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Economics question- Centralized Cartel

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Firms A and B operate as a centralized cartel . Their marginal cost functions are defined below: MCa = 25Qa MCb=6.25Qb The firms face the following market demand curve: Q=1000-0.10P Determine the market price that the firms should charge and the quantity of output that should be produced by each firm

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.

if the demand line is p = 10000 - 10q and the MR line has half the slope shouldn't it be MR=10000-20q? When I use either MR I my answer has decimal places.

The question also is asking how much each firm should produce. To find that I was going to set MCa = 25Qa and also for MCb.

the problem gave two MC's, the marginal cost was 25Qb for firm a, but we were also given MCb = 6.25Qb

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