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Question 2 NAT · 1.5 marks
Based on the above data, answer the given subquestions.
Calculate the output of paper if it is produced under competitive conditions and no attempt is
made to monitor or regulate the dumping of effluent. Q = ______
Published solution
**1. Read the market equations:** Demand is \(Q_D=160{,}000-2{,}000P\), while private supply is \(Q_S=40{,}000+2{,}000P\). Without pollution regulation, producers consider private costs and ignore the marginal external damage.
**2. Equate demand and private supply:**
\[160{,}000-2{,}000P=40{,}000+2{,}000P.\]
Hence \(120{,}000=4{,}000P\), giving \(P=30\).
**3. Find output:** \(Q=160{,}000-2{,}000(30)=100{,}000\) lots, with each lot containing 100 pounds. The unregulated equilibrium ignores pollution costs imposed on others.
**Requested value:** Competitive output is 100,000 lots.
**Answer: 100000.**
Based on the above data, answer the given subquestions.
Calculate the Price of paper if it is produced under competitive conditions and no attempt is made
to monitor or regulate the dumping of effluent. P = ________
Published solution
**1. Read the market equations:** Demand is \(Q_D=160{,}000-2{,}000P\), while private supply is \(Q_S=40{,}000+2{,}000P\). Without pollution regulation, producers consider private costs and ignore the marginal external damage.
**2. Equate demand and private supply:**
\[160{,}000-2{,}000P=40{,}000+2{,}000P.\]
Hence \(120{,}000=4{,}000P\), giving \(P=30\).
**3. Find output:** \(Q=160{,}000-2{,}000(30)=100{,}000\) lots, with each lot containing 100 pounds. The unregulated equilibrium ignores pollution costs imposed on others.
**Requested value:** The competitive price is 30 per 100-pound lot.
**Answer: 30.**
Based on the above data, answer the given subquestions.
Determine the socially efficient price of paper. P = ____________
Published solution
**1. Express marginal benefit and private cost:** Inverse demand gives \(MB=80-0.0005Q\). Inverse private supply gives \(MPC=0.0005Q-20\). The source’s marginal external cost is \(MEC=0.0006Q\).
**2. Include pollution damage:** Social marginal cost is the private production cost plus harm imposed on others:
\[MSC=MPC+MEC=0.0011Q-20.\]
**3. Find efficient quantity:** Set marginal benefit equal to social marginal cost: \(80-0.0005Q=0.0011Q-20\). Thus \(100=0.0016Q\), giving \(Q^*=62{,}500\) lots.
**4. Find the corresponding demand price:** \(P^*=80-0.0005(62{,}500)=48.75\) per lot. Private marginal cost there is 11.25 and marginal external damage is 37.50; their sum is 48.75. Efficient output is lower than unregulated output because pollution is costly.
**Requested value:** The socially efficient consumer price is 48.75.
**Answer: 48.75.**
Based on the above data, answer the given subquestions.
Determine the socially efficient quantity of paper. Q = __________
Published solution
**1. Express marginal benefit and private cost:** Inverse demand gives \(MB=80-0.0005Q\). Inverse private supply gives \(MPC=0.0005Q-20\). The source’s marginal external cost is \(MEC=0.0006Q\).
**2. Include pollution damage:** Social marginal cost is the private production cost plus harm imposed on others:
\[MSC=MPC+MEC=0.0011Q-20.\]
**3. Find efficient quantity:** Set marginal benefit equal to social marginal cost: \(80-0.0005Q=0.0011Q-20\). Thus \(100=0.0016Q\), giving \(Q^*=62{,}500\) lots.
**4. Find the corresponding demand price:** \(P^*=80-0.0005(62{,}500)=48.75\) per lot. Private marginal cost there is 11.25 and marginal external damage is 37.50; their sum is 48.75. Efficient output is lower than unregulated output because pollution is costly.
**Requested value:** Socially efficient output is 62,500 lots.
**Answer: 62500.**
Based on the above data, answer the given subquestions.
Published solution
**1. Set up the simultaneous quantity game:** Demand is \(P=70-Q_1-Q_2\), and both firms have constant average and marginal cost 10. Firm 1’s profit is \(\pi_1=(60-Q_1-Q_2)Q_1\); Firm 2 has the corresponding expression.
**2. Derive best responses:** Holding the other firm’s output fixed, differentiate profit:
\[60-2Q_1-Q_2=0,\qquad60-Q_1-2Q_2=0.\]
Thus \(Q_1=(60-Q_2)/2\) and \(Q_2=(60-Q_1)/2\) for positive outputs. The second derivative in own output is -2, so each best response maximizes own profit.
**3. Solve jointly:** Symmetry gives \(Q_1=Q_2=q\). Then \(3q=60\), so both quantities are 20. Total output is 40 and \(P=70-40=30\).
**4. Compute profits:** Each firm earns \((30-10)(20)=400\). These are mutual best responses, so neither firm can profit by changing only its own quantity.
**Requested value:** Firm 1 output is 20.
**Answer: 20.**
Based on the above data, answer the given subquestions.
Published solution
**1. Set up the simultaneous quantity game:** Demand is \(P=70-Q_1-Q_2\), and both firms have constant average and marginal cost 10. Firm 1’s profit is \(\pi_1=(60-Q_1-Q_2)Q_1\); Firm 2 has the corresponding expression.
**2. Derive best responses:** Holding the other firm’s output fixed, differentiate profit:
\[60-2Q_1-Q_2=0,\qquad60-Q_1-2Q_2=0.\]
Thus \(Q_1=(60-Q_2)/2\) and \(Q_2=(60-Q_1)/2\) for positive outputs. The second derivative in own output is -2, so each best response maximizes own profit.
**3. Solve jointly:** Symmetry gives \(Q_1=Q_2=q\). Then \(3q=60\), so both quantities are 20. Total output is 40 and \(P=70-40=30\).
**4. Compute profits:** Each firm earns \((30-10)(20)=400\). These are mutual best responses, so neither firm can profit by changing only its own quantity.
**Requested value:** Firm 2 output is 20.
**Answer: 20.**
Based on the above data, answer the given subquestions.
Published solution
**1. Set up the simultaneous quantity game:** Demand is \(P=70-Q_1-Q_2\), and both firms have constant average and marginal cost 10. Firm 1’s profit is \(\pi_1=(60-Q_1-Q_2)Q_1\); Firm 2 has the corresponding expression.
**2. Derive best responses:** Holding the other firm’s output fixed, differentiate profit:
\[60-2Q_1-Q_2=0,\qquad60-Q_1-2Q_2=0.\]
Thus \(Q_1=(60-Q_2)/2\) and \(Q_2=(60-Q_1)/2\) for positive outputs. The second derivative in own output is -2, so each best response maximizes own profit.
**3. Solve jointly:** Symmetry gives \(Q_1=Q_2=q\). Then \(3q=60\), so both quantities are 20. Total output is 40 and \(P=70-40=30\).
**4. Compute profits:** Each firm earns \((30-10)(20)=400\). These are mutual best responses, so neither firm can profit by changing only its own quantity.
**Requested value:** Market price is 30.
**Answer: 30.**
Based on the above data, answer the given subquestions.
Published solution
**1. Set up the simultaneous quantity game:** Demand is \(P=70-Q_1-Q_2\), and both firms have constant average and marginal cost 10. Firm 1’s profit is \(\pi_1=(60-Q_1-Q_2)Q_1\); Firm 2 has the corresponding expression.
**2. Derive best responses:** Holding the other firm’s output fixed, differentiate profit:
\[60-2Q_1-Q_2=0,\qquad60-Q_1-2Q_2=0.\]
Thus \(Q_1=(60-Q_2)/2\) and \(Q_2=(60-Q_1)/2\) for positive outputs. The second derivative in own output is -2, so each best response maximizes own profit.
**3. Solve jointly:** Symmetry gives \(Q_1=Q_2=q\). Then \(3q=60\), so both quantities are 20. Total output is 40 and \(P=70-40=30\).
**4. Compute profits:** Each firm earns \((30-10)(20)=400\). These are mutual best responses, so neither firm can profit by changing only its own quantity.
**Requested value:** Firm 1 profit is 400.
**Answer: 400.**
Based on the above data, answer the given subquestions.
Published solution
**1. Set up the simultaneous quantity game:** Demand is \(P=70-Q_1-Q_2\), and both firms have constant average and marginal cost 10. Firm 1’s profit is \(\pi_1=(60-Q_1-Q_2)Q_1\); Firm 2 has the corresponding expression.
**2. Derive best responses:** Holding the other firm’s output fixed, differentiate profit:
\[60-2Q_1-Q_2=0,\qquad60-Q_1-2Q_2=0.\]
Thus \(Q_1=(60-Q_2)/2\) and \(Q_2=(60-Q_1)/2\) for positive outputs. The second derivative in own output is -2, so each best response maximizes own profit.
**3. Solve jointly:** Symmetry gives \(Q_1=Q_2=q\). Then \(3q=60\), so both quantities are 20. Total output is 40 and \(P=70-40=30\).
**4. Compute profits:** Each firm earns \((30-10)(20)=400\). These are mutual best responses, so neither firm can profit by changing only its own quantity.
**Requested value:** Firm 2 profit is 400.
**Answer: 400.**
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.
Published solution
**1. Use backward induction:** Firm 1 chooses output first. After observing it, Firm 2 maximizes \(\pi_2=(60-Q_1-Q_2)Q_2\), giving response \(Q_2=(60-Q_1)/2\) when positive.
**2. Let the leader anticipate this response:** Substitute the follower’s choice into Firm 1’s profit:
\[\pi_1=\left(60-Q_1-\frac{60-Q_1}{2}\right)Q_1=30Q_1-\frac12Q_1^2.\]
Differentiating gives \(30-Q_1=0\), so \(Q_1^*=30\). Its second derivative is -1, confirming a maximum.
**3. Recover follower output and price:** \(Q_2^*=(60-30)/2=15\). Total output is 45, giving \(P^*=70-45=25\).
**4. Calculate profits:** \(\pi_1=(25-10)(30)=450\) and \(\pi_2=(25-10)(15)=225\). Commitment lets the leader earn more by anticipating the follower’s response.
**Requested value:** Leader output is 30.
**Answer: 30.**
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.
Published solution
**1. Use backward induction:** Firm 1 chooses output first. After observing it, Firm 2 maximizes \(\pi_2=(60-Q_1-Q_2)Q_2\), giving response \(Q_2=(60-Q_1)/2\) when positive.
**2. Let the leader anticipate this response:** Substitute the follower’s choice into Firm 1’s profit:
\[\pi_1=\left(60-Q_1-\frac{60-Q_1}{2}\right)Q_1=30Q_1-\frac12Q_1^2.\]
Differentiating gives \(30-Q_1=0\), so \(Q_1^*=30\). Its second derivative is -1, confirming a maximum.
**3. Recover follower output and price:** \(Q_2^*=(60-30)/2=15\). Total output is 45, giving \(P^*=70-45=25\).
**4. Calculate profits:** \(\pi_1=(25-10)(30)=450\) and \(\pi_2=(25-10)(15)=225\). Commitment lets the leader earn more by anticipating the follower’s response.
**Requested value:** Follower output is 15.
**Answer: 15.**
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.
Published solution
**1. Use backward induction:** Firm 1 chooses output first. After observing it, Firm 2 maximizes \(\pi_2=(60-Q_1-Q_2)Q_2\), giving response \(Q_2=(60-Q_1)/2\) when positive.
**2. Let the leader anticipate this response:** Substitute the follower’s choice into Firm 1’s profit:
\[\pi_1=\left(60-Q_1-\frac{60-Q_1}{2}\right)Q_1=30Q_1-\frac12Q_1^2.\]
Differentiating gives \(30-Q_1=0\), so \(Q_1^*=30\). Its second derivative is -1, confirming a maximum.
**3. Recover follower output and price:** \(Q_2^*=(60-30)/2=15\). Total output is 45, giving \(P^*=70-45=25\).
**4. Calculate profits:** \(\pi_1=(25-10)(30)=450\) and \(\pi_2=(25-10)(15)=225\). Commitment lets the leader earn more by anticipating the follower’s response.
**Requested value:** Market price is 25.
**Answer: 25.**
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.
Published solution
**1. Use backward induction:** Firm 1 chooses output first. After observing it, Firm 2 maximizes \(\pi_2=(60-Q_1-Q_2)Q_2\), giving response \(Q_2=(60-Q_1)/2\) when positive.
**2. Let the leader anticipate this response:** Substitute the follower’s choice into Firm 1’s profit:
\[\pi_1=\left(60-Q_1-\frac{60-Q_1}{2}\right)Q_1=30Q_1-\frac12Q_1^2.\]
Differentiating gives \(30-Q_1=0\), so \(Q_1^*=30\). Its second derivative is -1, confirming a maximum.
**3. Recover follower output and price:** \(Q_2^*=(60-30)/2=15\). Total output is 45, giving \(P^*=70-45=25\).
**4. Calculate profits:** \(\pi_1=(25-10)(30)=450\) and \(\pi_2=(25-10)(15)=225\). Commitment lets the leader earn more by anticipating the follower’s response.
**Requested value:** Leader profit is 450.
**Answer: 450.**
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.
Published solution
**1. Use backward induction:** Firm 1 chooses output first. After observing it, Firm 2 maximizes \(\pi_2=(60-Q_1-Q_2)Q_2\), giving response \(Q_2=(60-Q_1)/2\) when positive.
**2. Let the leader anticipate this response:** Substitute the follower’s choice into Firm 1’s profit:
\[\pi_1=\left(60-Q_1-\frac{60-Q_1}{2}\right)Q_1=30Q_1-\frac12Q_1^2.\]
Differentiating gives \(30-Q_1=0\), so \(Q_1^*=30\). Its second derivative is -1, confirming a maximum.
**3. Recover follower output and price:** \(Q_2^*=(60-30)/2=15\). Total output is 45, giving \(P^*=70-45=25\).
**4. Calculate profits:** \(\pi_1=(25-10)(30)=450\) and \(\pi_2=(25-10)(15)=225\). Commitment lets the leader earn more by anticipating the follower’s response.
**Requested value:** Follower profit is 225.
**Answer: 225.**
Based on the above data, answer the given subquestions.
Expected value of first product is __________(in $)
**NOTE:** Enter the exact answer without any extra space in the beginning or at the end.
Published solution
**1. Read the first product’s outcomes:** Gourmet marmite pays $0.5 million with probability 0.3, $1 million with probability 0.4 and $1.5 million with probability 0.3.
**2. Compute the probability-weighted payoff:**
\[E[I_M]=0.3(0.5)+0.4(1)+0.3(1.5)=0.15+0.40+0.45=1.00\text{ million dollars}.\]
**3. Express the requested dollar amount:** One million dollars is 1,000,000 dollars. Expected value averages payoffs, not their utilities or squared deviations.
**Answer: 1000000.**
Based on the above data, answer the given subquestions.
Expected value of second product is __________ (in $)
**NOTE:** Enter the exact answer without any extra space in the beginning or at the end.
Published solution
**1. Read the second product’s outcomes:** Gourmet honey pays $0.5 million with probability 0.2, $1 million with probability 0.6 and $1.5 million with probability 0.2.
**2. Calculate expected payoff:**
\[E[I_H]=0.2(0.5)+0.6(1)+0.2(1.5)=0.10+0.60+0.30=1.00\text{ million dollars}.\]
**3. Convert units:** The expected payoff is 1,000,000 dollars. Having the same mean as marmite does not imply having the same risk.
**Answer: 1000000.**
Based on the above data, answer the given subquestions.
Choose the correct alternative(s)
6406536925389.
The second product is riskier than the first product
6406536925390.
Second product has lower variance than the first product
6406536925391.
First product has a lower variance than the second product
6406536925392.
The first product is riskier than the second product
Published solution
**1. Compare distributions at their common mean:** Both products have expected payoff 1 million dollars. Measure payoffs in millions, so squared deviations are in million-dollars squared.
**2. Compute each variance:**
\[\mathrm{Var}(I_M)=0.3(0.5-1)^2+0.4(1-1)^2+0.3(1.5-1)^2=0.15.\]
\[\mathrm{Var}(I_H)=0.2(0.5-1)^2+0.6(1-1)^2+0.2(1.5-1)^2=0.10.\]
**3. Rank risk:** Marmite puts more probability on the low and high extreme outcomes and less on the mean. Its variance is larger. Thus the first product is riskier, and the second has lower variance.
**Answer: B, D — Selected: Second product has lower variance than the first product; The first product is riskier than the second product.**
A: **Incorrect:** The second product has smaller variance, not greater risk in this comparison.
B: **Correct:** Honey’s variance 0.10 is below marmite’s 0.15 in the stated units.
C: **Incorrect:** The first product’s variance is higher, not lower.
D: **Correct:** The first product assigns more weight to extreme payoffs and has higher variance.
Based on the above data, answer the given subquestions.
A risk-loving decision maker has the utility function U(I) = 25I\(^{2}\) where I denotes the payoff of the
product.
Choose the correct alternative(s) for this risk-loving decision maker
6406536925393.
Expected utility of investing in gourmet marmite is more than expected utility
of investing in gourmet honey
6406536925394.
A risk-loving decision maker prefers investing in gourmet honey to investing in
gourmet marmite
6406536925395.
Expected utility of investing in gourmet marmite is less than expected utility of
investing in gourmet honey
6406536925396.
A risk-loving decision-maker prefers investing in gourmet marmite to investing
in gourmet honey
Published solution
**1. Interpret utility:** \(U(I)=25I^2\) is convex for nonnegative payoffs, since \(U''(I)=50>0\). This decision maker likes a mean-preserving increase in payoff risk.
**2. Compute expected utility:** Using millions of dollars as the common payoff unit,
\[E[U_M]=25[0.3(0.5)^2+0.4(1)^2+0.3(1.5)^2]=25(1.15)=28.75.\]
\[E[U_H]=25[0.2(0.5)^2+0.6(1)^2+0.2(1.5)^2]=25(1.10)=27.50.\]
**3. Choose the larger utility:** Marmite gives greater expected utility, so it is preferred. Measuring I in dollars instead multiplies both expected utilities by \(10^{12}\), leaving the ranking unchanged.
**Answer: A, D — Selected: Expected utility of investing in gourmet marmite is more than expected utility of investing in gourmet honey; A risk-loving decision-maker prefers investing in gourmet marmite to investing in gourmet honey.**
A: **Correct:** 28.75 exceeds 27.50 when payoffs are measured in millions.
B: **Incorrect:** The specified convex utility favors marmite here, not honey.
C: **Incorrect:** Marmite has higher expected utility, so this inequality is reversed.
D: **Correct:** Marmite is the expected-utility-maximizing choice under the given utility.
India currently imports all of its palm oil. The annual demand for palm oil by Indian consumers is
given by the demand curve **Q=2000-4P**, where Q is quantity of palm oil in thousand litres and P is
market price in INR per litre. World producers can harvest and ship palm oil to Indian distributors
at a constant marginal cost (=average cost) of INR 50 and Indian distributors can distribute it at a
cost of INR 10 per litre. Consider market for palm oil to be competitive.
Indian government is considering a tariff on palm oil import of INR 10 per litre.
Based on the above data, answer the given subquestions.
If there is no tariff, what is the quantity demanded (in thousand litres) ___________
Published solution
**1. Find the untaxed delivered cost:** World production/shipping costs INR 50 per litre and domestic distribution costs INR 10. Under the stated competitive constant-cost conditions, price equals \(50+10=60\).
**2. Substitute into demand:**
\[Q_0=2000-4P_0=2000-4(60)=2000-240=1760.\]
**3. Keep units:** Q is measured in thousand litres, so demand is 1,760 thousand litres, or 1.76 million litres.
**Answer: 1760.**
India currently imports all of its palm oil. The annual demand for palm oil by Indian consumers is
given by the demand curve **Q=2000-4P**, where Q is quantity of palm oil in thousand litres and P is
market price in INR per litre. World producers can harvest and ship palm oil to Indian distributors
at a constant marginal cost (=average cost) of INR 50 and Indian distributors can distribute it at a
cost of INR 10 per litre. Consider market for palm oil to be competitive.
Indian government is considering a tariff on palm oil import of INR 10 per litre.
Based on the above data, answer the given subquestions.
If the tariff is imposed, how much a consumer will pay for a litre of palm oil _____________
Published solution
**1. Identify all per-litre costs:** Production/shipping is INR 50, distribution INR 10 and the proposed tariff INR 10.
**2. Apply the competitive constant-cost assumption:** The tariff raises delivered marginal cost by its full amount:
\[P_1=50+10+10=70\text{ INR per litre}.\]
**3. Interpret:** Consumers pay INR 70 per litre, compared with INR 60 without the tariff. This assumes the supplied constant world cost and full pass-through in the question’s competitive market.
**Answer: 70.**
India currently imports all of its palm oil. The annual demand for palm oil by Indian consumers is
given by the demand curve **Q=2000-4P**, where Q is quantity of palm oil in thousand litres and P is
market price in INR per litre. World producers can harvest and ship palm oil to Indian distributors
at a constant marginal cost (=average cost) of INR 50 and Indian distributors can distribute it at a
cost of INR 10 per litre. Consider market for palm oil to be competitive.
Indian government is considering a tariff on palm oil import of INR 10 per litre.
Based on the above data, answer the given subquestions.
What is the new quantity demanded now (in thousand litres)? ___________
Published solution
**1. Find the taxed price:** The delivered cost includes INR 50 production/shipping, INR 10 distribution and INR 10 tariff, so \(P_1=70\).
**2. Use the demand curve:**
\[Q_1=2000-4(70)=2000-280=1720.\]
**3. Report units and compare:** Demand is 1,720 thousand litres. Relative to the untaxed \(2000-4(60)=1760\), consumption falls by 40 thousand litres.
**Answer: 1720.**
India currently imports all of its palm oil. The annual demand for palm oil by Indian consumers is
given by the demand curve **Q=2000-4P**, where Q is quantity of palm oil in thousand litres and P is
market price in INR per litre. World producers can harvest and ship palm oil to Indian distributors
at a constant marginal cost (=average cost) of INR 50 and Indian distributors can distribute it at a
cost of INR 10 per litre. Consider market for palm oil to be competitive.
Indian government is considering a tariff on palm oil import of INR 10 per litre.
Based on the above data, answer the given subquestions.
What will be the lost consumer surplus due to the imposed tariff (in thousand INR) ____________
Published solution
**1. Find the before/after equilibria:** Without tariff, \(P_0=60\) and \(Q_0=1760\). With tariff, \(P_1=70\) and \(Q_1=1720\). Quantities are in thousand litres.
**2. Split the lost consumer surplus:** Consumers pay INR 10 more on the 1,720 thousand litres still bought, losing a rectangle of \(10(1720)=17{,}200\) thousand INR. Lost purchases contribute a triangle of \(\tfrac12(10)(1760-1720)=200\) thousand INR.
**3. Add:**
\[\Delta CS_{\mathrm{loss}}=17{,}200+200=17{,}400\text{ thousand INR}.\]
Consumer-surplus loss exceeds government revenue because some mutually beneficial purchases disappear.
**Answer: 17400.**
India currently imports all of its palm oil. The annual demand for palm oil by Indian consumers is
given by the demand curve **Q=2000-4P**, where Q is quantity of palm oil in thousand litres and P is
market price in INR per litre. World producers can harvest and ship palm oil to Indian distributors
at a constant marginal cost (=average cost) of INR 50 and Indian distributors can distribute it at a
cost of INR 10 per litre. Consider market for palm oil to be competitive.
Indian government is considering a tariff on palm oil import of INR 10 per litre.
Based on the above data, answer the given subquestions.
Tax revenue for the government will be (in thousand INR) ________________
Published solution
**1. Identify tariff and taxed volume:** The government receives INR 10 for each imported litre. After the tariff, consumers buy \(2000-4(70)=1720\) thousand litres, all imported under the assumptions.
**2. Multiply:**
\[R=tQ_1=10(1720)=17{,}200\text{ thousand INR}.\]
**3. Check units:** This equals INR 17.2 million. Use the post-tariff quantity, not the larger pre-tariff quantity.
**Answer: 17200.**
India currently imports all of its palm oil. The annual demand for palm oil by Indian consumers is
given by the demand curve **Q=2000-4P**, where Q is quantity of palm oil in thousand litres and P is
market price in INR per litre. World producers can harvest and ship palm oil to Indian distributors
at a constant marginal cost (=average cost) of INR 50 and Indian distributors can distribute it at a
cost of INR 10 per litre. Consider market for palm oil to be competitive.
Indian government is considering a tariff on palm oil import of INR 10 per litre.
Based on the above data, answer the given subquestions.
Tariff results in
6406536925402.
Net gain for the society
6406536925403.
Net loss for the society
6406536925404.
Neither loss nor gain
6406536925405.
Cannot compute
Published solution
**1. Calculate the quantity distortion:** The tariff raises price from INR 60 to INR 70 and reduces demand from 1,760 to 1,720 thousand litres.
**2. Compare loss and transfer:** Consumer surplus falls by \(10(1720)+\tfrac12(10)(40)=17{,}400\) thousand INR. Government revenue is \(10(1720)=17{,}200\) thousand INR.
**3. Find net social loss:** Revenue is a transfer within society, so the net loss is \(17{,}400-17{,}200=200\) thousand INR. This is the consumption deadweight-loss triangle under the constant world-cost assumptions.
**Answer: B — Selected: Net loss for the society.**
A: **Incorrect:** There is a positive deadweight loss, rather than a net gain.
B: **Correct:** The lost consumer gains exceed tax revenue by 200 thousand INR.
C: **Incorrect:** Tax revenue does not recover the surplus lost on purchases that no longer occur.
D: **Incorrect:** Demand and costs provide enough information to compute the loss.
A monopolist faces the demand curve **P = 48 - 6Q**, where P is measured in dollars per unit and Q in
thousands of units. The monopolist has a constant average cost of $12 per unit.
Based on the above data, answer the given subquestions.
What is the monopolist’s profit-maximizing price and quantity? P*= _________
Published solution
**1. Derive marginal revenue:** Demand is \(P=48-6Q\), with Q in thousands. Revenue in thousands of dollars is \(TR=48Q-6Q^2\), giving \(MR=48-12Q\).
**2. Equate MR and MC:** Constant average cost 12 implies marginal cost 12. Hence \(48-12Q=12\), so \(Q^*=3\) thousand units. The profit second derivative is -12, confirming a maximum.
**3. Find the selling price from demand:** \(P^*=48-6(3)=30\) dollars per unit. A monopolist sets quantity using MR=MC and then reads price from demand; it does not set price equal to marginal revenue.
**Answer: 30.**
A monopolist faces the demand curve **P = 48 - 6Q**, where P is measured in dollars per unit and Q in
thousands of units. The monopolist has a constant average cost of $12 per unit.
Based on the above data, answer the given subquestions.
What is the monopolist’s profit-maximizing price and quantity? Q*= ________
Published solution
**1. Find marginal revenue:** With \(P=48-6Q\), revenue is \(48Q-6Q^2\), so \(MR=48-12Q\).
**2. Maximize profit:** Constant average and marginal cost are both 12. Solving \(48-12Q=12\) gives \(Q=3\).
**3. Convert the quantity units:** The demand equation measures Q in thousands of units. Thus \(3\times1000=3000\) physical units are produced. The answer field’s key uses physical units, rather than the value 3 used in the demand equation.
**Answer: 3000.**
A monopolist faces the demand curve **P = 48 - 6Q**, where P is measured in dollars per unit and Q in
thousands of units. The monopolist has a constant average cost of $12 per unit.
Based on the above data, answer the given subquestions.
The resulting profit to the monopolist will be π = ______________
Published solution
**1. Find the monopoly choice:** Equating \(MR=48-12Q\) to \(MC=12\) gives \(Q=3\) thousand units. Demand then gives \(P=48-6(3)=30\).
**2. Compute the per-unit margin:** \(P-AC=30-12=18\) dollars per unit.
**3. Multiply by physical output:**
\[\pi=(P-AC)q=18(3000)=54{,}000\text{ dollars}.\]
Equivalently, revenue is $90,000 and total cost is $36,000.
**Answer: 54000.**
A monopolist faces the demand curve **P = 48 - 6Q**, where P is measured in dollars per unit and Q in
thousands of units. The monopolist has a constant average cost of $12 per unit.
Based on the above data, answer the given subquestions.
What is firm’s degree of monopoly power using the Lerner index ___________
Published solution
**1. Define the Lerner index:** It measures markup relative to price:
\[L=\frac{P-MC}{P}.\]
**2. Find the monopoly price:** From \(MR=48-12Q=12\), \(Q=3\) thousand and \(P=48-6(3)=30\). Marginal cost is 12.
**3. Calculate:** \(L=(30-12)/30=18/30=0.6\). The markup is 60% of price; this differs from markup expressed as a percentage of cost.
**Answer: 0.6.**
Mohan quits his IT job, where he was earning a salary of ₹700,000 per year, to start his own
restaurant business in a building that he owns and was previously renting out for ₹290,000 per
year. In his first year of business, he has the following expenses: salary paid to himself, ₹500,000;
rent, ₹0; other expenses, ₹340,000.
Based on the above data, answer the given subquestions.
The accounting cost associated with Mohan’s restaurant business is ____________
Published solution
**1. Define accounting cost:** Under the exercise’s business accounting treatment, it counts recorded expenses, including the salary paid to Mohan.
**2. List the payments:** Salary paid to himself is INR 500,000; paid rent is zero because he owns the building; other expenses are INR 340,000.
**3. Add:** \(500{,}000+0+340{,}000=840{,}000\) rupees. Foregone outside salary and rental income are opportunity costs, not extra recorded payments in this accounting-cost calculation.
**Answer: 840000.**
Mohan quits his IT job, where he was earning a salary of ₹700,000 per year, to start his own
restaurant business in a building that he owns and was previously renting out for ₹290,000 per
year. In his first year of business, he has the following expenses: salary paid to himself, ₹500,000;
rent, ₹0; other expenses, ₹340,000.
Based on the above data, answer the given subquestions.
The economic cost associated with Mohan’s restaurant business is ____________
Published solution
**1. Define economic cost:** It values resources by their best alternative use. Mohan gives up an IT salary of INR 700,000 and building rent of INR 290,000 by using his own time and property in the restaurant.
**2. Avoid double counting owner labor:** The INR 500,000 salary paid to himself is an internal allocation for valuing his own work. Replace that accounting amount with his INR 700,000 opportunity wage, rather than charging both.
**3. Add external expenses and opportunity costs:**
\[C_E=340{,}000+700{,}000+290{,}000=1{,}330{,}000\text{ INR}.\]
Equivalently, start from accounting cost 840,000, subtract owner salary 500,000 and add the two foregone incomes.
**Answer: 1330000.**
There are 40 low-risk people and 60 high-risk people. A low-risk person has an average of $1500 in
medical expenses each year and is willing to pay $1800 for medical insurance (this person is risk-
averse). A high-risk person has an average of $2200 in medical expenses each year and is willing to
pay $2600 for medical insurance. Insurance companies are unable to differentiate who is high-risk
and who is low-risk.
Based on the above data, answer the given subquestions.
If the insurance provider offered medical insurance at a price of $2000
6406536925412.
Everyone will enroll for the insurance, irrespective of the type
6406536925413.
The provider will lose money
6406536925414.
Both Everyone will enroll for the insurance, irrespective of the type and The
provider will lose money
6406536925415.
None of these
Published solution
**1. Determine who buys at $2,000:** Low-risk people will pay at most $1,800, so they decline. High-risk people will pay up to $2,600, so all 60 high-risk people enroll.
**2. Calculate the insurer’s expected margin:** Every enrolled person has expected medical expenses of $2,200, exceeding the $2,000 premium by $200.
**3. Compute the loss:** \(60(2000-2200)=-12{,}000\) dollars. This illustrates adverse selection: pricing cannot assume low-risk customers remain in the pool when they prefer to leave.
**Answer: B — Selected: The provider will lose money.**
A: **Incorrect:** Low-risk people reject a price above their $1,800 willingness to pay.
B: **Correct:** The provider expects to lose $200 per high-risk enrollee, totaling $12,000.
C: **Incorrect:** The loss claim is true but the everyone-enrolls claim is false, so the conjunction is false.
D: **Incorrect:** The provider-loss option is a correct available statement.
There are 40 low-risk people and 60 high-risk people. A low-risk person has an average of $1500 in
medical expenses each year and is willing to pay $1800 for medical insurance (this person is risk-
averse). A high-risk person has an average of $2200 in medical expenses each year and is willing to
pay $2600 for medical insurance. Insurance companies are unable to differentiate who is high-risk
and who is low-risk.
Based on the above data, answer the given subquestions.
If the insurance company offered medical insurance at a price of $2400
6406536925416.
Low-risk people would not be insured
6406536925417.
Total surplus will be $12000, if the price is $2400
6406536925418.
Both Low-risk people would not be insured and Total surplus will be $12000, if
the price is $2400
6406536925419.
None of these
Published solution
**1. Determine enrollment at $2,400:** Low-risk people decline because their willingness to pay is only $1,800. The 60 high-risk people enroll because $2,400 is below their $2,600 willingness to pay.
**2. Separate surplus components:** High-risk consumer surplus is \(60(2600-2400)=12{,}000\) dollars. Insurer expected profit is \(60(2400-2200)=12{,}000\) dollars.
**3. Calculate total surplus:** \(12{,}000+12{,}000=24{,}000\) dollars. Thus “low-risk people would not be insured” is true, but “total surplus is $12,000” confuses one component with the total.
**Answer: A — Selected: Low-risk people would not be insured.**
A: **Correct:** The price exceeds low-risk people’s willingness to pay, so they remain uninsured.
B: **Incorrect:** Total surplus is $24,000; $12,000 is each of the two individual components.
C: **Incorrect:** The first claim is true but the total-surplus claim is false.
D: **Incorrect:** A is a correct available statement.
The production function for a product is given by **q = 450KL**. If the price of capital is INR 30 per day
and the price of labour is INR 150 per day.
Based on the above data, answer the given subquestions.
What is the cost minimizing quantity of labour and capital respectively for producing 9000 units of
output? L\(^{*}\) =________
Published solution
**1. State the production target:** \(q=450KL=9000\) implies \(KL=20\). Daily input cost is \(C=30K+150L\).
**2. Match marginal product per rupee:** \(MP_L=450K\) and \(MP_K=450L\). At the interior cost minimum,
\[\frac{MP_L}{MP_K}=\frac{150}{30}\quad\Rightarrow\quad\frac{K}{L}=5.\]
Thus \(K=5L\).
**3. Solve the production constraint:** \(5L^2=20\), so the positive solution is \(L=2\), with \(K=10\). Substituting \(K=20/L\) into cost gives \(C=600/L+150L\), which has a positive second derivative for positive L and confirms a minimum.
**Answer: 2.**
The production function for a product is given by **q = 450KL**. If the price of capital is INR 30 per day
and the price of labour is INR 150 per day.
Based on the above data, answer the given subquestions.
What is the cost minimizing quantity of labour and capital respectively for producing 9000 units of
output? K\(^{*}\) = _________
Published solution
**1. Use the required output:** \(450KL=9000\) gives \(KL=20\).
**2. Apply least-cost input choice:** Equal marginal product per rupee requires \((450K)/150=(450L)/30\). Simplifying gives \(K=5L\).
**3. Find the capital amount:** Substitute \(L=K/5\) into \(KL=20\): \(K^2/5=20\), so \(K^2=100\). The positive input choice is \(K=10\), paired with \(L=2\). This combination meets output: \(450(10)(2)=9000\).
**Answer: 10.**
The production function for a product is given by **q = 450KL**. If the price of capital is INR 30 per day
and the price of labour is INR 150 per day.
Based on the above data, answer the given subquestions.
What is the minimum cost of producing 9000 units of output in INR?
Published solution
**1. Find the least-cost input ratio:** From \(MP_L/MP_K=K/L\) and input-price ratio \(150/30=5\), the optimum has \(K=5L\).
**2. Meet output:** \(450KL=9000\) implies \(KL=20\). Therefore \(5L^2=20\), giving \(L=2\) and \(K=10\).
**3. Calculate minimum daily cost:**
\[C_{\min}=150(2)+30(10)=300+300=600\text{ INR per day}.\]
Spending is equal across the two inputs because they enter this Cobb-Douglas production function with equal exponents.
**Answer: 600.**
Based on the above data, answer the given subquestions.
Find the optimal bundle of goods 1 and 2 for this consumer. The optimal bundle will consist of X1=
_________
Published solution
**1. Read preferences and budget:** Utility is \(U=\log X_1+\log X_2\), with \(2X_1+6X_2=240\). Both goods have positive marginal utility, so the optimal bundle uses the full budget.
**2. Equalize marginal utility per rupee:** The marginal utilities are proportional to \(1/X_1\) and \(1/X_2\). Thus
\[\frac{1/X_1}{2}=\frac{1/X_2}{6}\quad\Rightarrow\quad X_1=3X_2.\]
The log base cancels from this condition.
**3. Solve:** \(2(3X_2)+6X_2=240\), so \(12X_2=240\), \(X_2=20\), and \(X_1=60\). Concavity of log utility confirms this interior optimum.
**Answer: 60.**
Based on the above data, answer the given subquestions.
Find the optimal bundle of goods 1 and 2 for this consumer. The optimal bundle will consist of
X2=__________
Published solution
**1. Identify the budget and preferences:** \(U=\log X_1+\log X_2\) and \(2X_1+6X_2=240\).
**2. Use the optimal allocation rule:** Equal-weight log preferences allocate equal spending to the two goods. Equivalently, equating marginal utility per rupee gives \(X_1=3X_2\).
**3. Calculate good 2:** Half the budget is \(240/2=120\). At price 6, \(X_2=120/6=20\). Good 1 is \(120/2=60\), and the complete bundle costs \(2(60)+6(20)=240\).
**Answer: 20.**
