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Managerial Economics · Quiz 2 · May 2026

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Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

Question 2 MCQ · 0.5 marks

A monotonic transformation preserves the exact same ranking of consumer preferences.
  1. True
  2. False

Published solution

**1. Compare two bundles:** if \(U(A)>U(B)\), a strictly increasing transformation \(f\) gives \(f(U(A))>f(U(B))\). Equal utilities remain equal. **Answer: A — True.** A strictly increasing transformation changes utility numbers, not preference rankings. A: **Correct:** A strictly increasing transformation preserves both strict preferences and indifference. B: **Incorrect:** Utility measures preference order; changing its scale need not change that order.

Question 3 MCQ · 0.5 marks

If the price elasticity of demand for a product is greater than one, a price increase will always increase total revenue for the seller
  1. True
  2. False

Published solution

**1. Use elastic demand:** \(|\varepsilon|>1\) means quantity falls proportionately more than price rises. **2. Check revenue:** for a small price change, \(d(PQ)/dP=Q(1-|\varepsilon|)<0\). **Answer: B — False.** A price increase reduces revenue in the elastic region. A: **Incorrect:** This reverses the revenue effect of elastic demand; the quantity reduction outweighs the higher price. B: **Correct:** Elastic demand implies that a price rise lowers total revenue, rather than always increasing it.

Question 4 MCQ · 0.5 marks

If demand for a good is perfectly inelastic, consumers bear none of the burden of a per-unit tax placed on the good
  1. True
  2. False

Published solution

**1. Use perfectly inelastic demand:** buyers purchase the same quantity even when their price rises. **2. Apply the tax wedge:** in the standard competitive model, the buyer price rises by the full per-unit tax while the seller’s net price stays unchanged. **Answer: B — False.** Consumers bear the entire tax burden, not none. A: **Incorrect:** With perfectly inelastic demand, consumers cannot reduce purchases in response to the higher price. B: **Correct:** A vertical demand curve makes consumers bear the full per-unit tax burden in the standard competitive model.

Question 5 MCQ · 0.5 marks

First degree price discrimination is the practice of charging each customer her reservation price.
  1. True
  2. False

Published solution

**1. Recall the definition:** perfect first-degree discrimination charges each buyer their maximum willingness to pay for each unit. **Answer: A — True.** This maximum is the buyer’s reservation price. A: **Correct:** Charging the reservation price for each unit is first-degree price discrimination. B: **Incorrect:** Reservation-price charging is the defining feature of first-degree discrimination.

Question 6 MCQ · 0.5 marks

The cross price elasticity of demand of substitutes is positive.
  1. True
  2. False

Published solution

**1. Consider substitutes:** when the price of good \(Y\) rises, buyers switch toward good \(X\), increasing its demand. **Answer: A — True.** \(\varepsilon_{XY}=(\partial Q_X/\partial P_Y)(P_Y/Q_X)>0\). A: **Correct:** Substitutes have positive cross-price elasticity because demand shifts toward the alternative good. B: **Incorrect:** Negative cross-price elasticity characterizes complements, not substitutes.

Question 7 MCQ · 0.5 marks

A good with an income elasticity of demand greater than zero is classified as a normal good
  1. True
  2. False

Published solution

**1. Interpret income elasticity:** \(\varepsilon_I>0\) means demand increases when income increases, holding other factors fixed. **Answer: A — True.** That is the definition of a normal good. A: **Correct:** Normal goods have positive income elasticity. B: **Incorrect:** Inferior goods have negative income elasticity; a positive value indicates a normal good.

Question 8 NAT · 1.0 marks

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Equilibrium quantity (in millions) in the market before the subsidy will be Q\(^{*}\)= _______
Source diagram or notation

    Published solution

    **1. Equate demand and supply:** before subsidy, buyers and sellers face the same price \(P\): \(20-0.5P=P-1\). **2. Solve:** \(1.5P=21\), so \(P=14\). Hence \(Q=14-1=13\). **Answer: 13 million units.**

    Question 9 NAT · 1.0 marks

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    Equilibrium price in the market before the subsidy will be P\(^{*}\)= _______
    Source diagram or notation

      Published solution

      **1. Use one market price before subsidy:** \(P^B=P^S=P\). **2. Clear the market:** \(20-0.5P=P-1\Rightarrow1.5P=21\Rightarrow P=14\). **Answer: 14 per unit.**

      Question 10 NAT · 1.0 marks

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      New equilibrium quantity after the subsidy Q\(^{S}\)= _________
      Source diagram or notation

        Published solution

        **1. Introduce the subsidy wedge:** \(P^S=P^B+3\). Supply is therefore \(Q^S=P^B+2\). **2. Clear the market:** \(20-0.5P^B=P^B+2\Rightarrow P^B=12\). **3. Find quantity:** \(Q=20-0.5(12)=14\). **Answer: 14 million units.**

        Question 11 NAT · 1.0 marks

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        Price that buyers pay now will be P\(^{B}\)= ________
        Source diagram or notation

          Published solution

          **1. Use the subsidy:** \(P^S=P^B+3\), so supply equals \(P^B+2\). **2. Equate demand and supply:** \(20-0.5P^B=P^B+2\Rightarrow1.5P^B=18\). **Answer: 12 per unit**, paid by buyers.

          Question 12 NAT · 1.0 marks

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          Price that the producers receive per unit will be P\(^{S}\)= _________
          Source diagram or notation

            Published solution

            **1. Find the buyer price:** \(20-0.5P^B=P^B+2\), giving \(P^B=12\). **2. Add the subsidy:** \[P^S=P^B+3=12+3=15.\] **3. Verify market clearing:** demand \(20-0.5(12)=14\); supply \(15-1=14\). **Answer: 15 per unit**, received by sellers. **Review note:** the supplied key says 17. That would imply a subsidy of 5 rather than the stated 3, and supply \(17-1=16\) would not equal demand 14. The key needs correction.

            Question 13 NAT · 1.0 marks

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            Total cost (in millions $) to the government will be _______
            Source diagram or notation

              Published solution

              **1. Find subsidized quantity:** \(20-0.5P^B=P^B+2\) gives \(P^B=12\) and \(Q=14\) million units. **2. Multiply subsidy by units sold:** \[\text{Government cost}=3\times14=42.\] **Answer: 42 million dollars.**

              Question 14 NAT · 1.0 marks

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              Suppose the government acts weirdly and removes the subsidy to impose a tax of $6 excise tax per unit to producers New equilibrium quantity (in millions $) after the incidence of tax Q\(^{t}\)= ________
              Source diagram or notation

                Published solution

                **1. Replace the subsidy with a tax:** \(P^B=P^S+6\), so \(Q^S=P^B-7\). **2. Clear the market:** \(20-0.5P^B=P^B-7\Rightarrow P^B=18\). **3. Find quantity:** \(Q=20-0.5(18)=11\). **Answer: 11 million units.** Quantity is measured in units, despite the dollar label in the question.

                Question 15 NAT · 1.0 marks

                [[IMAGE:de77b992bbe5eb99_3_2]]
                Suppose the government acts weirdly and removes the subsidy to impose a tax of $6 excise tax per unit to producers The price that buyers pay now will be P\(^{B}\) = _______
                Source diagram or notation

                  Published solution

                  **1. Use the tax wedge:** sellers receive \(P^S=P^B-6\), giving supply \(P^B-7\). **2. Equate demand and supply:** \(20-0.5P^B=P^B-7\Rightarrow1.5P^B=27\). **Answer: 18 per unit**, paid by buyers.

                  Question 16 NAT · 1.0 marks

                  [[IMAGE:de77b992bbe5eb99_3_2]]
                  Suppose the government acts weirdly and removes the subsidy to impose a tax of $6 excise tax per unit to producers Price that seller receives per unit will be P\(^{S}\)= _______
                  Source diagram or notation

                    Published solution

                    **1. Solve for the buyer price:** \(20-0.5P^B=P^B-7\Rightarrow P^B=18\). **2. Subtract the tax:** \[P^S=18-6=12.\] **Answer: 12 per unit**, received by sellers.

                    Question 17 NAT · 1.0 marks

                    Suppose a monopolist has a constant marginal cost MC = 2 and faces the demand curve P = 20 − Q. There are no fixed costs. Based on the above data, answer the given subquestions.
                    What will be the price charged by this monopolist? P\(^{*}\)= _______

                      Published solution

                      **1. Find marginal revenue:** \(TR=(20-Q)Q=20Q-Q^2\), so \(MR=20-2Q\). **2. Set \(MR=MC\):** \(20-2Q=2\Rightarrow Q=9\). **3. Use demand:** \(P=20-9=11\). **Answer: 11 per unit.**

                      Question 18 NAT · 1.0 marks

                      Suppose a monopolist has a constant marginal cost MC = 2 and faces the demand curve P = 20 − Q. There are no fixed costs. Based on the above data, answer the given subquestions.
                      Suppose price discrimination is not allowed (or is not possible). How large will the producer surplus be? PS= _______

                        Published solution

                        **1. Find the uniform-price optimum:** \(20-2Q=2\Rightarrow Q=9\), so \(P=11\). **2. Calculate producer surplus:** with constant marginal cost 2, \[PS=(P-MC)Q=(11-2)\times9=81.\] **Answer: 81.** With no fixed costs, this is also profit.

                        Question 19 NAT · 1.0 marks

                        Suppose a monopolist has a constant marginal cost MC = 2 and faces the demand curve P = 20 − Q. There are no fixed costs. Based on the above data, answer the given subquestions.
                        Suppose the firm can engage in perfect first-degree price discrimination. What is the increase in producer surplus when a monopolist switches from uniform pricing to perfect first-degree price discrimination? PS= ______

                          Published solution

                          **1. Uniform pricing:** \(Q=9\), \(P=11\), so producer surplus is \(81\). **2. Perfect discrimination:** produce until willingness to pay equals marginal cost: \(20-Q=2\Rightarrow Q=18\). The entire area above marginal cost goes to the producer: \[PS_{\mathrm{PD}}=\int_0^{18}(20-Q-2)\,dQ=\frac12(18)(18)=162.\] **3. Find the increase:** \(162-81=81\). **Answer: 81.**

                          Question 20 NAT · 1.0 marks

                          [[IMAGE:de77b992bbe5eb99_8_3]] Based on the above data, answer the given subquestions.
                          Suppose that both Air India and Indigo charge a price of $300 each for a round-trip ticket between Kolkata and Delhi. What is the price elasticity of demand for Indigo flights between Kolkata and Delhi? (please ignore the sign)
                          Source diagram or notation

                            Published solution

                            **1. Find Indigo’s quantity:** \(Q_I=90{,}000-200(300)+100(300)=60{,}000\). **2. Hold Air India’s price fixed:** \(\partial Q_I/\partial P_I=-200\). **3. Calculate own-price elasticity:** \[\varepsilon_I=(-200)\frac{300}{60{,}000}=-1.\] **Answer: 1**, ignoring the sign.

                            Question 21 NAT · 1.0 marks

                            [[IMAGE:de77b992bbe5eb99_8_3]] Based on the above data, answer the given subquestions.
                            What is the market-level price elasticity of demand for air travel between Kolkata and Delhi when both airlines charge a price of $300? (please ignore the sign)
                            Source diagram or notation

                              Published solution

                              **1. Add both airline demands:** \(Q=180{,}000-100P_I-100P_A\). **2. Vary both prices together:** set \(P_I=P_A=P\), so \(Q=180{,}000-200P\). At \(P=300\), \(Q=120{,}000\). **3. Calculate market elasticity:** \[\varepsilon=(-200)\frac{300}{120{,}000}=-0.5.\] **Answer: 0.5**, ignoring the sign. Unlike own-price elasticity, this includes both airlines raising price together.

                              Question 22 MCQ · 1.0 marks

                              [[IMAGE:de77b992bbe5eb99_9_4]] Based on the above data, answer the given subquestions.
                              M weakly dominates T
                              Source diagram or notation
                              1. True
                              2. False

                              Published solution

                              **Player 1’s payoff table:** rows are player 1’s actions; columns are player 2’s actions. Only player 1’s payoffs are provided. \[\begin{array}{c|cc}&L&R\\ \hline T&0&1\\ M&2&1\\ B&3&2\end{array}\] **1. Compare M with T:** against \(L\), \(2>0\); against \(R\), \(1=1\). **Answer: A — True.** M is never worse and is strictly better against at least one action, so it weakly dominates T. A: **Correct:** M gives at least T’s payoff in both columns, with a strict improvement against L. B: **Incorrect:** The equality against R does not prevent weak dominance; strict inequality is required in only one or more cases.

                              Question 23 MCQ · 1.0 marks

                              [[IMAGE:de77b992bbe5eb99_9_4]] Based on the above data, answer the given subquestions.
                              B strictly dominates M
                              Source diagram or notation
                              1. True
                              2. False

                              Published solution

                              **Player 1’s payoff table:** rows are player 1’s actions; columns are player 2’s actions. Only player 1’s payoffs are provided. \[\begin{array}{c|cc}&L&R\\ \hline T&0&1\\ M&2&1\\ B&3&2\end{array}\] **1. Compare B with M:** against \(L\), \(3>2\); against \(R\), \(2>1\). **Answer: A — True.** B gives a strictly higher payoff against every opposing action, so it strictly dominates M. A: **Correct:** B outperforms M in both columns, which establishes strict dominance. B: **Incorrect:** There is no equality or reversal in either column; both comparisons are strict.

                              Question 24 MCQ · 1.0 marks

                              A consumer purchases two goods, food and clothing. He has the utility function U(x,y) = xy + 10x, where x denotes the amount of food consumed and y the amount of clothing. Based on the above data, answer the given subquestions.
                              Choose the correct alternative.
                              1. MUx is linear in x
                              2. MUx is linear in y
                              3. MUx includes both x and y terms
                              4. MUx is a fixed value

                              Published solution

                              **1. Differentiate with respect to food:** treating \(y\) as fixed, \[MU_x=\frac{\partial(xy+10x)}{\partial x}=y+10.\] **Answer: B — MUx is linear in y** (more precisely, affine in y). A: **Incorrect:** \(MU_x=y+10\) contains no \(x\) term. B: **Correct:** \(MU_x=y+10\) is a linear expression in \(y\), with intercept 10. C: **Incorrect:** only \(y\) and a constant remain after differentiation. D: **Incorrect:** marginal utility changes with \(y\); it is not fixed.

                              Question 25 MCQ · 1.0 marks

                              A consumer purchases two goods, food and clothing. He has the utility function U(x,y) = xy + 10x, where x denotes the amount of food consumed and y the amount of clothing. Based on the above data, answer the given subquestions.
                              Choose the correct alternative
                              1. MUy is linear in x
                              2. MUy is linear in y
                              3. MUy includes both x and y terms
                              4. MUy is a fixed value

                              Published solution

                              **1. Differentiate with respect to clothing:** treating \(x\) as fixed, \[MU_y=\frac{\partial(xy+10x)}{\partial y}=x.\] **Answer: A — MUy is linear in x.** A: **Correct:** \(MU_y=x\), a linear function of food consumption. B: **Incorrect:** \(MU_y\) has no \(y\) term. C: **Incorrect:** the derivative is just \(x\), not a combination of \(x\) and \(y\). D: **Incorrect:** \(MU_y\) changes when \(x\) changes.

                              Question 26 NAT · 1.0 marks

                              A consumer purchases two goods, food and clothing. He has the utility function U(x,y) = xy + 10x, where x denotes the amount of food consumed and y the amount of clothing. Based on the above data, answer the given subquestions.
                              Suppose the consumer's income is $100, and the price of food is $1 and clothing is $2. What is the slope of the budget line (ignore sign) ________

                                Published solution

                                **1. Write the budget:** \(x+2y=100\). **2. Put clothing on the vertical axis:** \(y=50-0.5x\), so the slope is \(-P_x/P_y=-1/2\). **Answer: 0.5**, ignoring the sign, with food on the horizontal axis.

                                Question 27 NAT · 1.0 marks

                                A consumer purchases two goods, food and clothing. He has the utility function U(x,y) = xy + 10x, where x denotes the amount of food consumed and y the amount of clothing. Based on the above data, answer the given subquestions.
                                Suppose the consumer's income is $100, and the price of food is $1 and clothing is $2. What is the optimal level of clothing? _______

                                  Published solution

                                  **1. Use the budget:** \(x=100-2y\), where \(0\le y\le50\). **2. Substitute into utility:** \(U=(100-2y)(y+10)=1000+80y-2y^2\). **3. Maximize:** \(dU/dy=80-4y=0\Rightarrow y=20\). Since \(d^2U/dy^2=-4<0\), this feasible interior point is the maximum. **Answer: 20 units of clothing.**

                                  Question 28 NAT · 1.0 marks

                                  A consumer purchases two goods, food and clothing. He has the utility function U(x,y) = xy + 10x, where x denotes the amount of food consumed and y the amount of clothing. Based on the above data, answer the given subquestions.
                                  Suppose the consumer's income is $100, and the price of food is $1 and clothing is $2. What is the optimal level of food? ________

                                    Published solution

                                    **1. Find optimal clothing:** substituting the budget into utility gives \(U(y)=1000+80y-2y^2\); its maximum occurs at \(y=20\). **2. Use the budget:** \[x=100-2(20)=60.\] **Answer: 60 units of food.**

                                    Question 29 NAT · 1.0 marks

                                    A consumer purchases two goods, food and clothing. He has the utility function U(x,y) = xy + 10x, where x denotes the amount of food consumed and y the amount of clothing. Based on the above data, answer the given subquestions.
                                    Suppose the consumer's income is $100, and the price of food is $1 and clothing is $2. What is the utility of the optimal bundle? ________

                                      Published solution

                                      **1. Find the optimal bundle:** maximizing \(U(y)=1000+80y-2y^2\) gives \(y=20\), then the budget gives \(x=60\). **2. Substitute into utility:** \[U(60,20)=60(20)+10(60)=1200+600=1800.\] **Answer: 1800 utility units.**