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Solution Economics

Content type
User Generated
Subject
Micro Economics
Type
Homework
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Solution 1
Demand for gasoline is given by, Q = 25 – 10P
Let P
1
= Price set by John
And P
2
= Price set by Adam
Let Q
1
= Quantities sold by John
And Q
2
= Quantities sold by Adam
=> Q = Q
1
+ Q
2
Marginal costs (MC) = $1.25 = same for both sellers
Since, in this case, gasoline is a homogeneous (i.e. undifferentiated) product, Marginal costs
are constant and both sellers are competing by setting prices, it is an example of Bertrand
competition. Now, according to Bertrand competition, if firms are competing by setting
prices instead of quantities, then the equilibrium would occur when price equals marginal
cost. It could be justified by the reasoning that since both are selling gasoline of the same
quality, and if one would set higher prices, then the consumers will purchase the gasoline
from the other seller at a cheaper price.
i.e. if P
1
< P
2
, then Q
1
= Q and Q
2
= 0
and if P
1
> P
2
, then Q
1
= 0 and Q
2
= Q
and if P
1
= P
2
, then Q
1
= Q
2
= Q/2
Moreover, the prices could not go below the marginal costs to ensure profitability. Thus, the
optimal condition is when the price for both the sellers equals the marginal cost.
Then, at equilibrium, P
1
= P
2
= MC
Since, MC = $1.25. Therefore P
1
= P
2
= $1.25
Hence, Market price level = $1.25
Putting P = $1.25 in demand function equation
i.e. Q = 25 – 10*1.25
=> Q = 12.5
=> Total quantity sold in the market = 12.5
=> Market output level = 12.5
Since both are selling gasoline of the same quality and their prices are also the same,
therefore it could be concluded that quantities sold by them would also be the same
=> Q
1
= Q
2
= Q/2 = 12.5/2 = 6.25
=> Both John and Adam will sell 6.25 units of gasoline
Moreover, since both the sellers are selling at price = MC, therefore their profits = 0

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Solution 2
Demand for video games is given by, Q = 150 – 0.1P
=> 0.1P = 150 – Q
=> P = 1500 – 10Q
Let Q
1
= Output level of GamePower
And Q
2
= Output level of Xeron
Total cost (TC
i
) = 0.25*(Q
i
)
2
When GamePower moves first, it forms the Stackelberg leadership model i.e. GamePower
becomes the leader firm and Xeron becomes the follower firm, which follows sequentially.
Both firms compete on quantity.
To determine Q1, GamePower will take the reaction function of Xeron into account.
So let us first maximize the Xeron’s profits to determine its reaction function.
(Profits)
Xeron
= Total revenue – Total Cost
= (P)*(Q
2
) – TC
2
= (P)*(Q
2
) – 0.25*(Q
2
)
2
= (1500 – 10(Q
1
+ Q
2
))*(Q
2
) – 0.25*(Q
2
)
2
= 1500* Q
2
– 10*(Q
1
)*(Q
2
) - 10*(Q
2
)
2
– 0.25*(Q
2
)
2
= 1500* Q
2
– 10*(Q
1
)*(Q
2
) – 10.25*(Q
2
)
2
To maximize Xeron’s profits, we would differentiate the above equation with respect to Q
2
and equate it to zero
i.e.
𝑑
𝑑Q2
{1500* Q
2
– 10*(Q
1
)*(Q
2
) – 10.25*(Q
2
)
2
} = 0
=> 1500 – 10Q
1
– 20.5Q
2
= 0
=> 20.5Q
2
= 1500 – 10Q
1
=> Q
2
= 73.17 – 0.49Q
1
=> Xeron’s reaction function is: Q
2
= 73.17 – 0.49Q
1
Now, GamePower’s profits are calculated as follows
(Profits)
GamePower
= Total revenue – Total Cost
= (P)*(Q
1
) – TC
1
= (P)*(Q
1
) – 0.25*(Q
1
)
2
= (1500 – 10(Q
1
+ Q
2
))*(Q
1
) – 0.25*(Q
1
)
2
= 1500* Q
1
– 10*(Q
1
)*(Q
2
) - 10*(Q
1
)
2
– 0.25*(Q
1
)
2

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Solution 1 Demand for gasoline is given by, Q = 25 – 10P Let P1 = Price set by John And P2 = Price set by Adam Let Q1 = Quantities sold by John And Q2 = Quantities sold by Adam => Q = Q1 + Q2 Marginal costs (MC) = $1.25 = same for both sellers Since, in this case, gasoline is a homogeneous (i.e. undifferentiated) product, Marginal costs are constant and both sellers are competing by setting prices, it is an example of Bertrand competition. Now, according to Bertrand competition, if firms are competing by setting prices instead of quantities, then the equilibrium would occur when price equals marginal cost. It could be justified by the reasoning that since both are selling gasoline of the same quality, and if one would set higher prices, then the consumers will purchase the gasoline from the other seller at a cheaper price. i.e. if P1 < P2, then Q1 = Q and Q2 = 0 and if P1 > P2, then Q1 = 0 and Q2 = Q and if P1 = P2, then Q1 = Q2 = Q/2 Moreover, the prices could not go below the marginal costs to ensure profitability. Thus, the optimal condition is when the price for both the sellers equals the marginal cost. Then, at equilibrium, P1 = P2 = MC Since, MC = $1.25. Therefore P1 = P2 ...
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