Suppose there are two competing hospitals in a region facing the samecommon dema

Question

Suppose there are two competing hospitals in a region facing the samecommon demand for medical care

that can be represented by the following demand equation and each firm possesses the same marginal cost

(MC) of producing medical care, determine the Cournot equilibrium

for the model. How is this different from a perfectly competitive setting?

How is it different from a monopoly setting? What are the total profits

earned under each of these scenarios?

a.

P=400-10Q

MC=10

b.

P=200-4Q

MC=10

c.

P=1000 - 20Q

MC=20

Explanation / Answer

a) Under cournot competition:

Response function of firm a : Profita = (400-10(qa+qb))qa - 10

or Profita = 400qa - 10qa2 -10qaqb - 10

To maximize profit dProfita/dqa = 0

400 - 20qa -10qb = 0

or qa = 20-0.5qb ........ eq i

Similarly,

response function of firm b: Profitb = (400-10(qa+qb))qb - 10

or Profitb = 400qb - 10qb2 -10qaqb - 10

To maximize profit dProfitb/dqb = 0

400 - 20qb -10qa = 0

or qa = 40-2qb ........ eq ii

from eq i and ii

40-2qb = 20-0.5qb

qb = 13.33

and hence qa = 40-2(13.33) = 13.33

and P = 400 - 10(13.33+13.33) = $133.33

Each firm's profit = (400-10(13.33+13.33))13.33 - 10 = $1768.22

Now, Under Monopoly:

TR = P*Q = (400-10Q)Q = 400Q-10Q2

MR = dTR/dQ = 400 - 20Q

Equate MR with MC

400-20Q = 10

Q = 19.5

at P = 400-10(19.5) = $205.

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