(Solved): There are Australian cotton farmers and international (non-Australian) cotton farmers. All farmers a ...

There are Australian cotton farmers and international (non-Australian) cotton farmers. All farmers are assumed to be perfectly competitive on the world market. The world demand for cotton is given by:

QD = 12000 – 100p

(a) To begin with, assume that all farmers are identical and the cost function for any farmer, Australian or international, is given by:

C = 0.5q2 + 162 ,

where q is the farmer’s output. There are 300 Australian and 200 international farmers. Find firm’s individual supply curve qs and the world market supply curve QS. Then calculate the world equilibrium price of cotton p*.
 

2. (b)  The Australian government decides to give a subsidy to the 300 Australian cotton farmers after which an Australian-farmers’ cost function becomes:

CA = 0.3q2Au + 162 .

The 200 international farmers have the same cost function as in (a). That is, CIn = 0.5q2In+ 162 ,

Assuming that the number of farmers does not change in the short run, find the new world supply QnS and calculate the new world equilibrium price (after this subsidy) p**.

3. (c)  Calculate the profits of Australian and international farmers at p**. What will happen to the international farmers in the long run?