Answer:
In equilibrium, total output by the two firms will be option e= 300.
Q =
+ ![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
Q = 100 + 200
Q = 300
Explanation:
Data Given:
Market Demand Curve = P = 1660-4Q
where, P = price and Q = total industry output
Each firm's marginal cost = $60 per unit of output
So, we know that Q =
+
where
being the individual firm output.
Solution:
P = 1660-4Q
P = 1660- 4(
+
)
P = 1660 - 4
- 4![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
Including the marginal cost of firm 1 and multiplying the whole equation by ![q_{1}](https://tex.z-dn.net/?f=q_%7B1%7D)
Let's suppose new equation is X
X = 1660
- 4
- 4![q_{1}](https://tex.z-dn.net/?f=q_%7B1%7D)
- 60![q_{1}](https://tex.z-dn.net/?f=q_%7B1%7D)
Taking the derivative w.r.t to
, we will get:
= 1660 - 8
- 4
- 60 = 0
Making rearrangements into the equation:
8
+
= 1660 - 60
8
+
= 1600
Dividing the whole equation by 4
2
+
= 400
Solving for ![q_{1}](https://tex.z-dn.net/?f=q_%7B1%7D)
2
= 400 - ![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
= 200 - 0.5
Including the marginal cost of firm 1 and multiplying the whole equation by ![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
P = 1660 - 4
- 4![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
Let's suppose new equation is Y
Y = 1660
- 4![q_{1}](https://tex.z-dn.net/?f=q_%7B1%7D)
-4
- 60![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
Pugging in the value of ![q_{1}](https://tex.z-dn.net/?f=q_%7B1%7D)
Y = 1660
- 4
(200 - 0.5
) -4
- 60![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
Y = 1660
- 800
+2
-4
- 60![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
Y = 1600
- 800
-2
Taking the derivative w.r.t ![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
= 1600 - 800 - 4
= 0
Solving for ![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
4
= 800
= 200
= 200 - 0.5
Plugging in the value of
to get the value of ![q_{1}](https://tex.z-dn.net/?f=q_%7B1%7D)
= 200 - 0.5 (200)
= 200 - 100
= 100
Q =
+ ![q_{2}](https://tex.z-dn.net/?f=q_%7B2%7D)
Q = 100 + 200
Q = 300
Hence, in equilibrium, total output by the two firms will be option
e= 300.