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Question 2 NAT · 1.0 marks
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
Q1*=……..
Published solution
**1. Derive reaction functions:** \(P=80-Q_1-Q_2\) and \(\pi_i=(72-Q_i-Q_j)Q_i\). The first-order condition gives \(Q_i=(72-Q_j)/2\).
**2. Solve simultaneously:** Identical costs give \(Q_1=Q_2=Q\). Then \(2Q=72-Q\), so each firm produces 24.
**3. Price and profit:** \(P=80-24-24=32\); each profit is \((32-8)24=576\).
**Answer: 24.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
Q2*=……………
Published solution
**1. Derive reaction functions:** \(P=80-Q_1-Q_2\) and \(\pi_i=(72-Q_i-Q_j)Q_i\). The first-order condition gives \(Q_i=(72-Q_j)/2\).
**2. Solve simultaneously:** Identical costs give \(Q_1=Q_2=Q\). Then \(2Q=72-Q\), so each firm produces 24.
**3. Price and profit:** \(P=80-24-24=32\); each profit is \((32-8)24=576\).
**Answer: 24.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
P*=............
Published solution
**1. Derive reaction functions:** \(P=80-Q_1-Q_2\) and \(\pi_i=(72-Q_i-Q_j)Q_i\). The first-order condition gives \(Q_i=(72-Q_j)/2\).
**2. Solve simultaneously:** Identical costs give \(Q_1=Q_2=Q\). Then \(2Q=72-Q\), so each firm produces 24.
**3. Price and profit:** \(P=80-24-24=32\); each profit is \((32-8)24=576\).
**Answer: 32.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
π1=………
Published solution
**1. Derive reaction functions:** \(P=80-Q_1-Q_2\) and \(\pi_i=(72-Q_i-Q_j)Q_i\). The first-order condition gives \(Q_i=(72-Q_j)/2\).
**2. Solve simultaneously:** Identical costs give \(Q_1=Q_2=Q\). Then \(2Q=72-Q\), so each firm produces 24.
**3. Price and profit:** \(P=80-24-24=32\); each profit is \((32-8)24=576\).
**Answer: 576.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
π2=…….
Published solution
**1. Derive reaction functions:** \(P=80-Q_1-Q_2\) and \(\pi_i=(72-Q_i-Q_j)Q_i\). The first-order condition gives \(Q_i=(72-Q_j)/2\).
**2. Solve simultaneously:** Identical costs give \(Q_1=Q_2=Q\). Then \(2Q=72-Q\), so each firm produces 24.
**3. Price and profit:** \(P=80-24-24=32\); each profit is \((32-8)24=576\).
**Answer: 576.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
Now suppose that the two firms are competing in the Stackelberg manner where one of the firms
makes its output decision before the other. Suppose Firm 1 is the Stackelberg leader (i.e., makes
its output decisions before Firm 2). Calculate the equilibrium quantity for the firms, equilibrium
market price and profits (π1, π2) of both the firms in equilibrium.
Q1………..
Published solution
**1. Use the follower’s response:** Firm 2 chooses \(Q_2=(72-Q_1)/2\). Firm 1 anticipates this response.
**2. Maximize the leader’s profit:** \[\pi_1=\left(36-\frac{Q_1}{2}\right)Q_1.\] Its derivative is \(36-Q_1\), giving \(Q_1=36\); the second derivative is −1.
**3. Recover other outcomes:** \(Q_2=18\), \(P=80-36-18=26\), \(\pi_1=(26-8)36=648\), and \(\pi_2=(26-8)18=324\).
**Answer: 36.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
Now suppose that the two firms are competing in the Stackelberg manner where one of the firms
makes its output decision before the other. Suppose Firm 1 is the Stackelberg leader (i.e., makes
its output decisions before Firm 2). Calculate the equilibrium quantity for the firms, equilibrium
market price and profits (π1, π2) of both the firms in equilibrium.
Q2………………
Published solution
**1. Use the follower’s response:** Firm 2 chooses \(Q_2=(72-Q_1)/2\). Firm 1 anticipates this response.
**2. Maximize the leader’s profit:** \[\pi_1=\left(36-\frac{Q_1}{2}\right)Q_1.\] Its derivative is \(36-Q_1\), giving \(Q_1=36\); the second derivative is −1.
**3. Recover other outcomes:** \(Q_2=18\), \(P=80-36-18=26\), \(\pi_1=(26-8)36=648\), and \(\pi_2=(26-8)18=324\).
**Answer: 18.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
Now suppose that the two firms are competing in the Stackelberg manner where one of the firms
makes its output decision before the other. Suppose Firm 1 is the Stackelberg leader (i.e., makes
its output decisions before Firm 2). Calculate the equilibrium quantity for the firms, equilibrium
market price and profits (π1, π2) of both the firms in equilibrium.
P*=............
Published solution
**1. Use the follower’s response:** Firm 2 chooses \(Q_2=(72-Q_1)/2\). Firm 1 anticipates this response.
**2. Maximize the leader’s profit:** \[\pi_1=\left(36-\frac{Q_1}{2}\right)Q_1.\] Its derivative is \(36-Q_1\), giving \(Q_1=36\); the second derivative is −1.
**3. Recover other outcomes:** \(Q_2=18\), \(P=80-36-18=26\), \(\pi_1=(26-8)36=648\), and \(\pi_2=(26-8)18=324\).
**Answer: 26.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
Now suppose that the two firms are competing in the Stackelberg manner where one of the firms
makes its output decision before the other. Suppose Firm 1 is the Stackelberg leader (i.e., makes
its output decisions before Firm 2). Calculate the equilibrium quantity for the firms, equilibrium
market price and profits (π1, π2) of both the firms in equilibrium.
π1…………
Published solution
**1. Use the follower’s response:** Firm 2 chooses \(Q_2=(72-Q_1)/2\). Firm 1 anticipates this response.
**2. Maximize the leader’s profit:** \[\pi_1=\left(36-\frac{Q_1}{2}\right)Q_1.\] Its derivative is \(36-Q_1\), giving \(Q_1=36\); the second derivative is −1.
**3. Recover other outcomes:** \(Q_2=18\), \(P=80-36-18=26\), \(\pi_1=(26-8)36=648\), and \(\pi_2=(26-8)18=324\).
**Answer: 648.**
Suppose two firms operate in a market and can produce at a constant average (and marginal) cost
of AC = MC = $8. Let Q1 be the output of the first firm and Q2 be the output of the second. Market
demand is given by Q1+ Q2 = 80 - P. Assuming that the firms are competing as per the Cournot
competition, find out the equilibrium quantity for each firm, equilibrium price and profit (π1, π2) of
each firm.
Based on the above data, answer the given subquestions.
Now suppose that the two firms are competing in the Stackelberg manner where one of the firms
makes its output decision before the other. Suppose Firm 1 is the Stackelberg leader (i.e., makes
its output decisions before Firm 2). Calculate the equilibrium quantity for the firms, equilibrium
market price and profits (π1, π2) of both the firms in equilibrium.
π2………
Published solution
**1. Use the follower’s response:** Firm 2 chooses \(Q_2=(72-Q_1)/2\). Firm 1 anticipates this response.
**2. Maximize the leader’s profit:** \[\pi_1=\left(36-\frac{Q_1}{2}\right)Q_1.\] Its derivative is \(36-Q_1\), giving \(Q_1=36\); the second derivative is −1.
**3. Recover other outcomes:** \(Q_2=18\), \(P=80-36-18=26\), \(\pi_1=(26-8)36=648\), and \(\pi_2=(26-8)18=324\).
**Answer: 324.**
In a market for dry cleaning, the inverse market demand function is given by P = 150 - Q and the
(private) marginal cost of production for the aggregation of all dry cleaning firms is given by MC
=30 + Q. Finally, the pollution generated by the dry cleaning process creates external damages
given by the marginal external cost curve MEC = 2Q.
Based on the above data, answer the given subquestions.
Calculate the output level and price of dry cleaning if it is produced under competitive conditions
without regulation.
Q*=.............
Published solution
**1. Equate demand with private marginal cost:** Unregulated competitive firms ignore external damage, so \(150-Q=30+Q\).
**2. Solve:** \(2Q=120\), giving \(Q=60\) and \(P=150-60=90\).
**Answer: 60.**
In a market for dry cleaning, the inverse market demand function is given by P = 150 - Q and the
(private) marginal cost of production for the aggregation of all dry cleaning firms is given by MC
=30 + Q. Finally, the pollution generated by the dry cleaning process creates external damages
given by the marginal external cost curve MEC = 2Q.
Based on the above data, answer the given subquestions.
Calculate the output level and price of dry cleaning if it is produced under competitive conditions
without regulation.
P*=.............
Published solution
**1. Equate demand with private marginal cost:** Unregulated competitive firms ignore external damage, so \(150-Q=30+Q\).
**2. Solve:** \(2Q=120\), giving \(Q=60\) and \(P=150-60=90\).
**Answer: 90.**
In a market for dry cleaning, the inverse market demand function is given by P = 150 - Q and the
(private) marginal cost of production for the aggregation of all dry cleaning firms is given by MC
=30 + Q. Finally, the pollution generated by the dry cleaning process creates external damages
given by the marginal external cost curve MEC = 2Q.
Based on the above data, answer the given subquestions.
Determine the socially efficient price and output of dry cleaning.
QS=.............
Published solution
**1. Add the external cost:** \(MSC=MC+MEC=30+Q+2Q=30+3Q\).
**2. Equate marginal benefit and social cost:** \(150-Q=30+3Q\) gives \(Q_s=30\). The demand-side efficient price is \(P_s=150-30=120\).
**Answer: 30.**
In a market for dry cleaning, the inverse market demand function is given by P = 150 - Q and the
(private) marginal cost of production for the aggregation of all dry cleaning firms is given by MC
=30 + Q. Finally, the pollution generated by the dry cleaning process creates external damages
given by the marginal external cost curve MEC = 2Q.
Based on the above data, answer the given subquestions.
Determine the socially efficient price and output of dry cleaning.
PS=.............
Published solution
**1. Add the external cost:** \(MSC=MC+MEC=30+Q+2Q=30+3Q\).
**2. Equate marginal benefit and social cost:** \(150-Q=30+3Q\) gives \(Q_s=30\). The demand-side efficient price is \(P_s=150-30=120\).
**Answer: 120.**
In a market for dry cleaning, the inverse market demand function is given by P = 150 - Q and the
(private) marginal cost of production for the aggregation of all dry cleaning firms is given by MC
=30 + Q. Finally, the pollution generated by the dry cleaning process creates external damages
given by the marginal external cost curve MEC = 2Q.
Based on the above data, answer the given subquestions.
Determine the tax (per unit) that would result in a competitive market producing the socially
efficient output.
t=.............
A published solution is not available for this question yet.
In a market for dry cleaning, the inverse market demand function is given by P = 150 - Q and the
(private) marginal cost of production for the aggregation of all dry cleaning firms is given by MC
=30 + Q. Finally, the pollution generated by the dry cleaning process creates external damages
given by the marginal external cost curve MEC = 2Q.
Based on the above data, answer the given subquestions.
Calculate the output and price of dry cleaning if it is produced under monopolistic conditions
without regulation.
Qm………….
Published solution
**1. Compute marginal revenue:** From \(P=150-Q\), \(TR=150Q-Q^2\) and \(MR=150-2Q\).
**2. Set MR equal to private MC:** \(150-2Q=30+Q\) gives \(Q_m=40\), then \(P_m=150-40=110\). External damage is ignored in this unregulated decision.
**Answer: 40.**
In a market for dry cleaning, the inverse market demand function is given by P = 150 - Q and the
(private) marginal cost of production for the aggregation of all dry cleaning firms is given by MC
=30 + Q. Finally, the pollution generated by the dry cleaning process creates external damages
given by the marginal external cost curve MEC = 2Q.
Based on the above data, answer the given subquestions.
Calculate the output and price of dry cleaning if it is produced under monopolistic conditions
without regulation.
Pm…………
Published solution
**1. Compute marginal revenue:** From \(P=150-Q\), \(TR=150Q-Q^2\) and \(MR=150-2Q\).
**2. Set MR equal to private MC:** \(150-2Q=30+Q\) gives \(Q_m=40\), then \(P_m=150-40=110\). External damage is ignored in this unregulated decision.
**Answer: 110.**
Based on the above data, answer the given subquestions.
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4
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3
Published solution
**1. Set marginal product per dollar equal:** For \(Q=120\sqrt{LK}\), \(MP_L/MP_K=K/L\). Cost minimization requires \(K/L=w/r=10/40=1/4\).
**Answer: B — \(K/L=1/4\).**
A: **Incorrect:** This reverses the cost-minimizing input ratio.
B: **Correct:** The input ratio equals wage divided by capital rental rate.
C: **Incorrect:** The required ratio is 1/4, not 1/3.
D: **Incorrect:** The required ratio is 1/4, not 3.
Based on the above data, answer the given subquestions.
What is the cost minimizing input combination if the firm wants to produce 720 units per year? L*=
.............
Published solution
**1. Set marginal product per dollar equal:** For \(Q=120\sqrt{LK}\), \(MP_L/MP_K=K/L\). Cost minimization requires \(K/L=w/r=10/40=1/4\).
**2. Produce 720 units:** \(LK=(720/120)^2=36\). With \(K=L/4\), \(L^2/4=36\), so \(L=12\) and \(K=3\).
**Answer: 12.**
Based on the above data, answer the given subquestions.
What is the cost minimizing input combination if the firm wants to produce 720 units per year?
K*= ..............
Published solution
**1. Set marginal product per dollar equal:** For \(Q=120\sqrt{LK}\), \(MP_L/MP_K=K/L\). Cost minimization requires \(K/L=w/r=10/40=1/4\).
**2. Produce 720 units:** \(LK=(720/120)^2=36\). With \(K=L/4\), \(L^2/4=36\), so \(L=12\) and \(K=3\).
**Answer: 3.**
Based on the above data, answer the given subquestions.
Find the expected value of return on investment A is ……….. (in $)
Published solution
**1. Weight each payoff:** Investment A pays 300,250,200 with probabilities 0.1,0.8,0.1.
**2. Sum:** \[E[I_A]=0.1(300)+0.8(250)+0.1(200)=250.\]
**Answer: 250.**
Based on the above data, answer the given subquestions.
The expected value of return on investment B is ……….. (in $)
Published solution
**1. Weight each payoff:** Investment B pays 300,250,200 with probabilities 0.3,0.4,0.3.
**2. Sum:** \[E[I_B]=0.3(300)+0.4(250)+0.3(200)=250.\]
**Answer: 250.**
Based on the above data, answer the given subquestions.
Jill has the utility function U=5I, where I denotes the payoff. What is Jill's expected utility from
investment A is EU = ................
Published solution
**1. Transform each payoff:** With \(U(I)=5I\), the utilities at 300,250,200 are 1500,1250,1000.
**2. Weight and sum:** \[EU=0.1(1500)+0.8(1250)+0.1(1000)=1250.\]
**Answer: 1250.**
Based on the above data, answer the given subquestions.
Jill’s expected utility from investment B is EU = .............
Published solution
**1. Transform each payoff:** With \(U(I)=5I\), the utilities at 300,250,200 are 1500,1250,1000.
**2. Weight and sum:** \[EU=0.3(1500)+0.4(1250)+0.3(1000)=1250.\]
**Answer: 1250.**
Based on the above data, answer the given subquestions.
According to these preferences Jill will prefer
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Investment A
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Investment B
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Jill is indifferent
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Cannot be determined
Published solution
**1. Compare expected utilities:** Since \(U(I)=5I\), both investments give \(EU=5(250)=1250\). Their different spreads do not matter under linear utility.
**Answer: C — Jill is indifferent.**
A: **Incorrect:** A has no higher expected utility.
B: **Incorrect:** B has no higher expected utility.
C: **Correct:** Both deliver the same expected utility.
D: **Incorrect:** Payoffs, probabilities and the utility function are given.
A monopolist faces the demand curve P=25-Q, where P is measured in dollars per unit and Q in
thousands of units. The monopolist has a constant average cost of $5 per unit. Answer the given
subquestions.
What are the monopolist’s profit-maximizing price and quantity? P*= ……
Published solution
**1. Account for units:** Q is measured in thousands. Constant average cost 5 implies marginal cost 5, so \(MR=25-2Q=5\).
**2. Solve:** \(Q=10\) thousand units, or 10000 actual units. Price is \(P=25-10=15\).
**Answer: 15.**
A monopolist faces the demand curve P=25-Q, where P is measured in dollars per unit and Q in
thousands of units. The monopolist has a constant average cost of $5 per unit. Answer the given
subquestions.
What are the monopolist’s profit-maximizing price and quantity? Q*= ……
Published solution
**1. Account for units:** Q is measured in thousands. Constant average cost 5 implies marginal cost 5, so \(MR=25-2Q=5\).
**2. Solve:** \(Q=10\) thousand units, or 10000 actual units. Price is \(P=25-10=15\).
**Answer: 10000 units (10 thousand units).**
**Convention note:** The solution is 10 in the demand equation’s thousand-unit convention, equivalent to 10000 actual units. The source scoring key expects actual units.
A monopolist faces the demand curve P=25-Q, where P is measured in dollars per unit and Q in
thousands of units. The monopolist has a constant average cost of $5 per unit. Answer the given
subquestions.
The resulting profit will be …………….
Published solution
**1. Account for units:** Q is measured in thousands. Constant average cost 5 implies marginal cost 5, so \(MR=25-2Q=5\).
**2. Solve:** \(Q=10\) thousand units, or 10000 actual units. Price is \(P=25-10=15\).
**3. Subtract total cost from revenue:** \[\pi=(15-5)(10000)=100000\text{ dollars}.\]
**Answer: 100000.**
A monopolist faces the demand curve P=25-Q, where P is measured in dollars per unit and Q in
thousands of units. The monopolist has a constant average cost of $5 per unit. Answer the given
subquestions.
The firm’s Lerner index is …………….
Published solution
**1. Account for units:** Q is measured in thousands. Constant average cost 5 implies marginal cost 5, so \(MR=25-2Q=5\).
**2. Solve:** \(Q=10\) thousand units, or 10000 actual units. Price is \(P=25-10=15\).
**3. Calculate the Lerner index:** \[\frac{P-MC}{P}=\frac{15-5}{15}=\frac23\approx0.6667.\]
**Answer: \(2/3\approx0.6667\).**
**1. Compare incremental gain and cost:** A marginal increase in advertising raises contribution by \((P-MC)\Delta Q\).
**2. Apply the interior optimality condition:** At the optimum, marginal contribution equals the stated advertising cost 1: \[(P-MC)\Delta Q=1.\]
**Answer: 1.**
Select the option that describes an indirect network effect
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The value of a product or service increases for one group of users as the
number of users on a complementary platform increases.
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The value of a product or service increases for an individual user as more
people adopt the same product or service
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A product is advertised through a television advertisement
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A product is advertised on social media
Published solution
**1. Identify the cross-group benefit:** An indirect network effect arises when more participants on one side or complementary platform increase value for the other group, such as users attracting more developers.
**Answer: A — The value of a product or service increases for one group of users as the .**
A: **Correct:** This describes a cross-group or complementary-platform effect.
B: **Incorrect:** This is a direct network effect among users of the same product.
C: **Incorrect:** Advertising alone is not a network effect.
D: **Incorrect:** A social-media advertisement is not itself a network effect.
**1. Apply the two tests:** A common resource is difficult to exclude people from, but one person’s use reduces what remains for others. Thus it is nonexcludable and rival.
**Answer: A — Rival and non excludable.**
A: **Correct:** Both defining properties of a common resource hold.
B: **Incorrect:** These are the properties of a club good.
C: **Incorrect:** These are the properties of a public good.
D: **Incorrect:** These are the properties of a private good.
**1. Relate revenue and elasticity:** With \(\epsilon<0\), \(MR=P(1+1/\epsilon)\). On the strictly inelastic segment, MR is negative.
**2. Reduce output:** A monopolist can raise total revenue while avoiding production cost by reducing output there. With nonnegative marginal cost, that segment cannot be a profit maximum.
**Answer: B — The inelastic region of a market demand curve.**
**Convention note:** This standard result assumes nonnegative marginal cost; with zero marginal cost, the optimum can be at unit elasticity.
A: **Incorrect:** With positive marginal cost the usual optimum lies in the elastic region.
B: **Correct:** A strictly inelastic point has negative marginal revenue.
C: **Incorrect:** Only the strictly inelastic region is ruled out by this argument.
D: **Incorrect:** The inelastic segment is ruled out.
If bad drivers can usually avoid being ticketed by the police, then insurance companies will
6406537375186.
Use one’s driving record as a signal
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Use one’s driving record as a screening device
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Not be able to use one’s driving record as a screening device
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Request driving records directly from the police and not the individual
applicant
Published solution
**1. Assess the information in the record:** If unsafe drivers avoid tickets, a clean driving record no longer reliably distinguishes low-risk from high-risk applicants.
**2. Infer the consequence:** The record loses effectiveness as a screening device for driving risk.
**Answer: C — Not be able to use one’s driving record as a screening device.**
A: **Incorrect:** Ticket avoidance makes the record an unreliable signal of safety.
B: **Incorrect:** Reliable screening requires the record to distinguish driver types.
C: **Correct:** Bad drivers can conceal their risk by avoiding recorded tickets.
D: **Incorrect:** Obtaining the same incomplete record from police does not fix missing violations.
Quasi linear preferences are linear in one good and non-linear in the other
good
6406537375191.
U=min{ax, by} represents complements
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U= ax+by represents substitutes
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If a person always chooses three units of one good for one unit of another
good then they have leontief preferences
Published solution
**1. Recognize preference forms:** Quasilinear utility is linear in one good; \(\min\{ax,by\}\) represents perfect complements, and \(ax+by\) perfect substitutes for positive coefficients.
**2. Distinguish choices from preference structure:** Observing a 3:1 consumption ratio does not by itself establish Leontief utility; other preferences can produce the same ratio at particular prices and income.
**Answer: D — A fixed chosen ratio alone does not prove Leontief preferences.**
**Convention note:** If “always” is meant to stipulate that the goods are useful only in a fixed 3:1 proportion, this would indeed describe Leontief preferences. The intended answer treats it as an inference from observed choices.
A: **Incorrect:** This is the usual quasilinear form, so do not select it as incorrect.
B: **Incorrect:** The minimum form represents fixed-proportion complements, so do not select it.
C: **Incorrect:** Linear utility represents perfect substitutes, so do not select it.
D: **Correct:** A chosen ratio alone does not establish perfect-complement preferences; this is the intended incorrect inference.
The fraction of quantity tax paid by buyers rises as supply becomes more own-
price elastic
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The fraction of quantity tax paid by buyers rises as demand becomes less own
price elastic
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Both the fraction of quantity tax paid by buyers rises as supply becomes more
own-price elastic and the fraction of quantity tax paid by buyers rises as demand becomes less
own price elastic
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None of these
Published solution
**1. Use tax incidence:** The buyer’s share of a small per-unit tax is \(E_S/(E_S+|E_D|)\), with positive supply elasticity \(E_S\).
**2. Compare changes:** Raising \(E_S\) or reducing \(|E_D|\) raises that share. Buyers bear more when supply is more elastic or demand is less elastic.
**Answer: C — Both statements.**
A: **Incorrect:** This is true, but the second claim is also true.
B: **Incorrect:** This is true, but the first claim is also true.
C: **Correct:** Both elasticity changes raise the buyer’s tax share.
D: **Incorrect:** Both statements are true.
