Question

Use the following to answer questions 6-10:

Suppose that firms 1, and 2 are Cournot duopolists in the salt industry. The market demand curve can be specified as Q=20-p, Q=q₁₊q₂

(The firms choose their quantities simultaneously.)

The cost to firm 1 is C(q₁)=1q₁.

The cost to firm 2 is C(q₂)=2q₂.

6)   Find Firm 1 optimal production levels q1=?.

Select one:

a.
  0<q1<2

b.
2<q1<4

c.
  4<q1<6

d.
6<q1

e.
None of the above

7)    Find Firm 2 optimal production levels q2=?.

Select one:

a.
0<q2<2

b.
2<q2<4

c.
  4<q2<6

d.
6<q2

e.
  None of the above

8)   Determine the equilibrium price? (p=?)

Select one:

a.
  0<P<3

b.
3<P<4

c.
  4<P<5

d.
  5<P

e. None of the above

9) Firm 1 will earn? (pi1=?)

Select one:

a.
  0<Pi1<10

b.
  10<Pi1<20

c.
  20<Pi1<22

d.
  22<Pi1<23

e.
  None of the above

10)   Firm 2 will earn? (pi2=?)

Select one:

a.
0<Pi2<10

b.
10<Pi2<20

c.
  20<Pi2<22

d.
  22<Pi2<23

e.
None of the above

Answer 1

Q = 20 - p

p = 20 - Q = 20 - q1 - q2

MC1 = dC1/dq1 = 1

MC2 = dC2/dq2 = 2

For firm 1,

TR1 = p x q1 = 20q1 - q12 - q1q2

MR1 = TR1/q1 = 20 - 2q1 - q2

Setting MR1 = MC1,

20 - 2q1 - q2 = 1

2q1 + q2 = 19.........(1) (best response, firm 1)

For firm 2,

TR2 = p x q2 = 20q2 - q1q2 - q22

MR2 = TR2/q2 = 20 - q1 - 2q2

Setting MR2 = MC2,

20 - q1 - 2q2 = 2

q1 + 2q2 = 18.........(2) (best response, firm 2)

(2) x 2 yields:

2q1 + 4q2 = 36.......(3)

2q2 + q2 = 19.......(1)

(3) - (1) yields:

3q2 = 17

q2 = 5.67

q1 = 18 - 2q2 [from (2)] = 18 - (2 x 5.67) = 18 - 11.34 = 6.66

Q = 6.66 + 5.67 = 12.33

P = 20 - 12.33 = 7.67

Profit, firm 1 = q1 x (p - MC1) = 6.66 x (7.67 - 1) = 6.66 x 6.67 = 44.42

Profit, firm 2 = q2 x (p - MC2) = 5.67 x (7.67 - 2) = 5.67 x 5.67 = 32.15

Therefore:

(6) (d)

(7) (c)

(8) (d)

(9) (e)

(10) (e)