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程序代写案例-ECON90015
时间：2022-06-18
ECON90015
Semester 2, 2021
Final exam suggested solutions
1. (a) The quantity of hand sanitiser supplied decreases as the price of gin increases. As
gin is not an input for the production of hand sanitiser, it follows that gin and hand
sanitiser are substitutes in production.
(b) Plugging in the given values, we obtain the following expression for the quantity
supplied as a function of the price of hand sanitiser:
Qs = −12.17 + 0.1Phs − 0.03(48)− 0.07(17) + 0.4(27)
= −12.17 + 0.1Phs − 1.44− 1.19 + 10.8
= −4 + 0.1Phs
(c) Setting the given quantity demanded and the quantity supplied we computed in the
previous part to be equal to each other, we obtain:
−4 + 0.1Phs = 20− 0.2Phs ⇔ 0.3Phs = 24⇔ P ∗ = $80.
Therefore, the equilibrium price is $80. Plugging the equilibrium price in either of
the expressions for quantity supplied or quantity demanded would then give us the
equilibrium quantity: it is Q∗ = −4 + 0.1(80) = 4.
(d) Directly from the formula, the point elasticity of supply at P ∗ is
∆Q
∆P
× P
∗
Q∗
= 0.1× 80
4
= 2,
where we derived ∆Q
∆P
from the expression for quantity supplied (Qs = −4 + 0.1P ).
The coefficient of supply elasticity exceeds 1 and, therefore, supply is elastic.
(e) As above, we can set the quantity supplied and the quantity demanded to be equal
to each other to obtain:
−4 + 0.1Phs = 20− 0.1Phs ⇔ 0.2Phs = 24⇔ P ∗∗ = $120
Plugging the equilibrium price of $120 into the expression for the quantity supplied
once again, we see that the equilibrium quantity is Q∗∗ = −4 + 0.1(120) = 8.
(f) Directly from the formula, the arc elasticity of supply when moving from P ∗ = $80
1
to P ∗∗ = $120 is
∆Q
∆P
×
∑
P∑
Q
=
Q∗∗ −Q∗
P ∗∗ − P ∗ ×
P ∗ + P ∗∗
Q∗ +Q∗∗
=
8− 4
120− 80 ×
80 + 120
4 + 8
=
4
40
× 200
12
=
5
3
≈1.67.
The computed coefficient of elasticity exceeds 1 and, so, supply is elastic.
(g) The increase in demand moved the equilibrium along the upward sloping supply
curve: both the equilibrium quantity and the equilibrium price increased. Therefore,
revenue increased. The elasticity of supply is not relevant for this conclusion: it does
not matter whether supply is elastic, inelastic, unit-elastic or, indeed, perfectly elastic
or perfectly inelastic. If demand increases, the revenue is guaranteed to increase as
well.
2
2. (a) Before the pandemic started, there are 2.5 million consumers who demand the prod-
uct and each one of them has inverse demand given by P = 2−0.5q. This corresponds
to direct demand of q = 4− 2P . Multiplying by the number of consumers, the total
quantity demanded in the market is Qd = 10, 000, 000− 5, 000, 000× P .
(b) After the pandemic started, there are 5 million consumers who demand the product
and each one of them has inverse demand given by P = 4 − q. This corresponds
to direct demand q = 4 − P . Multiplying by the number of consumers, the total
quantity demand is Qd = 20, 000, 000− 5, 000, 000× P .
(c) Setting the quantity demanded and the quantity supplied to be equal to each other,
we get
10, 000, 000− 5, 000, 000× P = 3, 000, 000× P.
Solving for P , we see that the equilibrium price pre-pandemic is 10/8 = $1.25.
Plugging that price in the expression for the quantity supplied, we see that the
equilibrium quantity is 3, 000, 000× 1.25 = 3, 750, 000.
(d) Setting the quantity demanded (after the start of the pandemic) and the quantity
supplied to be equal to each other, we get
20, 000, 000− 5, 000, 000× P = 3, 000, 000× P.
Solving for P , we see that the new equilibrium price is 20/8 = $2.50. Plugging
that price in the expression for the quantity supplied, we see that the equilibrium
quantity is 3, 000, 000× 2.50 = 7, 500, 000.
(e) As 1.2 × 1.25 = 1.5, the Lord Mayor’s plan amounts to banning the price of the
product from climbing above $1.50. As 1.5 < 2.5, the proposed law is a binding
price ceiling. Therefore, the market will fail to clear, the prevailing market price
at which the product will be traded will be the price ceiling $1.50, and there will
be excess demand at the price ceiling. It follows that the quantity traded would be
determined by supply. That quantity is 3, 000, 000 × 1.5 = 4, 500, 000. The price
corresponding to quantity demanded of 4, 500, 000 is $3.10: we can find this by
solving
20, 000, 000− 5, 000, 000× P = 4, 500, 000
for P . Therefore, the dead-weight loss equals the area of a triangle with base 3.1−
1.5 = 1.6 and height 7, 500, 000 − 4, 500, 000 = 3, 000, 000. Therefore, the dead-
weight loss is 1.6×3,000,000
2
= $2, 400, 000.
(f) At the equilibrium price after the start of the pandemic but before the government
intervention ($2.50), each of the 5,000,000 consumers demands 4− 2.5 = 1.5 packs.
Being limited to a single pack means that the total quantity demanded in the market
will be 5, 000, 000 packs. This would be the quantity traded in the market, as well. It
is sufficient to know the quantity traded in the market to compute the dead-weight
3
loss. That quantity corresponds to marginal cost (read off the supply curve) of
5, 000, 000/3, 000, 000 = $1.66 and a marginal benefit (read off the individual inverse
demand curve) of 4 − 1 = $3.1 Therefore, the dead-weight loss equals the area of
a triangle with base 3 − 1.66 and height 7, 500, 000 − 5, 000, 000. Therefore, the
dead-weight loss is $1.67 million dollars.
The dead-weight loss is clearly less under the rationing scheme than it is under the
proposed price-ceiling law. The reason is that while both of them lead to inefficient
underproduction/underconsumption relative to the efficient level of 7, 500, 000 packs,
the quantity traded under the rationing scheme will be closer to the efficient level.
1Alternatively, one can solve 20, 000, 000− 5, 000, 000× P = 5, 000, 000 for P .
4
3. (a) The inverse demand curve in New Zealand is given by PNZ = 5−QNZ . Note that the
maximum willingness to pay in New Zealand ($5) is less than the marginal cost of
$10. Therefore, it would never be profitable to sell a positive quantity of the vaccine
in NZ. The problem reduces to determining the profit-maximising price in Australia.
Its inverse demand is given by PAU = 20.5−QAU and, therefore, its marginal revenue
is MRAU = 20.5 − 2QAU . Setting that to equal the marginal cost of $10, we find
that the quantity sold in Australia would be Q∗AU = 5.25, which corresponds to a
price of P ∗AU = (20.5 − 5.25 =)$15.25. The quantity sold in New Zealand would be
Q∗NZ = 0 and either Pfizeneca would not market the vaccine in New Zealand at all
or it would set a price at or above $5 (P ∗NZ ≥ 5).
(b) The profit-maximising condition for the firm is MRAU = MRCA = MRNZ = MC.
We already computed the marginal revenue in the Australian market. The marginal
revenue in the Canadian market is the same as the Australian market. Setting these
two marginal revenues to equal the marginal cost of $10, we reach the answers similar
to those in the previous part: P ∗AU = P
∗
CA = $15.25 and Q
∗
AU = Q
∗
CA = 5.25. As
before, it cannot be profitable for the firm to sell in New Zealand: Q∗NZ = 0 and
either P ∗NZ ≥ 5 or P ∗NZ is undefined.
(c) Note that the maximum quantity that Australia and New Zealand can demand
together is 25.5: this happens when the price of the covbegonium is $0. Therefore
the largest that the marginal cost at the new plant can become is $2.55 (this happens
if the new plant is producing the entire quantity of covbegnoium sold in Australia
and New Zealand at zero price), which is less than the old marginal cost. Therefore,
it would never be optimal (i.e. part of a profit-maximising plan) to produce at the
old plant and Pfizeneca would produce the entirety of its output at the new plant.
Therefore, Pfizeneca’s marginal cost is MC = 0.1Q = 0.1(QAU +QNZ).
The profit-maximising condition for the firm is MRAU = MRNZ = MC. We found
that MRAU = 20.5 − 2QAU . Similarly, we can check that MRNZ = 5 − 2QNZ .
As MRAU = MRNZ holds, this means that 20.5 − 2QAU = 5 − 2QNZ or QAU =
QNZ + 7.75. From MRNZ =MC, we have:
5−2QNZ = 0.1( QAU︸︷︷︸
=QNZ+7.75
+QNZ) = 0.1(QNZ+7.75+QNZ)⇔ 50−20QNZ = 2QNZ+7.75
Solving for QNZ , we get Q
∗
NZ ≈ 1.92. Therefore (and skipping some simple arith-
metic here), Q∗AU ≈ 9.67, P ∗NZ ≈ 3.08, P ∗AU ≈ 10.83. Pfizeneca would produce
the entirety of its output at the new plant for the reasons outlined above (i.e. the
marginal cost at the new plant is guaranteed to be lower than the marginal cost at
the old plant over the relevant range of possible production levels).
(d) Setting MRAU and MRCA to be equal to MRNZ , we have:
20.5− 2QCA = 20.5− 2QAU = 5− 2QNZ
5
Therefore, as above, we have
QAU = QCA = QNZ + 7.75. (1)
Similarly to the previous part, the maximum demand in the three countries is 20.5+
20.5 + 5 = 46 and, therefore, the marginal cost at the new plant can be no more
than 4.6, which is once again less than the cost at the old plant. Therefore, the old
plant would not be used and Pfizeneca would produce all of its output at the new
plant. Therefore, the firm’s MC is 0.1(QAU +QCA +QNZ) at the profit maximising
optimum. Setting that equal to the MRNZ and using (1), we have:
5− 2QNZ = 0.1(QNZ + 7.75 +QNZ + 7.75 +QNZ) = 0.1(3QNZ + 15.5)
Solving for QNZ , we get Q
∗
NZ = 1.5. Therefore (skipping some arithmetic), Q
∗
AU =
Q∗CA = 1.5 + 7.75 = 9.25, P
∗
NZ = 3.5, P
∗
AU = P
∗
CA = 11.25.
The reason that the profit-maximising quantity in New Zealand decreased relative to
the previous part of the problem was the lifting of the restrictions in the Canadian
market. More specifically, as Canadian consumers’ willingness to pay for covbe-
gonium tends to be larger than New Zealand consumers’, the opportunity cost of
selling additional units in New Zealand is now greater: those marginal units may be
sold more profitably in Canada instead. This causes the equilibrium output in New
Zealand to decrease.
6
4. (a) The two goods are substitutes: increasing the price of one increases demand for the
other one.
(b) The inverse demand for firm 1 is P1 = (6 + 0.5P2)−Q1 and, therefore, its marginal
revenue is MR1 = (6 + 0.5P2) − 2Q1. Setting that equal to the zero marginal cost
gives us Q∗1 = 3 + 0.25P2. Plugging that back into the inverse demand function, we
have P ∗1 (P2) = 3+0.25P2. Therefore, firm 1 is maximising its profits if it sets a price
that equals 3 + 0.25P2, where P2 is the price chosen by the other firm.
The problem is symmetric. Therefore, the corresponding equation for the other
firm is P ∗2 (P1) = 3 + 0.25P1. At a Nash equilibrium, both firms are maximising
their profits. Therefore, both equations hold simultaneously. To find the Nash
equilibrium, it suffices to plug one into the other:
P ∗1 = 3 + 0.25(3 + 0.25P
∗
1 ).
Solving for P ∗1 , we get P
∗
1 = 4. Then P
∗
2 = 3 + 0.25(4) = 4. Plugging the two
equilibrium prices into the given demand equations, we get Q∗1 = Q
∗
2 = 4.
(c) Following the previous part, firm 2 would choose the price P ∗2 (P1) = 3 + 0.25P1
if firm 1 chooses P1. Therefore, using the backward-induction logic of the rollback
equilibrium, firm 1 knows that firm 2 would do that. Therefore, the demand function
that firm 1 is facing becomes:
Q1 = 6− P1 + 0.5(3 + 0.25P1) = 7.5− 7
8
P1
Deriving inverse demand (P1 =
8
7
7.5− 8
7
Q1), marginal revenue (MR1 =
8
7
7.5− 16
7
Q1),
and setting the latter to equal zero, we find Q∗1 = 3.75. Plugging that into the
inverse demand, we compute P ∗1 ≈ 4.29. In response to that, firm 2 would choose
P ∗2 ≈ 3 + 0.25(4.29) ≈ 4.07. Firm 2’s quantity traded would be
Q2 ≈ 6 + 0.5(4.29)− 4.07 ≈ 4.075.
7
Semester 2, 2021
Final exam suggested solutions
1. (a) The quantity of hand sanitiser supplied decreases as the price of gin increases. As
gin is not an input for the production of hand sanitiser, it follows that gin and hand
sanitiser are substitutes in production.
(b) Plugging in the given values, we obtain the following expression for the quantity
supplied as a function of the price of hand sanitiser:
Qs = −12.17 + 0.1Phs − 0.03(48)− 0.07(17) + 0.4(27)
= −12.17 + 0.1Phs − 1.44− 1.19 + 10.8
= −4 + 0.1Phs
(c) Setting the given quantity demanded and the quantity supplied we computed in the
previous part to be equal to each other, we obtain:
−4 + 0.1Phs = 20− 0.2Phs ⇔ 0.3Phs = 24⇔ P ∗ = $80.
Therefore, the equilibrium price is $80. Plugging the equilibrium price in either of
the expressions for quantity supplied or quantity demanded would then give us the
equilibrium quantity: it is Q∗ = −4 + 0.1(80) = 4.
(d) Directly from the formula, the point elasticity of supply at P ∗ is
∆Q
∆P
× P
∗
Q∗
= 0.1× 80
4
= 2,
where we derived ∆Q
∆P
from the expression for quantity supplied (Qs = −4 + 0.1P ).
The coefficient of supply elasticity exceeds 1 and, therefore, supply is elastic.
(e) As above, we can set the quantity supplied and the quantity demanded to be equal
to each other to obtain:
−4 + 0.1Phs = 20− 0.1Phs ⇔ 0.2Phs = 24⇔ P ∗∗ = $120
Plugging the equilibrium price of $120 into the expression for the quantity supplied
once again, we see that the equilibrium quantity is Q∗∗ = −4 + 0.1(120) = 8.
(f) Directly from the formula, the arc elasticity of supply when moving from P ∗ = $80
1
to P ∗∗ = $120 is
∆Q
∆P
×
∑
P∑
Q
=
Q∗∗ −Q∗
P ∗∗ − P ∗ ×
P ∗ + P ∗∗
Q∗ +Q∗∗
=
8− 4
120− 80 ×
80 + 120
4 + 8
=
4
40
× 200
12
=
5
3
≈1.67.
The computed coefficient of elasticity exceeds 1 and, so, supply is elastic.
(g) The increase in demand moved the equilibrium along the upward sloping supply
curve: both the equilibrium quantity and the equilibrium price increased. Therefore,
revenue increased. The elasticity of supply is not relevant for this conclusion: it does
not matter whether supply is elastic, inelastic, unit-elastic or, indeed, perfectly elastic
or perfectly inelastic. If demand increases, the revenue is guaranteed to increase as
well.
2
2. (a) Before the pandemic started, there are 2.5 million consumers who demand the prod-
uct and each one of them has inverse demand given by P = 2−0.5q. This corresponds
to direct demand of q = 4− 2P . Multiplying by the number of consumers, the total
quantity demanded in the market is Qd = 10, 000, 000− 5, 000, 000× P .
(b) After the pandemic started, there are 5 million consumers who demand the product
and each one of them has inverse demand given by P = 4 − q. This corresponds
to direct demand q = 4 − P . Multiplying by the number of consumers, the total
quantity demand is Qd = 20, 000, 000− 5, 000, 000× P .
(c) Setting the quantity demanded and the quantity supplied to be equal to each other,
we get
10, 000, 000− 5, 000, 000× P = 3, 000, 000× P.
Solving for P , we see that the equilibrium price pre-pandemic is 10/8 = $1.25.
Plugging that price in the expression for the quantity supplied, we see that the
equilibrium quantity is 3, 000, 000× 1.25 = 3, 750, 000.
(d) Setting the quantity demanded (after the start of the pandemic) and the quantity
supplied to be equal to each other, we get
20, 000, 000− 5, 000, 000× P = 3, 000, 000× P.
Solving for P , we see that the new equilibrium price is 20/8 = $2.50. Plugging
that price in the expression for the quantity supplied, we see that the equilibrium
quantity is 3, 000, 000× 2.50 = 7, 500, 000.
(e) As 1.2 × 1.25 = 1.5, the Lord Mayor’s plan amounts to banning the price of the
product from climbing above $1.50. As 1.5 < 2.5, the proposed law is a binding
price ceiling. Therefore, the market will fail to clear, the prevailing market price
at which the product will be traded will be the price ceiling $1.50, and there will
be excess demand at the price ceiling. It follows that the quantity traded would be
determined by supply. That quantity is 3, 000, 000 × 1.5 = 4, 500, 000. The price
corresponding to quantity demanded of 4, 500, 000 is $3.10: we can find this by
solving
20, 000, 000− 5, 000, 000× P = 4, 500, 000
for P . Therefore, the dead-weight loss equals the area of a triangle with base 3.1−
1.5 = 1.6 and height 7, 500, 000 − 4, 500, 000 = 3, 000, 000. Therefore, the dead-
weight loss is 1.6×3,000,000
2
= $2, 400, 000.
(f) At the equilibrium price after the start of the pandemic but before the government
intervention ($2.50), each of the 5,000,000 consumers demands 4− 2.5 = 1.5 packs.
Being limited to a single pack means that the total quantity demanded in the market
will be 5, 000, 000 packs. This would be the quantity traded in the market, as well. It
is sufficient to know the quantity traded in the market to compute the dead-weight
3
loss. That quantity corresponds to marginal cost (read off the supply curve) of
5, 000, 000/3, 000, 000 = $1.66 and a marginal benefit (read off the individual inverse
demand curve) of 4 − 1 = $3.1 Therefore, the dead-weight loss equals the area of
a triangle with base 3 − 1.66 and height 7, 500, 000 − 5, 000, 000. Therefore, the
dead-weight loss is $1.67 million dollars.
The dead-weight loss is clearly less under the rationing scheme than it is under the
proposed price-ceiling law. The reason is that while both of them lead to inefficient
underproduction/underconsumption relative to the efficient level of 7, 500, 000 packs,
the quantity traded under the rationing scheme will be closer to the efficient level.
1Alternatively, one can solve 20, 000, 000− 5, 000, 000× P = 5, 000, 000 for P .
4
3. (a) The inverse demand curve in New Zealand is given by PNZ = 5−QNZ . Note that the
maximum willingness to pay in New Zealand ($5) is less than the marginal cost of
$10. Therefore, it would never be profitable to sell a positive quantity of the vaccine
in NZ. The problem reduces to determining the profit-maximising price in Australia.
Its inverse demand is given by PAU = 20.5−QAU and, therefore, its marginal revenue
is MRAU = 20.5 − 2QAU . Setting that to equal the marginal cost of $10, we find
that the quantity sold in Australia would be Q∗AU = 5.25, which corresponds to a
price of P ∗AU = (20.5 − 5.25 =)$15.25. The quantity sold in New Zealand would be
Q∗NZ = 0 and either Pfizeneca would not market the vaccine in New Zealand at all
or it would set a price at or above $5 (P ∗NZ ≥ 5).
(b) The profit-maximising condition for the firm is MRAU = MRCA = MRNZ = MC.
We already computed the marginal revenue in the Australian market. The marginal
revenue in the Canadian market is the same as the Australian market. Setting these
two marginal revenues to equal the marginal cost of $10, we reach the answers similar
to those in the previous part: P ∗AU = P
∗
CA = $15.25 and Q
∗
AU = Q
∗
CA = 5.25. As
before, it cannot be profitable for the firm to sell in New Zealand: Q∗NZ = 0 and
either P ∗NZ ≥ 5 or P ∗NZ is undefined.
(c) Note that the maximum quantity that Australia and New Zealand can demand
together is 25.5: this happens when the price of the covbegonium is $0. Therefore
the largest that the marginal cost at the new plant can become is $2.55 (this happens
if the new plant is producing the entire quantity of covbegnoium sold in Australia
and New Zealand at zero price), which is less than the old marginal cost. Therefore,
it would never be optimal (i.e. part of a profit-maximising plan) to produce at the
old plant and Pfizeneca would produce the entirety of its output at the new plant.
Therefore, Pfizeneca’s marginal cost is MC = 0.1Q = 0.1(QAU +QNZ).
The profit-maximising condition for the firm is MRAU = MRNZ = MC. We found
that MRAU = 20.5 − 2QAU . Similarly, we can check that MRNZ = 5 − 2QNZ .
As MRAU = MRNZ holds, this means that 20.5 − 2QAU = 5 − 2QNZ or QAU =
QNZ + 7.75. From MRNZ =MC, we have:
5−2QNZ = 0.1( QAU︸︷︷︸
=QNZ+7.75
+QNZ) = 0.1(QNZ+7.75+QNZ)⇔ 50−20QNZ = 2QNZ+7.75
Solving for QNZ , we get Q
∗
NZ ≈ 1.92. Therefore (and skipping some simple arith-
metic here), Q∗AU ≈ 9.67, P ∗NZ ≈ 3.08, P ∗AU ≈ 10.83. Pfizeneca would produce
the entirety of its output at the new plant for the reasons outlined above (i.e. the
marginal cost at the new plant is guaranteed to be lower than the marginal cost at
the old plant over the relevant range of possible production levels).
(d) Setting MRAU and MRCA to be equal to MRNZ , we have:
20.5− 2QCA = 20.5− 2QAU = 5− 2QNZ
5
Therefore, as above, we have
QAU = QCA = QNZ + 7.75. (1)
Similarly to the previous part, the maximum demand in the three countries is 20.5+
20.5 + 5 = 46 and, therefore, the marginal cost at the new plant can be no more
than 4.6, which is once again less than the cost at the old plant. Therefore, the old
plant would not be used and Pfizeneca would produce all of its output at the new
plant. Therefore, the firm’s MC is 0.1(QAU +QCA +QNZ) at the profit maximising
optimum. Setting that equal to the MRNZ and using (1), we have:
5− 2QNZ = 0.1(QNZ + 7.75 +QNZ + 7.75 +QNZ) = 0.1(3QNZ + 15.5)
Solving for QNZ , we get Q
∗
NZ = 1.5. Therefore (skipping some arithmetic), Q
∗
AU =
Q∗CA = 1.5 + 7.75 = 9.25, P
∗
NZ = 3.5, P
∗
AU = P
∗
CA = 11.25.
The reason that the profit-maximising quantity in New Zealand decreased relative to
the previous part of the problem was the lifting of the restrictions in the Canadian
market. More specifically, as Canadian consumers’ willingness to pay for covbe-
gonium tends to be larger than New Zealand consumers’, the opportunity cost of
selling additional units in New Zealand is now greater: those marginal units may be
sold more profitably in Canada instead. This causes the equilibrium output in New
Zealand to decrease.
6
4. (a) The two goods are substitutes: increasing the price of one increases demand for the
other one.
(b) The inverse demand for firm 1 is P1 = (6 + 0.5P2)−Q1 and, therefore, its marginal
revenue is MR1 = (6 + 0.5P2) − 2Q1. Setting that equal to the zero marginal cost
gives us Q∗1 = 3 + 0.25P2. Plugging that back into the inverse demand function, we
have P ∗1 (P2) = 3+0.25P2. Therefore, firm 1 is maximising its profits if it sets a price
that equals 3 + 0.25P2, where P2 is the price chosen by the other firm.
The problem is symmetric. Therefore, the corresponding equation for the other
firm is P ∗2 (P1) = 3 + 0.25P1. At a Nash equilibrium, both firms are maximising
their profits. Therefore, both equations hold simultaneously. To find the Nash
equilibrium, it suffices to plug one into the other:
P ∗1 = 3 + 0.25(3 + 0.25P
∗
1 ).
Solving for P ∗1 , we get P
∗
1 = 4. Then P
∗
2 = 3 + 0.25(4) = 4. Plugging the two
equilibrium prices into the given demand equations, we get Q∗1 = Q
∗
2 = 4.
(c) Following the previous part, firm 2 would choose the price P ∗2 (P1) = 3 + 0.25P1
if firm 1 chooses P1. Therefore, using the backward-induction logic of the rollback
equilibrium, firm 1 knows that firm 2 would do that. Therefore, the demand function
that firm 1 is facing becomes:
Q1 = 6− P1 + 0.5(3 + 0.25P1) = 7.5− 7
8
P1
Deriving inverse demand (P1 =
8
7
7.5− 8
7
Q1), marginal revenue (MR1 =
8
7
7.5− 16
7
Q1),
and setting the latter to equal zero, we find Q∗1 = 3.75. Plugging that into the
inverse demand, we compute P ∗1 ≈ 4.29. In response to that, firm 2 would choose
P ∗2 ≈ 3 + 0.25(4.29) ≈ 4.07. Firm 2’s quantity traded would be
Q2 ≈ 6 + 0.5(4.29)− 4.07 ≈ 4.075.
7
