Hey DeliaLee, thanks for the opportunity to answer your question.

There are a few rules we need to know to be able to solve this problem. We need to know that a cartel faces the same type of profit maximization trends that a monopoly faces. Second, we need to know that marginal revenue bisects the horizontal distance between the y axis and the demand (that means it has twice as steep of a slope).

Since companies A and B are working together, their marginal cost is combined. This creates an MC function of MC = 31.25q.

To find marginal revenue, we double the slope of the demand curve. So MR = 1000 -.05p.

To mathematically find where they intersect, we need to set them equal to each other. This means we need to change the MR terms so Q is the variable.

Q = 1000 - .1p

Q/.1 = 1000/.1 - p

p = 10000 - Q/.1 (or p = 10000 - 10q)

Then we double the slop to get MR = 10000 - 10q

So we need to find where they intersect to find the best price and output. We will need to set MR = MC to find what Q equals.

10,000 - 10q = 31.25q

10,000 = 41.25q

q = 242 Units

Now that we know what the combined quanitity is, we can find the best price.

We use the demand formula and plug in Q to find P (remember price is set by demand, so we use this formula).

p = 10,000 - 10(242)

p = 10,000 - 2420

p = $7580

So there you go. These companies should produce 242 units combined and set the price at $7,580.

Hope this helps. If it does, and you have the time, I would greatly appreciate some good feedback. Thanks.

-Steve

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