Consider a portfolio manager with a $20,500,000 equity portfolio under management. The manager wishes to hedge against a decline
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Answer:
In equilibrium, total output by the two firms will be option e= 300.
Q = +
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
Including the marginal cost of firm 1 and multiplying the whole equation by
Let's suppose new equation is X
X = 1660 - 4
- 4
- 60
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
2 = 400 -
= 200 - 0.5
Including the marginal cost of firm 1 and multiplying the whole equation by
P = 1660 - 4 - 4
Let's suppose new equation is Y
Y = 1660 - 4
-4
- 60
Pugging in the value of
Y = 1660 - 4
(200 - 0.5
) -4
- 60
Y = 1660 - 800
+2
-4
- 60
Y = 1600 - 800
-2
Taking the derivative w.r.t
= 1600 - 800 - 4
= 0
Solving for
4 = 800
= 200
= 200 - 0.5
Plugging in the value of to get the value of
= 200 - 0.5 (200)
= 200 - 100
= 100
Q = +
Q = 100 + 200
Q = 300
Hence, in equilibrium, total output by the two firms will be option
e= 300.