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Economics question- Centralized Cartel

Customer Question

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
Submitted: 5 years ago.
Category: Homework
Expert:  Steve replied 5 years ago.

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

Customer: replied 5 years ago.

Hi Steve,

 

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.

 

Do you have any input?

 

thanks,

 

D

Expert:  Steve replied 5 years ago.
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Customer: replied 5 years ago.
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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