The inverse demand for a homogeneous-product Stackelberg duopoly is P = 16,000 - 4Q. The cost structures for the leader and the
follower, respectively, are CL(QL) = 4,000QL and CF (QF) = 6,000QF..
a. What is the followers reaction function?
QF =
b. Determine the equilibrium output level for both the leader and the follower.
Leader output:
Follower output:
c. Determine the equilibrium market price.
$
d. Determine the profits of the leader and the follower.
Leader profits: $
Follower profits: $
a. What is the followers reaction function?
QF =
b. Determine the equilibrium output level for both the leader and the follower.
Leader output:
Follower output:
c. Determine the equilibrium market price.
$
d. Determine the profits of the leader and the follower.
Leader profits: $
Follower profits: $
1 answer:
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Answer:
Ans.
a) BEP (units) =727; BEP($)= $36,350
b) BEP (units) =690; BEP($)=$34,500
Explanation:
Hi, in order to find the break even point in units, we have to use the following equation in both cases.
Since the sales mix is different in both scenarios, let´s find the average variable cost for a) (notice that there is no need to find the average price because both, the stool and the chair have the same price)
Now, the fraction aside each of the price is 1/2 in both cases, because the sale mix 1:1 means that the company makes 1 stool for every chair it makes, in fraction that is, for every 2 items that the company makes, 1 is a stool (1/2) and 1 is a chair (1/2).
So, our BEP in units is:
That means that the company has to make 727 units, which 363 are chairs and 364 are stools (you could say 364 chairs and 363 stools too, because we are heavily rouding numbers). This is represented in $36,350 in sales.
Now, for b), our average cost is:
As you can see, the fraction changed, that is because of the new sales mix of 1:4, that is: the company makes 4 stool for every chair it makes, in fraction that is, for every 5 items that the company makes, 4 are a stools (4/5) and 1 is a chair (1/5).
Now, let´s find our new BEP in units and dollars.
That means that the company has to make 690 products, which 138 are chairs and 552 are stools. This is represented in $34,500 in sales.
Best of luck.