Problem 1.

Radish farmer's cost function is given as follows:

CR = R 2 + 8 (1)

Fishing company's cost function is expressed as follows:

CT (R, T) = T 2 + T R + 4 (2)

Suppose the prices for radish and fishing trip are PR = 11, PT = 10. 1.1. Derive farmer's and fishing company's marginal cost function.

1.2. Suppose the farmer and fishing company merged. Write down the profit maximization problem of the merged firm, and solve the efficient allocation (i.e. efficient radish(R), fishing trip(T) and the profit of the merged firm). From now, we assume the farmer and fishing company cannot be merged.

1.3. Suppose the property right (i.e. right to emit polluants from fertilizer) is not clearly assigned to anyone. Write down the profit maximization problem of the farmer and fishing company, and solve each firm's profits (R, T ) and the levels of production (R, T). Compare the each firm's profit with the profit of the merged firm.

1.4. Now, we assume that the property rights are assigned to the fishing company (victim). Find the profits of the fishing company and the farmer, and the production of the radish(R) and fishing trip (T).

1.5. Now, we assume that the property rights are assigned to the farmer (polluter). Find the profits of the fishing company and the farmer, and the production of the radish(R) and fishing trip (T).

1.6. Describe the Coase theorem with the results of 1.1 to 1.5