispute and separate from each other as a joint workforce, now each of them decides on their own the amount of oil that they pull out. (b.1) How much oil do each of them produce? Obtain their individual profits. (b.2) The government wants that the total production be the same as in part (a). Should the government levy a tax (per unit of capital) or pay a subsidy (per unit of capital)? Explain briefly. Calculate the tax or subsidy on the price of capital required to achieve the level of output that you found in part (a). (c) Suppose that we are back in the situation without taxes or subsidies. This time, however, Ben installs first the capital, and, upon observing that, Jerry makes his own decision. Find the amount of capital that each of them uses. Ben and Jerry drill oil in Texas and operate in the same oil deposit. The quantity of oil pulled from the deposit is determined by the joint total amount of capital in the deposit: q=50015K where q is the amount of oil pulled out per unit of capital and K is the total amount of capital in the deposit. The price of each unit of capital is 100 dollars and oil can be sold at 25 dollars per unit. (a) Ben and Jerry have a good friendship and manage to operate as just one to maximise their joint profits. Compute the amount of oil that each of them drills and the profits each of them obtains if everything is split in half. (b) Ben and Jerry have a dispute and separate from each other as a joint workforce, now each of them decides on their own the amount of oil that they pull out. (b.1) How much oil do each of them produce? Obtain their individual profits. (b.2) The government wants that the total production be the same as in part (a). Should the government levy a tax (per unit of capital) or pay a subsidy (per unit of capital)? Explain briefly. Calculate the tax or subsidy on the price of capital required to achieve the level of output that you found in part (a). (c) Suppose that we are back in the situation without taxes or subsidies. This time, however, Ben installs first the capital, and, upon observing that, Jerry makes his own decision. Find the amount of capital that each of them uses
