I am really struggling with the following question:
A company produces a product that they sell in two different countries. Because of transport costs, customs etc. it is not profitable for someone to buy the product in one country, to sell it in the other.
The demand in one country (country A), is given by PA = 1000 - QA, where PA is the price, and QA is the quantity.
In the other country (country B) demand is given by PB = 2000 - 0.2Qb. For the company, the cost per unit sold is the same in both markets. The companies cost can be expressed as: TC(Q) = 100(QA + QB) + 1 000 000.
What is the optimal profit for the company?
The answer is apparently 3 715 000, but I am not sure why.
My reasoning so far:
I know that profit is equal to TR(Q) - TC(Q), and optimal profit can probably be found by taking the derivative of the expression, and setting the derivative to 0. We are given TC(Q), from the expression above, but I am not sure how to find TR(Q). Also, I am not sure if I am on the right track at all. I also don't understand why the first piece of information (that it is not profitable to buy the product in one country, and sell it in the other) was given.
Any hints, or more detailed solutions, would be greatly appreciated!