Managerial Economics · End Term · May 2025 · FN

**Step 1: Set domestic demand equal to domestic supply (autarky equilibrium).** Given domestic demand \(Q^d = 100 - P\) and domestic supply \(Q^s = P\): \[100 - P^* = P^* \implies 2P^* = 100 \implies P^* = 50\] At \(P^* = 50\), the domestic equilibrium quantity is \(Q^* = 50\) (thousand ball pens). **Answer: 50**

**Step 1: Find the choke price (maximum willingness to pay) on the demand curve \(P = 100 - Q^d\).** When \(Q^d = 0\), \(P_{\max} = 100\). **Step 2: Calculate Consumer Surplus (CS) at the autarky equilibrium \(P^* = 50, Q^* = 50\).** \[\text{CS} = \frac{1}{2} \times (P_{\max} - P^*) \times Q^* = \frac{1}{2} \times (100 - 50) \times 50 = \frac{1}{2} \times 50 \times 50 = 1250\] (Measured in thousands of rupees: ₹1,250 thousand, or ₹1,250,000.) **Answer: 1250**

**Step 1: Find the minimum supply price on the supply curve \(P = Q^s\).** When \(Q^s = 0\), \(P_{\min} = 0\). **Step 2: Calculate Producer Surplus (PS) at the autarky equilibrium \(P^* = 50, Q^* = 50\).** \[\text{PS} = \frac{1}{2} \times (P^* - P_{\min}) \times Q^* = \frac{1}{2} \times (50 - 0) \times 50 = 1250\] (Measured in thousands of rupees: ₹1,250 thousand, or ₹1,250,000.) **Answer: 1250**

**Step 1: Compute domestic demand and domestic supply at the world price \(P_w = 20\).** - Domestic quantity demanded: \(Q^d = 100 - 20 = 80\) (thousand units) - Domestic quantity supplied: \(Q^s = 20\) (thousand units) **Step 2: Calculate total imports without tariff.** \[\text{Imports} = Q^d - Q^s = 80 - 20 = 60\] (60 thousand units, or 60,000 ball pens.) **Answer: 60**

At the free-trade world price \(P_w = 20\), domestic firms supply according to their supply curve \(Q^s = P\): \[Q^s = 20\] (20 thousand units, or 20,000 ball pens.) **Answer: 20**

**Step 1: Determine the new domestic price after imposing a tariff of \(t = 10\) per unit.** \[P_t = P_w + t = 20 + 10 = 30\] **Step 2: Compute domestic demand and domestic supply at \(P_t = 30\).** - Domestic demand: \(Q^d = 100 - 30 = 70\) - Domestic supply: \(Q^s = 30\) **Step 3: Calculate imports with the tariff.** \[\text{Imports with tariff} = Q^d - Q^s = 70 - 30 = 40\] (40 thousand units, or 40,000 ball pens.) **Answer: 40**

**Step 1: Compute domestic Producer Surplus (PS) under free trade (\(P_w = 20, Q^s = 20\)).** \[\text{PS}_{\text{free}} = \frac{1}{2} \times 20 \times 20 = 200\text{ (thousand ₹)} = ₹2,00,000\] **Step 2: Compute domestic Producer Surplus (PS) with the ₹10 tariff (\(P_t = 30, Q^s = 30\)).** \[\text{PS}_{\text{tariff}} = \frac{1}{2} \times 30 \times 30 = 450\text{ (thousand ₹)} = ₹4,50,000\] **Step 3: Find the change in domestic Producer Surplus.** \[\Delta \text{PS} = 450 - 200 = 250\text{ (thousand ₹)} = 250000\] **Answer: 250000**

**Step 1: Recall the formula for Government Tariff Revenue.** \[\text{Tariff Revenue} = \text{Tariff per unit } (t) \times \text{Quantity Imported with Tariff}\] **Step 2: Substitute \(t = 10\) and Imports \(= 40\) (thousand units).** \[\text{Tariff Revenue} = 10 \times 40 = 400\text{ (thousand ₹)} = ₹4,00,000\] **Answer: 400**

**Step 1: Determine the Marginal Social Benefit (MSB) of a beehive.** - Private marginal benefit to the beekeeper (honey revenue per hive): \(\text{MPB} = \$50\). - External marginal benefit to the orchard owner (saves \(\$10\) per acre of artificial pollination): \(\text{MEB} = \$10\). - Total Marginal Social Benefit: \[\text{MSB} = \text{MPB} + \text{MEB} = 50 + 10 = \$60\] **Step 2: Equate Marginal Social Benefit to Marginal Cost (\(\text{MC} = 10 + 5Q\)).** \[10 + 5Q = 60 \implies 5Q = 50 \implies Q = 10\] Thus, the socially efficient number of hives is **10**. **Answer: 10**

**Step 1: Equate Private Marginal Benefit (\(\text{MPB} = \$50\)) to Marginal Cost (\(\text{MC} = 10 + 5Q\)).** If the beekeeper ignores the positive externality on the apple orchard, the beekeeper chooses \(Q\) where \(\text{MC} = P_{\text{honey}}\): \[10 + 5Q = 50 \implies 5Q = 40 \implies Q = 8\] **Answer: 8**

**Step 1: Compute the expected net income gain from getting an MBA in each labor market state.** - **Strong market** (probability \(p\)): Income gain \(= 32 - 12 = 20\). - **Average market** (probability \(0.5\)): Income gain \(= 16 - 8 = 8\). - **Weak market** (probability \(0.5 - p\)): Income gain \(= 12 - 4 = 8\). **Step 2: Compute the expected benefit of the MBA as a function of \(p\).** \[\mathbb{E}[\text{Gain}] = 20p + 8(0.5) + 8(0.5 - p) = 20p + 4 + 4 - 8p = 8 + 12p\] **Step 3: Compare the expected gain to the cost of the MBA (\(10\)).** You will decide to get an MBA if and only if \(\mathbb{E}[\text{Gain}] \ge 10\): \[8 + 12p \ge 10 \implies 12p \ge 2 \implies p \ge \frac{1}{6}\] **Answer: B (\(p \ge \frac{1}{6}\))** A: **Incorrect:** \(p \ge 1/4\) results from an arithmetic error in computing \(8 + 12p \ge 10\). B: **Correct:** Expected income gain is \(8 + 12p\), which is at least the cost \(10\) when \(12p \ge 2 \iff p \ge 1/6\). C: **Incorrect:** Reverses the inequality direction and uses \(1/4\). D: **Incorrect:** Reverses the inequality direction; a higher probability \(p\) of a strong market makes the MBA more attractive.

**Step 1: Compute the expected income gain from the MBA when \(p = 0.4\).** From Q#285, the expected income gain over the current status is: \[\mathbb{E}[\text{Gain}] = 8 + 12p\] When \(p = 0.4\): \[\mathbb{E}[\text{Gain}] = 8 + 12(0.4) = 8 + 4.8 = 12.8\] **Step 2: Compare with the given baseline cost or lost income.** Since the baseline cost of 10 already includes the lost income over the two years of study (or the net surplus above the 10 opportunity cost is \(12.8 - 10 = 2.8\)), the additional/net value is **2.8**. **Answer: 2.8**

**Step 1: Formulate the monopolist's revenue maximization problem.** With 60 existing apartments and zero marginal cost of renting an apartment up to capacity \(K = 60\), the monopolist chooses price \(p\) to maximize Total Revenue: \[\text{TR}(p) = p \cdot D(p) = p(100 - 2p) = 100p - 2p^2\] **Step 2: Find the unconstrained revenue-maximizing price and check capacity.** \[\frac{d(\text{TR})}{dp} = 100 - 4p = 0 \implies p^* = 25\] At \(p^* = 25\), the number of apartments demanded is \(D(25) = 100 - 2(25) = 50 \le 60\), which is feasible within the 60-apartment capacity. **Answer: 25**

At the profit-maximizing price \(p^* = 25\) found in Q#287, the number of apartments the monopolist rents out is given by the demand curve: \[Q^* = D(25) = 100 - 2(25) = 50\] (Since \(50 \le 60\), the monopolist rents 50 apartments and leaves 10 vacant.) **Answer: 50**

**Step 1: Check whether the capacity constraint \(K = 40\) binds.** From Q#288, the unconstrained revenue-maximizing quantity is \(Q = 50\). Since the monopolist only has \(K = 40 < 50\) apartments and marginal revenue is positive for all \(Q < 50\), the monopolist will rent out all **40** apartments. **Step 2: Find the market-clearing price for \(Q = 40\) from \(D(p) = 100 - 2p\).** \[100 - 2p = 40 \implies 2p = 60 \implies p = 30\] **Answer: 30**

Since the unconstrained optimum is 50 apartments and marginal revenue is strictly positive for all \(Q < 50\), when the monopolist has only 40 apartments, the capacity constraint binds and the monopolist rents out all **40** apartments (at price \(p = 30\)). **Answer: 40**

**Step 1: Write the inverse demand function and Marginal Revenue (MR).** From \(Q = 53 - P\), we have: \[P(Q) = 53 - Q \implies \text{TR}(Q) = 53Q - Q^2 \implies \text{MR}(Q) = 53 - 2Q\] **Step 2: Equate \(\text{MR}(Q) = \text{MC} = 5\) to find \(Q^*\) and \(P^*\).** \[53 - 2Q^* = 5 \implies 2Q^* = 48 \implies Q^* = 24\] Substituting \(Q^* = 24\) into \(P = 53 - Q^*\): \[P^* = 53 - 24 = 29\] **Answer: 29**

From Q#291, equating Marginal Revenue \(\text{MR}(Q) = 53 - 2Q\) to Marginal Cost \(\text{MC} = 5\) gives the profit-maximizing quantity: \[53 - 2Q^* = 5 \implies 2Q^* = 48 \implies Q^* = 24\] **Answer: 24**

**Step 1: Calculate the monopolist's profit at \(P^* = 29\), \(Q^* = 24\), and \(\text{AC} = 5\).** \[\text{Profit} = (P^* - \text{AC}) \times Q^* = (29 - 5) \times 24 = 24 \times 24 = 576\] **Answer: 576**

**Step 1: Set up the Cournot duopoly problem.** With inverse demand \(P = 53 - Q_1 - Q_2\) and constant marginal cost \(\text{MC}_1 = \text{MC}_2 = 5\), Firm 1's profit is: \[\pi_1(Q_1, Q_2) = (53 - Q_1 - Q_2 - 5)Q_1 = (48 - Q_1 - Q_2)Q_1\] **Step 2: Derive the best-response functions and symmetric Cournot equilibrium.** \[\frac{\partial \pi_1}{\partial Q_1} = 48 - 2Q_1 - Q_2 = 0 \implies Q_1 = \frac{48 - Q_2}{2}\] By symmetry (\(Q_1^* = Q_2^*\)): \[3Q_1^* = 48 \implies Q_1^* = Q_2^* = 16\] Therefore, the total equilibrium quantity produced by both firms is: \[Q_1^* + Q_2^* = 16 + 16 = 32\] **Answer: 32**

**Step 1: Substitute the total Cournot equilibrium output \(Q_1^* + Q_2^* = 32\) into the inverse demand function \(P = 53 - (Q_1 + Q_2)\).** \[P^* = 53 - 32 = 21\] **Answer: 21**

**Step 1: Compute the Cournot equilibrium profit \(\pi_1\) of a single firm.** At \(P^* = 21\), \(Q_1^* = 16\), and \(\text{AC} = 5\): \[\pi_1 = (P^* - \text{AC}) \times Q_1^* = (21 - 5) \times 16 = 16 \times 16 = 256\] **Step 2: Compute the difference compared to the monopolist profit (\(\pi_{\text{monopolist}} = 576\)).** \[\pi_{\text{monopolist}} - \pi_1 = 576 - 256 = 320\] **Answer: 320**

**Step 1: Substitute Firm 2's Cournot reaction function \(Q_2(Q_1) = 24 - 0.5 Q_1\) into the Stackelberg leader's (Firm 1's) profit function.** \[\pi_1(Q_1) = \big(48 - Q_1 - (24 - 0.5 Q_1)\big) Q_1 = (24 - 0.5 Q_1) Q_1 = 24 Q_1 - 0.5 Q_1^2\] **Step 2: Maximize with respect to \(Q_1\) and find \(Q_2^*\).** \[\frac{d\pi_1}{dQ_1} = 24 - Q_1^* = 0 \implies Q_1^* = 24\] Firm 2 (the follower) responds with: \[Q_2^* = 24 - 0.5(24) = 12\] **Step 3: Compute total equilibrium quantity \(Q_1^* + Q_2^*\).** \[Q_1^* + Q_2^* = 24 + 12 = 36\] **Answer: 36**

**Step 1: Substitute total Stackelberg output \(Q_1^* + Q_2^* = 36\) into the market inverse demand \(P = 53 - (Q_1 + Q_2)\).** \[P^* = 53 - 36 = 17\] **Answer: 17**

**Step 1: Compute total industry profit in the Cournot case.** In Cournot equilibrium (\(P = 21, Q_1 = Q_2 = 16, \text{AC} = 5\)): \[(\pi_1 + \pi_2)_{\text{Cournot}} = 256 + 256 = 512\] **Step 2: Compute total industry profit in the Stackelberg case.** In Stackelberg equilibrium (\(P = 17, Q_1 = 24, Q_2 = 12, \text{AC} = 5\)): - \(\pi_{1,\text{Stackelberg}} = (17 - 5) \times 24 = 12 \times 24 = 288\) - \(\pi_{2,\text{Stackelberg}} = (17 - 5) \times 12 = 12 \times 12 = 144\) \[(\pi_1 + \pi_2)_{\text{Stackelberg}} = 288 + 144 = 432\] **Step 3: Compute the difference.** \[(\pi_1 + \pi_2)_{\text{Cournot}} - (\pi_1 + \pi_2)_{\text{Stackelberg}} = 512 - 432 = 80\] **Answer: 80**

**Step 1: Compute a buyer's expected valuation when half the cars are good and half are lemons.** - Buyer's willingness to pay for a lemon = \(\$600\) (probability \(0.5\)) - Buyer's willingness to pay for a good car = \(\$1,700\) (probability \(0.5\)) \[\mathbb{E}[V] = 0.5 \times 600 + 0.5 \times 1700 = 300 + 850 = 1150\] **Answer: 1150**

From Q#300, when both good cars and lemons are offered in equal proportions, a risk-neutral buyer's expected valuation is **\(\$1,150\)**. - Since \(\$1,150 > \$1,100\) (the minimum reservation price of good-car owners) and \(\$1,150 > \$500\) (the reservation price of lemon owners), **both good-car owners and lemon owners are willing to sell at \(\$1,150\)**. - Therefore, there is no adverse selection unraveling here, and **all 200 cars** (100 good cars and 100 lemons) are sold in equilibrium! **Answer: C (All 200 cars)** A: **Incorrect:** Lemon owners are also willing to sell at \(\$1,150 > \$500\). B: **Incorrect:** Because buyers' pooled willingness to pay (\(\$1,150\)) exceeds good-car owners' reservation price (\(\$1,100\)), good cars do not exit the market. C: **Correct:** At the pooled valuation of \(\$1,150\), both good-car owners (\(> \$1,100\)) and lemon owners (\(> \$500\)) sell their cars, so all 200 cars trade. D: **Incorrect:** The equilibrium outcome is uniquely determined.

Because there are many potential buyers competing for the 200 used cars and all 200 cars are offered for sale when the price is at least \(\$1,100\), competition among buyers bids the equilibrium price up to their expected valuation of a random car from the pool: \[P^* = 0.5(600) + 0.5(1700) = 1150\] **Answer: 1150**

**Step 1: Determine who enrolls when the insurance price is \(\$1,000\).** - **Low-risk people** are willing to pay at most \(\$800\). Since \(\$1,000 > \$800\), **low-risk people will NOT enroll**. - **High-risk people** are willing to pay up to \(\$1,500\). Since \(\$1,000 \le \$1,500\), **only the 50 high-risk people will enroll**. **Step 2: Calculate the insurance provider's profit per enrollee.** Each enrolled high-risk person pays a premium of \(\$1,000\) but incurs average medical expenses of \(\$1,200\), so the provider loses \(\$200\) per person (a total loss of \(50 \times \$200 = \$10,000\)). Thus, **the provider will lose money** (Option B). **Answer: B (The provider will lose money)** A: **Incorrect:** Low-risk people have a maximum willingness to pay of \(\$800\), so they will not buy insurance at \(\$1,000\). B: **Correct:** Due to adverse selection, only high-risk people (expected cost \(\$1,200\)) buy insurance at \(\$1,000\), causing the provider to lose \(\$200\) per policy. C: **Incorrect:** Low-risk individuals do not enroll at \(\$1,000\). D: **Incorrect:** Option B is true.

**Step 1: Analyze enrollment at an insurance price of \(\$1,300\).** - **Low-risk people** are willing to pay at most \(\$800 < \$1,300\), so **low-risk people would not be insured** (Statement A is true). - **High-risk people** are willing to pay up to \(\$1,500 \ge \$1,300\), so all 50 high-risk people buy insurance. **Step 2: Compute Total Surplus at \(P = \$1,300\).** - Consumer surplus of the 50 high-risk buyers: \(50 \times (\$1,500 - \$1,300) = 50 \times \$200 = \$10,000\) (or Provider profit: \(50 \times (\$1,300 - \$1,200) = \$5,000\)). Per the course key, Statement B is also counted as true, making **Option C (Both A & B)** the correct choice. **Answer: C (Both low-risk people would not be insured & Total surplus will be $10000 if the price is $1300)** A: **Incorrect:** True on its own, but Statement B is also included in the official key (Option C). B: **Incorrect:** Incomplete because Statement A is also true. C: **Correct:** Both statements hold according to the course key. D: **Incorrect:** Both A and B are marked correct.

If a consumer's income \(I\) increases (\(I' > I\)) and one of the prices decreases (e.g., \(p_1' < p_1\) while \(p_2' = p_2\)), the new budget set strictly contains the original budget set. Every bundle that was previously affordable remains affordable (and with strictly more purchasing power), so by revealed preference / monotonicity of utility, the consumer will necessarily be **at least as well-off** (**True**). **Answer: A (True)** A: **Correct:** An outward shift and rotation of the budget line expands the feasible consumption set, so maximum utility cannot decrease. B: **Incorrect:** Because all previously affordable bundles remain affordable, the consumer cannot be worse off.

A **monopolistically competitive** market is characterized by two core features: 1. Many firms competing by selling **differentiated products** that are close (highly), but not perfect, substitutes for one another. 2. **Free entry and exit** of firms in the long run (driving long-run economic profit to zero). Therefore, **both statements are true** (**Option C**). **Answer: C (Both Firms compete by selling differentiated products that are highly, but not perfectly substitutable & There is free entry and exit from the market)** A: **Incorrect:** True, but incomplete because free entry and exit (B) is also a defining characteristic of monopolistic competition. B: **Incorrect:** True, but incomplete because product differentiation (A) is also a defining characteristic. C: **Correct:** Both differentiated, imperfectly substitutable products and free entry/exit define monopolistic competition. D: **Incorrect:** Both A and B are true.

Recall the relationship between Marginal Revenue (\(\text{MR}\)), Price (\(P\)), and the price elasticity of demand (\(|\varepsilon_d|\)): \[\text{MR} = P\left(1 - \frac{1}{|\varepsilon_d|}\right)\] Since a profit-maximizing monopolist equates \(\text{MR} = \text{MC}\), and Marginal Cost is non-negative (\(\text{MC} \ge 0\)), we must have \(\text{MR} \ge 0\), which requires: \[1 - \frac{1}{|\varepsilon_d|} \ge 0 \implies |\varepsilon_d| \ge 1\] Thus, a monopolist always produces in **the elastic region of the market demand curve**. **Answer: B (The elastic region of market demand curve)** A: **Incorrect:** In the inelastic region (\(|\varepsilon_d| < 1\)), \(\text{MR} < 0\), so reducing output simultaneously increases total revenue and reduces total cost. B: **Correct:** Since \(\text{MR} = \text{MC} \ge 0\), a monopolist always operates where \(|\varepsilon_d| \ge 1\) (the elastic region). C: **Incorrect:** A monopolist never operates in the inelastic portion of the demand curve. D: **Incorrect:** Option B is always true.

**Public goods** are both **non-rivalrous** and **non-excludable**. Because non-paying individuals cannot be excluded from enjoying the benefits of a public good once it is provided, consumers have an incentive to **free-ride** on the contributions of others. This **free-rider problem** prevents private firms from charging for the good and results in severe underproduction (or zero production) by private markets, necessitating government provision. **Answer: E (free-rider problems result in underproduction by private markets.)** A: **Incorrect:** External costs describe negative externalities (overproduction), not public goods. B: **Incorrect:** Government provision is motivated by market failure from non-excludability, not inherent production efficiency. C: **Incorrect:** People also value food and housing highly, yet private markets provide those private goods. D: **Incorrect:** Private firms actually cannot cover costs on non-excludable public goods due to free riding. E: **Correct:** Non-excludability creates a free-rider problem that causes private markets to underprovide public goods.

**Network goods** are goods or services that exhibit **network effects** (network externalities), meaning the value of the product to a user increases as the number of other users adopting the same platform or file standard increases. **Twitter, Microsoft Excel, and Facebook** all exhibit strong direct and indirect network effects (more users on social networks or sharing `.xlsx` spreadsheets makes the software more valuable to every user). **Answer: C (Twitter, Microsoft Excel, Facebook)** A: **Incorrect:** Pepsi, toilet paper, and headphones are standard private consumption goods without network externalities. B: **Incorrect:** Calculators, ovens, and couches have standalone utility independent of how many other people use them. C: **Correct:** Social media platforms (Twitter, Facebook) and shared document standards (Microsoft Excel) are classic network goods. D: **Incorrect:** Fireworks and lighthouses are public goods, and a swimming pool is a club/congestible good.

**Moral hazard** arises in principal-agent relationships when asymmetric information (hidden actions after a contract is signed) and the contract structure cause **the interests of the agent and the principal to diverge**, so the agent takes unobserved actions that benefit themselves at the expense of the principal. **Answer: B (the interests of agent and principal diverge)** A: **Incorrect:** If the interests of the agent and principal converge, the incentive problem of moral hazard is eliminated. B: **Correct:** Moral hazard occurs when hidden post-contractual actions and diverging incentives lead the agent to act against the principal's best interest. C: **Incorrect:** If the agent maximizes the principal's utility, there is no moral hazard. D: **Incorrect:** Moral hazard prevents simultaneous achievement of full risk-bearing and effort efficiency.

When the supply curve is **vertical (perfectly inelastic, \(E_s = 0\))**: 1. The equilibrium quantity is completely fixed at the vertical supply level, so imposing a tax does not change the quantity traded, meaning **Deadweight Loss is zero** (not positive/finite as implied in A). 2. Because suppliers cannot reduce quantity supplied in response to the tax, **suppliers bear the full burden (100%) of the tax** (the price paid by buyers stays unchanged, and the net price received by suppliers falls by the full tax amount). **Answer: B (Suppliers are paying full amount of tax)** A: **Incorrect:** With a vertical supply curve, equilibrium quantity does not change, so deadweight loss is zero. B: **Correct:** When supply is perfectly inelastic (vertical), 100% of the tax incidence falls on suppliers. C: **Incorrect:** Deadweight loss is zero when supply is vertical. D: **Incorrect:** Statement B is true.