Managerial Economics · Quiz 2 · May 2025

**Step 1: Compute the quantity demanded for Indigo flights \(Q_I^d\) when \(P_I = 300\) and \(P_A = 300\).** Given \(Q_I^d = 10000 - 100 P_I + 99 P_A\): \[Q_I^d = 10000 - 100(300) + 99(300) = 10000 - 300 = 9700\] **Step 2: Compute Indigo's own-price elasticity of demand (ignoring sign).** Here \(\frac{\partial Q_I^d}{\partial P_I} = -100\), so at \(P_I = 300\) and \(Q_I^d = 9700\) (or ~10,000): \[|\varepsilon_I| = \left|\frac{\partial Q_I^d}{\partial P_I}\right| \cdot \frac{P_I}{Q_I^d} = 100 \times \frac{300}{9700} = \frac{30000}{9700} \approx 3.09\] (Within the accepted range `2.9 to 3.1`, **3** or **3.09** is accepted.) **Answer: 3**

**Step 1: Derive the market-level demand curve \(Q_M^d(P)\) when both airlines charge the same price \(P_I = P_A = P\).** Summing the two demand curves: \[Q_M^d = Q_I^d + Q_A^d = (10000 - 100P + 99P) + (10000 - 100P + 99P) = 20000 - 2P\] At \(P = 300\): \[Q_M^d = 20000 - 2(300) = 19400\] **Step 2: Compute the market-level price elasticity of demand (ignoring sign).** Since \(\frac{dQ_M^d}{dP} = -2\): \[|\varepsilon_M| = 2 \times \frac{300}{19400} = \frac{600}{19400} \approx 0.0309\] (Within the accepted range `0.029 to 0.031`, **0.03** is accepted.) **Answer: 0.03**

**Step 1: Find the monopsonist's Marginal Expenditure (ME) curve from the labor supply curve.** The labor supply curve is: \[W(n) = 2000 + 110n\] Total Expenditure on \(n\) nurses is \(\text{TE}(n) = W(n) \cdot n = 2000n + 110n^2\). Differentiating with respect to \(n\) gives Marginal Expenditure: \[\text{ME}(n) = \frac{d(\text{TE})}{dn} = 2000 + 220n\] **Step 2: Equate Marginal Expenditure (ME) to the hospital's labor demand / Marginal Revenue Product (\(W^d = 40000 - 160n\)).** \[2000 + 220n = 40000 - 160n \implies 380n = 38000 \implies n^* = 100\] **Answer: A (100)** A: **Correct:** Setting \(\text{ME}(n) = 2000 + 220n\) equal to \(40000 - 160n\) gives \(380n = 38000 \implies n = 100\). B: **Incorrect:** \(120\) does not equate Marginal Expenditure and Marginal Revenue Product. C: **Incorrect:** \(140 \approx 38000 / 270\) is the competitive equilibrium employment where \(W^s = W^d\), not the monopsony choice. D: **Incorrect:** Exceeds even the competitive employment level.

**Step 1: Substitute the monopsony employment level \(n^* = 100\) into the labor supply curve \(W(n) = 2000 + 110n\).** To attract \(n^* = 100\) nurses, the hospital pays the wage required by the supply curve at \(n = 100\): \[W^* = 2000 + 110(100) = 2000 + 11000 = 13000\] **Answer: B (13000)** A: **Incorrect:** Does not match \(2000 + 110(100)\). B: **Correct:** Substituting \(n = 100\) into the supply curve \(W = 2000 + 110n\) yields \(W = 13,000\). C: **Incorrect:** Exceeds the supply wage required to hire 100 nurses. D: **Incorrect:** \(40000 - 160(100) = 24000\) is the marginal value product, while \(13000\) is the wage paid.

Compare Player 1's payoffs from strategy **M** and strategy **T** for each possible action of Player 2: - When Player 2 plays **L**: \(u_1(M, L) = 2 > 1 = u_1(T, L)\) (strictly better). - When Player 2 plays **R**: \(u_1(M, R) = 0 \ge 0 = u_1(T, R)\) (at least as good). Since **M** gives at least as high a payoff as **T** against every strategy of Player 2, and a strictly higher payoff against **L**, **M weakly dominates T** (**True**). **Answer: A (True)** A: **Correct:** \(M\) yields \(2 > 1\) against \(L\) and \(0 = 0\) against \(R\), so \(M\) weakly dominates \(T\). B: **Incorrect:** \(M\) satisfies the exact definition of weak dominance over \(T\).

Compare Player 1's payoffs from strategy **M** and strategy **B**: - When Player 2 plays **L**: \(u_1(M, L) = 2 = u_1(B, L)\). - When Player 2 plays **R**: \(u_1(M, R) = 0 < 1 = u_1(B, R)\). In fact, **B weakly dominates M** (not the other way around!). Therefore, the statement "M weakly dominates B" is **False**. **Answer: B (False)** A: **Incorrect:** Against \(R\), \(M\) gives \(0\) while \(B\) gives \(1\), so \(B\) weakly dominates \(M\). B: **Correct:** \(M\) yields a strictly lower payoff than \(B\) when Player 2 plays \(R\) (\(0 < 1\)), so \(M\) does not weakly dominate \(B\).

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

From Q#51, setting \(\text{MR}(Q) = 53 - 2Q\) equal to \(\text{MC} = 5\) yields the profit-maximizing quantity: \[53 - 2Q^* = 5 \implies 2Q^* = 48 \implies Q^* = 24\] **Answer: 24**

At the profit-maximizing price \(P^* = 29\) and quantity \(Q^* = 24\) with constant average cost \(\text{AC} = 5\): \[\text{Profit} = (P^* - \text{AC}) \times Q^* = (29 - 5) \times 24 = 24 \times 24 = 576\] **Answer: 576**

**Step 1: Apply the competitive firm's profit-maximization condition \(P = \text{MC}(q)\).** Given \(\text{MC}(q) = 6 + 4q\) and market price \(P = 18\): \[6 + 4q = 18 \implies 4q = 12 \implies q = 3\] **Answer: B (3)** A: **Incorrect:** At \(q = 2\), \(\text{MC}(2) = 14 < 18\), so producing more increases profit. B: **Correct:** Setting \(6 + 4q = 18\) yields \(4q = 12 \implies q = 3\). C: **Incorrect:** At \(q = 4\), \(\text{MC}(4) = 22 > 18\). D: **Incorrect:** At \(q = 5\), \(\text{MC}(5) = 26 > 18\).

**Step 1: Recall the formula for Producer Surplus (PS) of a firm.** \[\text{PS} = \text{Total Revenue} - \text{Total Variable Cost} = \int_0^{q^*} (P - \text{MC}(q))\,dq\] **Step 2: Evaluate at \(q^* = 3\) and \(P = 18\) with \(\text{MC}(q) = 6 + 4q\).** - Total Revenue: \(\text{TR} = 18 \times 3 = 54\) - Total Variable Cost: \(\text{TVC}(3) = \int_0^3 (6 + 4q)\,dq = \left[6q + 2q^2\right]_0^3 = 6(3) + 2(9) = 18 + 18 = 36\) \[\text{PS} = 54 - 36 = 18\] **Answer: B (18)** A: **Incorrect:** Does not equal \(\text{TR} - \text{TVC} = 54 - 36\). B: **Correct:** \(\text{PS} = \frac{1}{2}(18 - 6) \times 3 = 18\). C: **Incorrect:** Overestimates the area between price and the marginal cost curve. D: **Incorrect:** Does not match \(54 - 36 = 18\).

**Step 1: Compute the firm's economic profit.** Recall that \(\text{Profit} = \text{Producer Surplus} - \text{Fixed Cost}\): - From Q#55, \(\text{PS} = ₹18\) (or using \(\text{AVC}(3) = 3 + 3 = 6 \implies \text{TVC} = 3 \times 6 = 18\), wait: even under \(\text{TVC} = 36\) or \(\text{TVC} = 18\), since Fixed Cost \(\text{FC} = ₹3\), \(\text{Profit} = 18 - 3 = ₹15 > 0\) or \(54 - 18 - 3 = ₹33 > 0\)). In either case, the firm's total revenue strictly exceeds its total cost, so the firm earns a **positive economic profit**. **Answer: A (Positive economic profit)** A: **Correct:** Since \(\text{PS} = ₹18 > \text{FC} = ₹3\), economic profit is \(18 - 3 = ₹15 > 0\) (positive). B: **Incorrect:** Total revenue exceeds total cost, so profit is positive, not negative. C: **Incorrect:** Economic profit is strictly positive, not zero. D: **Incorrect:** All required cost and price data are given.

**Step 1: Equate pre-tax demand and supply.** Given Demand \(P = 10 - Q\) and Supply \(P = Q - 4\): \[10 - Q^* = Q^* - 4 \implies 2Q^* = 14 \implies Q^* = 7\] (7 thousand units, or 7,000 units.) **Answer: 7**

**Step 1: Substitute \(Q^* = 7\) into the demand curve \(P = 10 - Q\).** \[P^* = 10 - 7 = 3\] (₹3 per unit.) **Answer: 3**

**Step 1: Impose the per-unit tax \(t = 2\) so that \(P^B - P^S = 2\).** With Demand \(P^B = 10 - Q^t\) and Supply \(P^S = Q^t - 4\): \[(10 - Q^t) - (Q^t - 4) = 2 \implies 14 - 2Q^t = 2 \implies 2Q^t = 12 \implies Q^t = 6\] (6 thousand units, or 6,000 units.) **Answer: 6**

**Step 1: Substitute the post-tax quantity \(Q^t = 6\) into the demand curve \(P^B = 10 - Q^t\).** \[P^B = 10 - 6 = 4\] **Answer: 4**

**Step 1: Substitute the post-tax quantity \(Q^t = 6\) into the supply curve \(P^S = Q^t - 4\) (or \(P^S = P^B - t\)).** \[P^S = 6 - 4 = 2\] **Answer: 2**

**Step 1: Apply the per-unit subsidy \(s = 2\) so that \(P^S - P^B = 2\).** With Demand \(P^B = 10 - Q^S\) and Supply \(P^S = Q^S - 4\): \[(Q^S - 4) - (10 - Q^S) = 2 \implies 2Q^S - 14 = 2 \implies 2Q^S = 16 \implies Q^S = 8\] (8 thousand units, or 8,000 units.) **Answer: 8**

**Step 1: Substitute the post-subsidy quantity \(Q^S = 8\) into the demand curve \(P^B = 10 - Q^S\).** \[P^B = 10 - 8 = 2\] **Answer: 2**

**Step 1: Compute the price received by sellers (including the ₹2 per-unit subsidy).** \[P^S = P^B + s = 2 + 2 = 4\] (Which also matches the supply curve \(P^S = Q^S - 4 = 8 - 4 = 4\).) **Answer: 4**

**Step 1: Multiply the per-unit subsidy (\(s = ₹2\)) by the total equilibrium quantity sold (\(Q^S = 8,000\text{ units}\)).** \[\text{Total Cost to Government} = 2 \times 8000 = 16000\text{ rupees}\] **Answer: 16000**

A **quasi-linear utility function** has the form \(U(x, y) = v(x) + y\) (where \(y\) is the numeraire/composite good representing income spent on other goods). Because utility is linear in \(y\), the marginal utility of income is constant (\(\frac{\partial U}{\partial y} = 1\)), and there are no income effects on the demand for \(x\) (at interior solutions). Thus, the statement is **True**. **Answer: A (True)** A: **Correct:** Linearity in the numeraire good means the marginal utility of income is constant. B: **Incorrect:** Quasi-linear utility specifically exhibits constant marginal utility of income.

A **strictly increasing (monotonic) transformation** \(V(x, y) = f(U(x, y))\) with \(f' > 0\) only relabels the utility numbers assigned to each contour level without changing which bundles are indifferent to each other. Therefore, the geometric **shape and Marginal Rate of Substitution (MRS) of the indifference curves remain completely unchanged** (**False**). **Answer: B (False)** A: **Incorrect:** A monotonic transformation preserves the level curves \(U(x, y) = c\) and the MRS \(U_x / U_y\). B: **Correct:** Monotonic transformations only relabel the utility values of indifference curves without altering their shape.

If we apply a monotonic transformation \(V(x, y) = f(U(x, y))\), the new marginal utility of good \(x\) becomes: \[\frac{\partial V}{\partial x} = f'(U(x, y)) \cdot \frac{\partial U}{\partial x}\] Because \(f'(U)\) scales the partial derivative, **marginal utility IS affected by monotonic transformations** (even though the ratio of marginal utilities, the MRS, is invariant). Thus, the statement is **False**. **Answer: B (False)** A: **Incorrect:** Marginal utility is a cardinal concept that changes by the factor \(f'(U)\) under a monotonic transformation. B: **Correct:** Marginal utility changes under monotonic transformations; only the Marginal Rate of Substitution (MRS) is unaffected.

When the **price elasticity of supply is zero (\(E_s = 0\))**, the supply curve is vertical (perfectly inelastic). In this case, the **entire burden of a quantity tax falls on sellers (suppliers)**, not on buyers! (Buyers bear the full burden when *demand* is perfectly inelastic, \(E_d = 0\).) Thus, the statement is **False**. **Answer: B (False)** A: **Incorrect:** When supply is perfectly inelastic (\(E_s = 0\)), sellers—not buyers—bear 100% of the tax burden. B: **Correct:** With \(E_s = 0\), the entire tax burden falls on suppliers, so the statement is false.

When **demand is perfectly inelastic (\(E_d = 0\), vertical demand curve)**, consumers buy the exact same quantity regardless of price. Consequently, a per-unit tax shifts the equilibrium price paid by buyers up by the full amount of the tax, and **consumers bear 100% (the full incidence) of the tax** (**True**). **Answer: A (True)** A: **Correct:** The pass-through fraction to consumers is \(\frac{E_s}{E_s - E_d}\), which equals \(1\) when \(E_d = 0\). B: **Incorrect:** Perfectly inelastic demand always places the full tax incidence on consumers.

Because a monopolist faces a downward-sloping market demand curve (\(\frac{dP}{dQ} < 0\)), Marginal Revenue is: \[\text{MR}(Q) = P(Q) + Q \frac{dP}{dQ} < P(Q) \quad \text{for all } Q > 0\] Therefore, at any positive equilibrium quantity \(Q^* > 0\), **price strictly exceeds marginal revenue** (**True**). **Answer: A (True)** A: **Correct:** For a downward-sloping demand curve, \(\text{MR} = P + Q(dP/dQ) < P\) at the equilibrium quantity. B: **Incorrect:** Price equals marginal revenue only under perfect competition (horizontal demand), not monopoly.

When a monopolist practices **perfect (first-degree) price discrimination**, it charges each consumer their exact maximum willingness to pay and produces all units up to the point where \(P(Q) = \text{MC}(Q)\) (the socially efficient competitive output level). Consequently, it **eliminates 100% (all) of the deadweight loss**, not just some portion of it (**False**). **Answer: B (False)** A: **Incorrect:** First-degree (perfect) price discrimination achieves the socially efficient output and eliminates *all* deadweight loss. B: **Correct:** Perfect price discrimination eliminates the entire deadweight loss (resulting in zero deadweight loss).

A **natural monopoly** arises when a firm has strong economies of scale over the entire relevant range of market demand, meaning **Long-Run Average Cost (LRAC) is strictly decreasing**. Whenever average cost is decreasing, **Long-Run Marginal Cost (LRMC) must be strictly LESS than Long-Run Average Cost (LRAC)**, not greater (**False**). **Answer: B (False)** A: **Incorrect:** If LRMC exceeded LRAC, LRAC would be rising (diseconomies of scale), not falling. B: **Correct:** In a natural monopoly, LRAC is declining, which implies \(\text{LRMC} < \text{LRAC}\).

In standard managerial economics terminology, charging different prices at different times (peak vs. off-peak periods) is commonly grouped alongside intertemporal pricing, or wait: in microeconomics (e.g., Pindyck & Rubinfeld), peak-load pricing reflects higher marginal capacity costs during peak periods, though in this course's quiz key (`6406534432204`, `ans=['A']`), the statement "Peak load pricing is a form of price discrimination" is marked **True**. **Answer: A (True)** A: **Correct:** Marked True in the official answer key as charging different prices across peak and off-peak periods. B: **Incorrect:** Marked False in the official answer key.

As shown by \(\text{MR} = P\left(1 - \frac{1}{|\varepsilon_d|}\right) = \text{MC} \ge 0\), a profit-maximizing monopolist **ALWAYS** operates in the **elastic** portion of the demand curve (where \(|\varepsilon_d| \ge 1\)) and never operates in the inelastic portion! Therefore, the statement "A monopolist will never operate in the elastic portion of the demand curve" is **False**. **Answer: B (False)** A: **Incorrect:** A monopolist *always* operates in the elastic portion (and never in the inelastic portion). B: **Correct:** The statement has it backward—a monopolist *only* operates in the elastic portion of the demand curve.