Please answer question e) using profit maximising function 10(100-K)K - Price of Capital * capital

Question 2 [34 marks). Jett and Bick are two oil drillers in Texas, operating in the same oil deposit. Pulling oil from the deposit requires them to use capital. The quantity of oil that each unit of capital can pull from the deposit is determined by the joint total amount of capital in the deposit: q = 100 K: where i; 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 400 dollars and oil can be sold at 10 dollars per unit. (a) Suppose that Jett and Bick have a good friendship and manage to operate as just one oil driller, maximising their joint profits. Compute the amount of oil that each of them pulls out from the deposit and the profits each of them obtains if everything is split in half. (8 marks) (b) Eventually. Jett and Bick have a disagreement. Now, each of them decides the amount of oil that each of them pulls out (not as onejoint producer}. How much oil does each of them produce? Obtain their individual profits. Compare these profits with their profits in part (a) and explain why they are greaterflower in part (b) (9 marks} (c) Suppose that now Jett installs his capital first, and, upon observing that, Bick makes his own decision. Obtain Jett's profit as a function of the amount of capital that Jett uses. {5 marks) (d) In the scenario of part (c) obtain the amount of capital that each of them uses if the government imposes a quota. forcing each of them to use at most 25 units of capital. [3 marks) (e) Suppose that we are back in the scenario of part (b). but now Bick's cost of capital is 600 per unit, whereas Jett's cost of capital remains at 400 per unit. How much oil does each of them produce? Whose production is higher, Bick or Jett? Provide an economic reasoning explaining why this is the case. (9 marks)