1. ## Maximising profit

A company sells its product both in Australia and New Zealand, the company's total cost is TC = 60+3(x+y). In australia the price at which x units can be sold is p=10-0.1x . In New Zealand, the price at which y units can be sold is q = 20-0.2y. ( All values in NZ dollars)

Im having issues understanding what to do with this question.

b) How should the sales be allocated to the two countries to maximise profits?

What prices should be charge in the two countries at the allocation found in b?

I understand how to maximise profits buts i don't understand how i am to know how to allocate the sales?

Can anyone help?

2. Originally Posted by el123
A company sells its product both in Australia and New Zealand, the company's total cost is TC = 60+3(x+y). In australia the price at which x units can be sold is p=10-0.1x . In New Zealand, the price at which y units can be sold is q = 20-0.2y.
I'm not positive I've found the correct solution, but here's my attempt.

Revenue in Australia is $\displaystyle xp=10x-0.1x^2$, so marginal revenue is $\displaystyle (xp)'=10-0.2x$. Revenue in NZ is $\displaystyle xq=20x-0.2y^2$, so marginal revenue is $\displaystyle (xy)'=20-0.4y$.

$\displaystyle TC=60+3x+3y$, and we need to find the marginal cost for each good. That can be found by taking the partial derivative with respect to x, then the partial with respect to y.

$\displaystyle \frac{\partial TC}{\partial x} = 3$

$\displaystyle \frac{\partial TC}{\partial y} = 3$

Now you can set marginal revenue equal to marginal cost in each region.

So $\displaystyle 10-0.2x = 3$ and $\displaystyle 20-0.4y=3$. Solving each equation means x=35 and y=42.5 (the latter should probably be rounded down to 42).

Does that help?

3. That is helpful! I'm still unsure about a few things, those values are the profit maximising price for each? In which country? And how do i allocate sales?

4. Originally Posted by el123
That is helpful! I'm still unsure about a few things, those values are the profit maximising price for each? In which country? And how do i allocate sales?
x and y are the quantities to be sold in Oz and NZ, respectively. By setting MR to MC, you've found the optimal allocation between the countries. To find the prices at which they should be sold, plug them into your original equations (P= ...).