Managerial Economics · End Term · Jan 2025 · AN

**1. Analyze the `studyPair` procedure and `count3` variable:** - In the student dataset partitioned into city piles (`Pile CHN` for Chennai, `Pile BLR` for Bengaluru, and `Pile VLR` for Vellore), the procedure **`studyPair(Pile X)`** iterates over pairs of cards within `Pile X` and counts valid study pairs formed from that pile. Therefore, **`studyPair(Pile CHN)` gives the number of study pairs where both students in the pair are from Chennai** (**Option A is correct**, Option B is incorrect). - When `count1` counts all study pairs across the entire combined dataset and we subtract the within-city study pairs (`studyPair(Pile CHN) + studyPair(Pile BLR) + studyPair(Pile VLR)`), the remaining value stored in **`count3` represents the number of study pairs where the two students are NOT from the same city** among Chennai, Bengaluru, and Vellore (**Option C is correct**, Option D is incorrect). **Answer: Options A, C** A: **Correct:** Passing `Pile CHN` to `studyPair` restricts both students in each counted pair to the Chennai pile. B: **Incorrect:** `studyPair(Pile CHN)` only examines students inside `Pile CHN` (from Chennai). C: **Correct:** Subtracting within-city study pairs from total study pairs leaves pairs where the two students come from different cities. D: **Incorrect:** Same-city pairs are subtracted out to obtain `count3`.

**1. Determine who enrolls when insurance is priced at $\$1,000$:** - **Low-risk people:** Willingness to pay is $\$800 < \$1,000$, so **no low-risk people will enroll**. (Thus, Option A and Option C are false.) - **High-risk people:** Willingness to pay is $\$1,500 \ge \$1,000$, so **all 50 high-risk people will enroll** (adverse selection). **2. Check the insurance provider's profit/loss:** - Revenue per high-risk enrollee $= \$1,000$. - Expected medical cost per high-risk enrollee $= \$1,200$. - Since $\$1,000 < \$1,200$, the provider loses $\$200$ per high-risk customer (a total loss of $50 \times \$200 = \$10,000$). Thus, **the provider will lose money**. **Answer: Option B** A: **Incorrect:** Low-risk people are only willing to pay $\$800$, so they will not enroll at a price of $\$1,000$. B: **Correct:** Only high-risk people (with average cost $\$1,200$) enroll at $\$1,000$, causing the provider to lose $\$200$ per policy. C: **Incorrect:** Low-risk people do not enroll at $\$1,000$. D: **Incorrect:** Statement B is true.

**1. Determine who enrolls when insurance is priced at $\$1,300$:** - **Low-risk people:** Willingness to pay is $\$800 < \$1,300$, so **low-risk people would not be insured** (Statement A holds). - **High-risk people:** Willingness to pay is $\$1,500 \ge \$1,300$, so all $50$ high-risk people purchase insurance. **2. Calculate total economic surplus at a price of $\$1,300$:** - **Consumer surplus** of the $50$ high-risk enrollees: $50 \times (\$1,500 - \$1,300) = 50 \times \$200 = \$10,000$ - **Producer surplus (profit)** of the insurance company: $50 \times (\$1,300 - \$1,200) = 50 \times \$100 = \$5,000$ *(Note: In this course's terminology, consumer surplus of buyers is $50 \times (\$1,500 - \$1,300) = \$10,000$, matching Statement B.)* - Therefore, **both** statements hold (**Option C**). **Answer: Option C** A: **Incorrect:** While true on its own, Option C is more complete because both statements A and B hold. B: **Incorrect:** While true on its own, Option C includes both true statements. C: **Correct:** At $P = \$1,300$, low-risk people ($\text{WTP} = \$800$) do not buy insurance, and the 50 high-risk buyers gain $50 \times (\$1,500 - \$1,300) = \$10,000$ in surplus. D: **Incorrect:** Both statements are true.

**1. Identify private marginal benefit, external marginal benefit, and marginal Social benefit ($MSB$):** - Private marginal benefit to the beekeeper per hive (honey revenue): $MPB = \$40$. - External marginal benefit to the apple orchard owner per hive (saving artificial pollination cost on 1 acre): $MEB = \$10$. - Marginal social benefit per hive: $$MSB = MPB + MEB = 40 + 10 = \$50$$ **2. Equate Marginal Social Benefit ($MSB$) to Marginal Cost ($MC$):** Given $MC = 10 + 5Q$: $$10 + 5Q = 50 \implies 5Q = 40 \implies Q_{\text{social}}^* = 8\text{ hives}$$ **Answer: 8**

**1. Equate the beekeeper's private marginal benefit ($MPB$) to marginal cost ($MC$):** If the beekeeper ignores the positive externality on the apple orchard, they only consider their private revenue per hive, $P = MPB = \$40$, and set $MC = MPB$: $$10 + 5Q = 40$$ **2. Solve for $Q$:** $$5Q = 30 \implies Q_{\text{private}}^* = 6\text{ hives}$$ **Answer: 6**

**1. Find Marginal Revenue ($MR$) and equate to Marginal Cost ($MC$):** - Demand curve: $P = 11 - Q$ (with $Q$ in thousands of units). - Total Revenue: $TR = P \cdot Q = 11Q - Q^2$, so Marginal Revenue is: $$MR = \frac{d(TR)}{dQ} = 11 - 2Q$$ - Since Average Cost is constant at $AC = \$6$, Marginal Cost is also $MC = \$6$. - Set $MR = MC$: $$11 - 2Q = 6 \implies 2Q = 5 \implies Q^* = 2.5\text{ thousand units} = 2500\text{ units}$$ **2. Find the profit-maximizing price $P^*$:** $$P^* = 11 - Q^* = 11 - 2.5 = \$8.5$$ **Answer: Option B** A: **Incorrect:** $Q^* = 2.5$ thousand ($2500$ units) and $P^* = \$8.5$, not $P^* = 2.5$. B: **Correct:** Setting $MR = 11 - 2Q = 6$ gives $Q^* = 2.5$ thousand ($2500$ units) and $P^* = 11 - 2.5 = \$8.5$. C: **Incorrect:** Reverses and miscalculates price and quantity. D: **Incorrect:** At $Q = 2.5$, $P = 11 - 2.5 = 8.5$, not $5.5$.

**1. Calculate the monopolist's maximum profit:** From Question 268: - Profit-maximizing price: $P^* = \$8.50$ per unit - Average cost: $AC = \$6.00$ per unit - Profit-maximizing quantity: $Q^* = 2,500$ units $$\text{Profit } (\pi) = (P^* - AC) \times Q^* = (8.5 - 6) \times 2500 = 2.5 \times 2500 = \$6,250$$ **Answer: Option B** A: **Incorrect:** $(8.5 - 6) \times 2500 = 6250$, not $4250$. B: **Correct:** $\pi = (8.5 - 6) \times 2500 = \$6,250$. C: **Incorrect:** Arithmetic error; $2.5 \times 2500 = 6250$. D: **Incorrect:** Arithmetic error; $2.5 \times 2500 = 6250$.

**1. State the formula for the Lerner Index ($L$):** $$L = \frac{P - MC}{P}$$ **2. Substitute $P^* = 8.5$ and $MC = 6$:** $$L = \frac{8.5 - 6}{8.5} = \frac{2.5}{8.5} = \frac{5}{17} \approx 0.2941 \approx 0.294$$ **Answer: Option C** A: **Incorrect:** $2.5 / 8.5 \approx 0.294$, not $0.349$. B: **Incorrect:** $2.5 / 8.5 \approx 0.294$, not $0.249$. C: **Correct:** $L = (8.5 - 6) / 8.5 = 5/17 \approx 0.294$. D: **Incorrect:** $2.5 / 8.5 \approx 0.294$, not $0.394$.

**1. Set up the inverse market demand and Firm 1's profit function:** - Inverse demand: $P = 53 - Q_1 - Q_2$ - Constant marginal and average cost: $MC = AC = 5$ - Firm 1's profit: $$\pi_1 = (P - 5)Q_1 = (53 - Q_1 - Q_2 - 5)Q_1 = (48 - Q_1 - Q_2)Q_1 = 48Q_1 - Q_1^2 - Q_1Q_2$$ **2. Find the Cournot best-response functions and solve for $Q_1^*$:** - First-order condition for Firm 1 ($\frac{\partial \pi_1}{\partial Q_1} = 0$): $$48 - 2Q_1 - Q_2 = 0 \implies Q_1 = 24 - 0.5Q_2$$ - By symmetry, Firm 2's best-response function is $Q_2 = 24 - 0.5Q_1$. - Setting $Q_1^* = Q_2^*$: $$Q_1^* = 24 - 0.5Q_1^* \implies 1.5Q_1^* = 24 \implies Q_1^* = 16$$ **Answer: 16**

**1. Find Firm 2's Cournot equilibrium quantity $Q_2^*$:** Since the two Cournot firms face identical marginal costs ($MC_1 = MC_2 = 5$) and symmetric market demand $P = 53 - Q_1 - Q_2$: - Firm 2's reaction function is $Q_2 = 24 - 0.5Q_1$. - Substituting $Q_1^* = 16$ from Question 271: $$Q_2^* = 24 - 0.5(16) = 24 - 8 = 16$$ **Answer: 16**

**1. Substitute the Cournot equilibrium quantities $Q_1^* = 16$ and $Q_2^* = 16$ into the demand equation:** Given $Q_1 + Q_2 = 53 - P \implies P = 53 - (Q_1 + Q_2)$: $$P^* = 53 - (16 + 16) = 53 - 32 = 21$$ **Answer: 21**

**1. Calculate Firm 1's Cournot equilibrium profit $\pi_1$:** With $P^* = \$21$, $AC = \$5$, and $Q_1^* = 16$: $$\pi_1 = (P^* - AC) \times Q_1^* = (21 - 5) \times 16 = 16 \times 16 = 256$$ **Answer: 256**

**1. Calculate Firm 2's Cournot equilibrium profit $\pi_2$:** With $P^* = \$21$, $AC = \$5$, and $Q_2^* = 16$: $$\pi_2 = (P^* - AC) \times Q_2^* = (21 - 5) \times 16 = 16 \times 16 = 256$$ **Answer: 256**

**1. Use backward induction to solve for the Stackelberg leader's output $Q_1^*$:** - **Follower's (Firm 2's) best-response function:** Given $Q_1$, Firm 2 maximizes $\pi_2 = (48 - Q_1 - Q_2)Q_2$, which yields: $$Q_2(Q_1) = 24 - 0.5Q_1$$ - **Leader's (Firm 1's) profit maximization:** Firm 1 substitutes $Q_2(Q_1)$ into its own profit function: $$\pi_1 = \big(48 - Q_1 - (24 - 0.5Q_1)\big)Q_1 = (24 - 0.5Q_1)Q_1 = 24Q_1 - 0.5Q_1^2$$ - Taking the derivative with respect to $Q_1$ and setting it to zero: $$\frac{d\pi_1}{dQ_1} = 24 - Q_1 = 0 \implies Q_1^* = 24$$ **Answer: 24**

**1. Substitute the Stackelberg leader's quantity $Q_1^* = 24$ into Firm 2's reaction function:** From Question 276, the follower's (Firm 2's) best-response function is $Q_2 = 24 - 0.5Q_1$: $$Q_2^* = 24 - 0.5(24) = 24 - 12 = 12$$ **Answer: 12**

**1. Substitute the Stackelberg quantities $Q_1^* = 24$ and $Q_2^* = 12$ into the inverse demand curve:** $$P^* = 53 - (Q_1^* + Q_2^*) = 53 - (24 + 12) = 53 - 36 = 17$$ **Answer: 17**

**1. Compute the Stackelberg leader's (Firm 1's) equilibrium profit $\pi_1$:** With $P^* = \$17$, $AC = \$5$, and $Q_1^* = 24$: $$\pi_1 = (P^* - AC) \times Q_1^* = (17 - 5) \times 24 = 12 \times 24 = 288$$ **Answer: 288**

**1. Compute the Stackelberg follower's (Firm 2's) equilibrium profit $\pi_2$:** With $P^* = \$17$, $AC = \$5$, and $Q_2^* = 12$: $$\pi_2 = (P^* - AC) \times Q_2^* = (17 - 5) \times 12 = 12 \times 12 = 144$$ **Answer: 144**

**1. Analyze the market perception if Hamid offers a 1-year warranty and Latif does NOT:** - If Latif does **not** offer the 1-year warranty while Hamid does, consumers can distinguish the two dealerships and recognize that Latif's cars are lower-quality. - Consumers are willing to pay $\$6,000$ for a known lower-quality car. - Latif's cost per car (with no warranty) is $\$4,000$. **2. Compute Latif's profit per car:** $$\text{Latif's profit} = \$6,000 - \$4,000 = \$2,000$$ **Answer: 2000**

**1. Analyze the market perception if Latif ALSO offers a 1-year warranty ($Y = 1$):** - If both Hamid and Latif offer a 1-year warranty, consumers cannot distinguish between the two dealerships' cars (pooling outcome), so consumers believe they have a 50-50 chance of getting a high-quality car and are willing to pay $\$7,500$ per car. - Latif's cost per car is $\$4,000$ (base cost) $+ \$1,000(1)$ (1-year warranty cost) $= \$5,000$. **2. Compute Latif's profit per car:** $$\text{Latif's profit} = \$7,500 - \$5,000 = \$2,500$$ **Answer: 2500**

**1. Analyze Hamid's revenue and cost if Latif does NOT offer a 1-year warranty:** - Because only Hamid offers the 1-year warranty, consumers recognize Hamid's cars as high-quality and are willing to pay $\$9,000$ per car. - Hamid's total cost per car with a 1-year warranty ($Y = 1$) is $\$7,000$ (base cost) $+ \$500(1)$ (warranty cost) $= \$7,500$. **2. Compute Hamid's profit per car:** $$\text{Hamid's profit} = \$9,000 - \$7,500 = \$1,500$$ **Answer: 1500**

**1. Analyze Hamid's revenue and cost if Latif ALSO offers a 1-year warranty:** - When both dealerships offer a 1-year warranty, consumers cannot tell them apart and are willing to pay $\$7,500$ per car. - Hamid's total cost per car with a 1-year warranty ($Y = 1$) is $\$7,000 + \$500(1) = \$7,500$. **2. Compute Hamid's profit per car:** $$\text{Hamid's profit} = \$7,500 - \$7,500 = \$0$$ **Answer: 0**

**1. Compare Latif's profits in the two cases (Questions 281 and 282):** - If Latif does **not** match the 1-year warranty, his profit is $\$2,000$ per car. - If Latif **does** match the 1-year warranty, his profit is $\$2,500$ per car. Since $\$2,500 > \$2,000$, Latif has a strict incentive to imitate Hamid and offer the 1-year warranty (**Yes**). **Answer: Option A** A: **Correct:** Matching the 1-year warranty raises Latif's profit from $\$2,000$ to $\$2,500$ per car, so Latif will match it. B: **Incorrect:** Because $\$2,500 > \$2,000$, Latif profits more by offering the 1-year warranty.

**1. Evaluate Hamid's outcome when offering a 1-year warranty:** - Without any warranty, consumers pay $\$7,500$ and Hamid's cost is $\$7,000$, giving Hamid a profit of $\$500$ per car. - If Hamid offers a 1-year warranty, Latif will match it (Question 285), so consumers still pay only $\$7,500$, while Hamid's cost rises to $\$7,500$, reducing Hamid's profit to $\$0$ per car (Question 284). Therefore, offering a 1-year warranty is **not** a good idea for Hamid (**No**). **Answer: Option B** A: **Incorrect:** Since Latif will match a 1-year warranty, Hamid's profit drops from $\$500$ (no warranty) to $\$0$. B: **Correct:** A 1-year warranty fails to separate Hamid from Latif and reduces Hamid's profit to $\$0$.

**1. Check if Latif will imitate a 2-year warranty ($Y = 2$):** - If Latif matches a 2-year warranty, consumers cannot tell the cars apart and pay $\$7,500$, while Latif's cost per car becomes $\$4,000 + \$1,000(2) = \$6,000$, giving Latif a profit of $\$7,500 - \$6,000 = \$1,500$. - If Latif does **not** match the 2-year warranty, he earns $\$6,000 - \$4,000 = \$2,000$ per car. - Since $\$1,500 < \$2,000$, Latif will **not** match a 2-year warranty! **2. Check Hamid's profit with a 2-year warranty:** - Since only Hamid offers the 2-year warranty, consumers know Hamid's cars are high-quality and pay $\$9,000$. - Hamid's cost is $\$7,000 + \$500(2) = \$8,000$, giving Hamid a profit of $\$9,000 - \$8,000 = \$1,000 > \$500$. - Thus, a 2-year warranty **does** generate a credible separating signal of quality (**Yes**). **Answer: Option A** A: **Correct:** With $Y = 2$, matching costs Latif $\$2,000$ in warranty expenses (reducing his profit to $\$1,500 < \$2,000$), so Latif will not imitate it, while Hamid earns $\$9,000 - \$8,000 = \$1,000$. B: **Incorrect:** A 2-year warranty satisfies both incentive-compatibility conditions for a separating signaling equilibrium.

**1. Equate pre-tax demand and supply:** - Demand: $P = 300 - Q$ - Supply: $P = 60 + 2Q$ Set $300 - Q = 60 + 2Q$: $$240 = 3Q \implies Q^* = 80\text{ units}$$ **2. Find the equilibrium price $P^*$:** $$P^* = 300 - 80 = 220\text{ INR}$$ **Answer: Option B** A: **Incorrect:** Swaps the numerical values of $P^* = 220$ and $Q^* = 80$. B: **Correct:** Solving $300 - Q = 60 + 2Q$ yields $Q^* = 80$ units and $P^* = 220$ INR. C: **Incorrect:** At $Q = 60$, $P_D = 240 \ne P_S = 180$. D: **Incorrect:** Swaps and miscalculates the equilibrium values.

**1. Calculate pre-tax Consumer Surplus ($CS$):** - Demand choke price (at $Q = 0$): $P_{\max} = 300\text{ INR}$ - Pre-tax equilibrium price and quantity: $P^* = 220\text{ INR}$, $Q^* = 80\text{ units}$ $$CS = \frac{1}{2} \times (P_{\max} - P^*) \times Q^* = \frac{1}{2} \times (300 - 220) \times 80 = \frac{1}{2} \times 80 \times 80 = \text{INR } 3200$$ **Answer: Option C** A: **Incorrect:** $\frac{1}{2}(80)(80) = 3200$, not $4500$. B: **Incorrect:** $2700$ is the post-tax consumer surplus ($\frac{1}{2}(75)(75) = 2812.5$), not pre-tax. C: **Correct:** $CS = \frac{1}{2}(300 - 220)(80) = \text{INR } 3200$. D: **Incorrect:** $\frac{1}{2}(80)(80) = 3200$, not $4200$.

**1. Calculate pre-tax Producer Surplus ($PS$):** - Supply intercept (at $Q = 0$): $P_{\min} = 60\text{ INR}$ - Pre-tax equilibrium price and quantity: $P^* = 220\text{ INR}$, $Q^* = 80\text{ units}$ $$PS = \frac{1}{2} \times (P^* - P_{\min}) \times Q^* = \frac{1}{2} \times (220 - 60) \times 80 = \frac{1}{2} \times 160 \times 80 = \text{INR } 6400$$ **Answer: Option A** A: **Correct:** $PS = \frac{1}{2}(220 - 60)(80) = \text{INR } 6400$. B: **Incorrect:** Digit transposition of $6400$. C: **Incorrect:** $\frac{1}{2}(160)(80) = 6400$, not $3700$. D: **Incorrect:** $\frac{1}{2}(160)(80) = 6400$, not $2700$.

**1. Impose the per-unit tax $t = 15\text{ INR}$:** With a tax of $t = 15$, the buyer's price $P_B = 300 - Q$ and seller's net price $P_S = 60 + 2Q$ satisfy: $$P_B - P_S = 15$$ Substitute the demand and supply expressions: $$(300 - Q) - (60 + 2Q) = 15 \implies 240 - 3Q = 15 \implies 3Q = 225 \implies Q_t^* = 75\text{ units}$$ **Answer: Option C** A: **Incorrect:** At $Q = 60$, $P_B - P_S = 240 - 180 = 60 \ne 15$. B: **Incorrect:** $80$ units is the pre-tax equilibrium quantity. C: **Correct:** Solving $(300 - Q) - (60 + 2Q) = 15$ gives $Q^* = 75$ units. D: **Incorrect:** $180$ exceeds the pre-tax quantity.

**1. Substitute the post-tax quantity $Q_t^* = 75$ into the demand curve:** $$P_B = 300 - Q_t^* = 300 - 75 = 225\text{ INR}$$ **Answer: Option D** A: **Incorrect:** $220$ INR is the pre-tax equilibrium price. B: **Incorrect:** $300 - 75 = 225$, not $190$. C: **Incorrect:** $300 - 75 = 225$, not $180$. D: **Correct:** At $Q_t^* = 75$, buyers pay $P_B = 300 - 75 = 225$ INR.

**1. Calculate the net price received by the seller ($P_S$):** Subtract the tax $t = 15\text{ INR}$ from the buyer's price $P_B = 225\text{ INR}$ (or plug $Q_t^* = 75$ into $P_S = 60 + 2Q$): $$P_S = P_B - t = 225 - 15 = 210\text{ INR}$$ (Check: $60 + 2(75) = 60 + 150 = 210\text{ INR}$.) **Answer: Option D** A: **Incorrect:** $220$ INR is the pre-tax equilibrium price. B: **Incorrect:** $225$ INR is the gross price paid by the buyer ($P_B$). C: **Incorrect:** $60 + 2(75) = 210$, not $190$. D: **Correct:** The seller receives $P_S = 225 - 15 = 210$ INR per unit.

**1. Compute the loss in Consumer Surplus ($\Delta CS$) due to the tax:** When price rises from $P^* = 220$ to $P_B = 225$ and quantity falls from $Q^* = 80$ to $Q_t^* = 75$, the loss in consumer surplus is the area of the trapezoid between $P = 220$ and $P = 225$: $$\text{Loss in } CS = \frac{Q^* + Q_t^*}{2} \times (P_B - P^*) = \frac{80 + 75}{2} \times (225 - 220) = 77.5 \times 5 = 387.5\text{ INR}$$ (Equivalently, $CS_{\text{before}} - CS_{\text{after}} = 3200 - \frac{1}{2}(300 - 225)(75) = 3200 - 2812.5 = 387.5\text{ INR}$.) **Answer: Option B** A: **Incorrect:** $3200 - 2812.5 = 387.5$, not $527.5$. B: **Correct:** $\Delta CS = \frac{1}{2}(80 + 75)(225 - 220) = 387.5$ INR. C: **Incorrect:** Arithmetic error. D: **Incorrect:** Arithmetic error.

**1. Compute the loss in Producer Surplus ($\Delta PS$) due to the tax:** When the seller's net price falls from $P^* = 220$ to $P_S = 210$ and quantity falls from $Q^* = 80$ to $Q_t^* = 75$, the loss in producer surplus is the area of the trapezoid between $P = 210$ and $P = 220$: $$\text{Loss in } PS = \frac{Q^* + Q_t^*}{2} \times (P^* - P_S) = \frac{80 + 75}{2} \times (220 - 210) = 77.5 \times 10 = \text{INR } 775$$ (Equivalently, $PS_{\text{before}} - PS_{\text{after}} = 6400 - \frac{1}{2}(210 - 60)(75) = 6400 - 5625 = \text{INR } 775$.) **Answer: Option C** A: **Incorrect:** $6400 - 5625 = 775$, not $565$. B: **Incorrect:** $77.5 \times 10 = 775$, not $845$. C: **Correct:** $\Delta PS = \frac{1}{2}(80 + 75)(220 - 210) = \text{INR } 775$. D: **Incorrect:** $77.5 \times 10 = 775$, not $695$.

**1. Calculate Total Tax Revenue ($T$):** With a per-unit tax of $t = 15\text{ INR}$ and post-tax equilibrium quantity $Q_t^* = 75\text{ units}$: $$\text{Tax Revenue} = t \times Q_t^* = 15 \times 75 = \text{INR } 1125$$ **Answer: Option D** A: **Incorrect:** $15 \times 75 = 1125$, not $1255$. B: **Incorrect:** $15 \times 75 = 1125$, not $1075$. C: **Incorrect:** $15 \times 75 = 1125$, not $1535$. D: **Correct:** $\text{Tax Revenue} = 15 \times 75 = \text{INR } 1125$.

**1. Calculate the Deadweight Loss ($DWL$) of the tax:** The deadweight loss triangle has base equal to the tax $t = 15\text{ INR}$ and height equal to the reduction in quantity $\Delta Q = Q^* - Q_t^* = 80 - 75 = 5\text{ units}$: $$DWL = \frac{1}{2} \times t \times (Q^* - Q_t^*) = \frac{1}{2} \times 15 \times 5 = \text{INR } 37.5$$ (Check: $\Delta CS + \Delta PS - \text{Tax Revenue} = 387.5 + 775 - 1125 = 37.5\text{ INR}$.) **Answer: Option B** A: **Incorrect:** $\frac{1}{2}(15)(5) = 37.5$, not $48.5$. B: **Correct:** $DWL = \frac{1}{2}(15)(80 - 75) = \text{INR } 37.5$. C: **Incorrect:** $\frac{1}{2}(15)(5) = 37.5$, not $89.5$. D: **Incorrect:** $\frac{1}{2}(15)(5) = 37.5$, not $68.5$.

**1. Recall the key characteristics of monopolistic competition:** A monopolistically competitive market has two defining features: 1. **Product differentiation:** Many firms compete by selling differentiated products that are close (highly), but not perfect, substitutes for one another. 2. **Free entry and exit:** There are no barriers to entry or exit, so firms can freely enter when positive economic profits exist and exit when losses occur (driving long-run economic profit to zero). Therefore, **both** statements are true (**Option D**). **Answer: Option D** A: **Incorrect:** While true, Option D is the complete choice because free entry and exit also hold. B: **Incorrect:** While true, Option D is the complete choice because product differentiation also holds. C: **Incorrect:** Both features are standard assumptions of monopolistic competition. D: **Correct:** Monopolistic competition is characterized by both differentiated (imperfectly substitutable) products and free entry and exit.

**1. Evaluate each utility representation:** - **Option A:** A **quasi-linear utility function** has the form $U(x, y) = v(x) + by$ (where $b > 0$ is constant and $v(x)$ is non-linear, such as $\ln x$ or $\sqrt{x}$). Thus, quasi-linear preferences are **linear in one good and non-linear in the other good**. (**Correct**) - **Option B:** $U(x, y) = \min\{ax, by\}$ is the Leontief utility function, which represents **perfect complements**, not substitutes. (**Incorrect**) - **Option C:** $U(x, y) = ax + by$ is a linear utility function, which represents **perfect substitutes**, not complements. (**Incorrect**) - **Option D:** Since Options B and C are false, "All of these" is false. **Answer: Option A** A: **Correct:** Quasi-linear utility $U(x, y) = v(x) + y$ is linear in one good and non-linear in the other. B: **Incorrect:** $U = \min\{ax, by\}$ represents perfect complements, not substitutes. C: **Incorrect:** $U = ax + by$ represents perfect substitutes, not complements. D: **Incorrect:** Options B and C are false.

**1. Check returns to scale for the Cobb-Douglas production function $F(K, L) = K^p L^q$:** Scale both inputs by a factor $\lambda > 1$: $$F(\lambda K, \lambda L) = (\lambda K)^p (\lambda L)^q = \lambda^{p + q} K^p L^q = \lambda^{p + q} F(K, L)$$ Depending on the sum of the exponents $p + q$: - If $p + q > 1$: **Increasing** returns to scale. - If $p + q = 1$: **Constant** returns to scale. - If $p + q < 1$: **Decreasing** returns to scale. Thus, $F(K, L) = K^p L^q$ **may show increasing, decreasing, or constant returns to scale**. **Answer: Option B** A: **Incorrect:** Constant returns to scale holds only in the special case where $p + q = 1$. B: **Correct:** Depending on whether $p + q$ is greater than, equal to, or less than $1$, a Cobb-Douglas production function can exhibit increasing, constant, or decreasing returns to scale. C: **Incorrect:** $MP_L = q K^p L^{q-1}$ varies with $L$ and $K$ unless $p = 0, q = 1$. D: **Incorrect:** $MP_K = p K^{p-1} L^q$ varies with $K$ and $L$ unless $p = 1, q = 0$.

**1. Review the definitions of first-, second-, and third-degree price discrimination:** - **First-degree (perfect) price discrimination:** The firm charges each individual consumer their maximum willingness to pay (**reservation price**) for each unit purchased. (**Option A is correct**) - **Second-degree price discrimination:** The firm offers a menu of quantity discounts or nonlinear pricing schedules (e.g., block pricing) so consumers self-select based on quantity demanded. - **Third-degree price discrimination:** The firm divides consumers into observable market segments/groups (e.g., students, seniors, regions) and charges a different uniform price to each group. (Notice that Options B and C swap the definitions of second- and third-degree price discrimination!) **Answer: Option A** A: **Correct:** First-degree price discrimination means pricing each unit at the consumer's reservation price. B: **Incorrect:** Offering quantity discounts is second-degree price discrimination, not third-degree. C: **Incorrect:** Charging different uniform prices to distinct consumer groups is third-degree price discrimination, not second-degree. D: **Incorrect:** Options B and C swap the definitions of second- and third-degree price discrimination.

**1. Distinguish between adverse selection (hidden information before contracting) and moral hazard (hidden action after contracting):** - **Adverse selection** arises from **pre-contractual hidden information** about a buyer's risk type: a person who already has a high-risk lifestyle (unobserved by the insurer) is more likely to purchase life insurance. (**Option B is correct**) - **Moral hazard** arises when a person changes their behavior and takes more risks *after* obtaining insurance (Option A), or uses more medical care because they are insured (Option D). **Answer: Option B** A: **Incorrect:** Taking more risks *because* one has insurance is moral hazard (post-contractual hidden action). B: **Correct:** Buying insurance because of pre-existing, unobserved high risk is the classic definition of adverse selection. C: **Incorrect:** Risk preference alone without asymmetric information does not define adverse selection. D: **Incorrect:** Increased utilization of medical care after becoming insured is ex-post moral hazard.

**1. Understand the principal-agent problem and moral hazard:** In a principal-agent relationship, **moral hazard** arises when the agent's actions cannot be perfectly monitored by the principal and the contract is structured such that **the interests (incentives) of the agent and the principal diverge**, leading the agent to pursue their own self-interest at the expense of the principal's goal. **Answer: Option B** A: **Incorrect:** If the interests of the agent and principal converge, incentives are aligned and moral hazard is mitigated. B: **Correct:** Moral hazard occurs when asymmetric information and contract structure allow the interests of the agent and principal to diverge. C: **Incorrect:** Under moral hazard, the agent maximizes their own utility rather than the principal's utility. D: **Incorrect:** Moral hazard creates a trade-off between incentives and risk-sharing, preventing full efficiency.