Sample Exam 2 (practice) · Ido Eisdorfer · worked-solution

Sample Exam 2 — Worked Solutions

Part of: Microeconomics Sample Exam 2 (practice) — Micro 3 — Advanced Microeconomics | Tyomkin School of Economics, Reichman University Builds on: Topic 1 - Asymmetric Information · Topic 2 - Equilibrium in Different Market Structures · Topic 3 - Game Theory · Topic 4 - Price Competition with Complementary Goods Key concepts: Bundling, Moral Hazard, Two-Part Tariff, First-Degree Price Discrimination, Coordination Game, Cournot Competition, Bertrand Competition, Nash Equilibrium

No official solutions

Solved from scratch and checked in Python. Two questions are genuinely awkward as printed — Q3 (the cost-effectiveness numbers point the opposite way to the keyed pairing) and Q6 (the value works out to a number not in the option list). Both are flagged with a [!question] callout; check them against your instructor's key.

What this paper tests

The throughline: extracting surplus from heterogeneous buyers

Exam 2 leans hard on two-part tariffs and price discrimination (Q6, Open Q1) plus the quantity-vs-price competition contrast (Open Q2). The single most useful reflex: a first-degree two-part tariff sets per-unit price = MC and fixed fee = consumer surplus; a uniform tariff for two types has its fee pinned by the smaller consumer.

Q1, Q6, Open Q1 — bundling & two-part tariffs.

Q2, Q3 — health insurance, cost-effectiveness, moral hazard.

Q4, Open Q2 — differentiated competition: substitutes, Cournot vs Bertrand.

Q5 — Battle of the Sexes and counting equilibria.

Q1 — Screens sold separately

A profit-maximizing firm sells computers and screens. The willingness to pay for screens is:

Customer Screen

1 800

2 600

3 400

4 200

The marginal cost of a screen is $300. If the firm sells screens separately, what price maximizes profit from screens?
Q2 — Physician maximises the patient's expected utility

The following data is for questions 2-3.

Two treatment alternatives are available:

Treatment Cost Probability of Success

A 1,200 0.5

B 2,400 0.75

Treatment (B) yields 20 utility units and treatment (A) yields 4 utility units.

A physician seeks to maximize the expected utility units of an individual patient. Which treatment will the physician choose?
Q3 — HMO maximises utility per fixed budget

The following data is for questions 2-3.

Two treatment alternatives are available:

Treatment Cost Probability of Success

A 1,200 0.5

B 2,400 0.75

Treatment (B) yields 20 utility units and treatment (A) yields 4 utility units.

Suppose the Health Maintenance Organization (HMO) seeks to maximize total expected utility units subject to a fixed budget. Which statement is correct?
Q4 — Substitute products

Two producers, $i$ and $j$ , produce similar substitute products.

Producer $i$ faces demand: $q_{i} = A - p_{i} + p_{j}$ Producer $j$ faces demand: $q_{j} = A - p_{j} + p_{i}$ Both have constant marginal cost equal to zero. Which statement is correct?
Q5 — Ronit & Dan at the movies

Ronit and Dan want to go to the movies. Each must choose between "Rambo 5" and "Sense and Sensibility." Ronit has already seen "Rambo 5," so she prefers "Sense and Sensibility." However, if Dan goes to "Rambo 5," she prefers watching "Rambo 5" with him over watching "Sense and Sensibility" alone. Dan has not seen "Rambo 5" and prefers it to "Sense and Sensibility." However, he prefers watching "Sense and Sensibility" with Ronit over watching "Rambo 5" alone. How many Nash equilibria does this game have?
Q6 — Value of identifying consumer types

A monopolist produces a product for two consumers.

Consumer 1's demand is: $q_{1} = 9 - p$ Consumer 2's demand is: $q_{2} = 12 - p$ The monopolist has a constant marginal cost of: $MC = 2$ The monopolist cannot distinguish between consumers and must offer the same two-part tariff (TPT) to both consumers. A private investigation company offers to identify each consumer type.

Assuming the monopolist sells only once, what is the maximum amount it should be willing to pay the investigation company?
Open 1a — Pay M: separate two-part tariffs

A monopolist sells a product to two consumers, Consumer 1 and Consumer 2. The monopolist's cost function is: $TC(Q) = 20Q$ , where: $Q = q_{1} + q_{2}$ Consumer 1's demand is: $p = 200 - q_{1}$ Consumer 2's demand is: $p = 150 - q_{2}$

A. Assume the monopolist can pay a fixed one-time amount $M$ , allowing it to distinguish between the two consumers and offer each consumer a separate two-part tariff: $(p_{1},T_{1}),(p_{2},T_{2})$ , where $p_{i}$ is the per-unit price and $T_{i}$ is the fixed fee. Find the tariffs chosen by the monopolist.
Open 1b — No M: uniform tariff and maximum M

B. If the monopolist does not pay $M$ , it must charge a uniform two-part tariff: $(p,T)$ to both consumers. Find the maximum $M$ the monopolist is willing to pay.
Open 1c — Uniform tariff with general A

C. Now the monopolist must set a uniform tariff $(p,T)$ , and Consumer 2's demand is:

$p = A - q_{2}$ where: $A \leq 200$ . Assume the monopolist wants to sell to both consumers.

Find the optimal tariff $(p,T)$ as a function of $A$ . How does $p$ depend on $A$ ?
Open 1d — Serving only one consumer

D. Following section C, for which values of A the monopolist will prefer to sell only to one consumer?
Open 2a — Cournot (simultaneous quantities)

Two firms produce differentiated products $q_{1}$ and $q_{2}$ . Inverse demands are:

$p_{1} = 24 - q_{1} - 0.5q_{2}$

$p_{2} = 24 - q_{2} - 0.5q_{1}$

Marginal costs are zero.

A. Find the Simultaneous quantity competition equilibrium and profit.
Open 2b — Bertrand (simultaneous prices)

B. Find the Simultaneous Price competition equilibrium and profit (Hint: find both demand functions $q_i$ as a function of $p_1$ and $p_2$ ).
Open 2c — Firm 1 sets quantity, Firm 2 sets price

C. Find Equilibrium results if Firm 1 chooses quantity and Firm 2 chooses price (Hint: firm 2 price responds to $q_1$ , and firm 1 quantity responds to $p_2$ ).
Open 2d — The strategy game: choose Quantity or Price

D. Show in a matrix the two strategies each firm faces and find Nash Equilibrium.

Firm 1 / Firm 2 Quantity Price

Quantity

Price

Customer	Screen
1	800
2	600
3	400
4	200

Treatment	Cost	Probability of Success
A	1,200	0.5
B	2,400	0.75

Treatment	Cost	Probability of Success
A	1,200	0.5
B	2,400	0.75

One-page recap

Q	Topic	Tool	Answer
MC1	Bundling	Uniform price over WTP ladder	C — $600 (profit 600)
MC2	Insurance	Physician max expected utility	C — Treatment B ( $E[U]=15>2$ )
MC3	Cost-effectiveness	Utility per $ + moral hazard	D / likely-keyed E — see flag (B is the cost-effective one)
MC4	Substitutes	Symmetric eq.; output ↑	D — prices equal & welfare higher
MC5	Battle of the Sexes	Count NE	C — 3 (2 pure + 1 mixed)
MC6	Two-part tariff	$\pi^{\text{disc}}-\pi^{\text{uni}}$	E — value $=23.25$ (not listed)
Open 1A	First-degree TPT	$p=MC$ , $T=CS$	$(20,16200),(20,8450)$ ; $\pi=24{,}650$
Open 1B	Uniform TPT	$T=CS_2$	$p=45,\ T=5512.5$ ; $M_{\max}=7{,}125$
Open 1C	Uniform TPT, general $A$	maximise over $p$	$p^=120-\tfrac A2,\ T^=\tfrac98(A-80)^2$
Open 1D	Serve one vs both	$\pi^{\text{both}}=\pi^{\text{only1}}$	serve one iff $A<56+36\sqrt6\approx144.2$
Open 2A	Cournot	$MR=MC$	$q=p=9.6,\ \pi=92.16$
Open 2B	Bertrand	invert demand, $MR=MC$	$p=8,\ q=\tfrac{32}3,\ \pi=\tfrac{256}3$
Open 2C	Mixed Q/P	cross best-responses	$\pi_1\approx92.0,\ \pi_2\approx85.2$
Open 2D	Mode game	dominance	NE $=$ (Quantity, Quantity) = Cournot

Exam reflexes

First-degree TPT → $p = MC$ , $T = CS_i$ . Uniform TPT for two types → fee pinned by the smaller consumer; lean on the per-unit margin.

"Value of information / identifying types" → $\pi^{\text{discriminate}} - \pi^{\text{uniform}}$ , not either profit on its own.

Substitutes competing → lower prices, higher welfare. Complements → double marginalisation, lower welfare.

Cournot vs Bertrand (differentiated) → Bertrand price & profit are lower; given the choice of mode, Quantity dominates → firms land at Cournot.

Battle of the Sexes → 2 pure + 1 mixed = 3 equilibria.

PP_01-Sample Exam 1 — companion practice paper (same toolkit: bundling, PD, two-part tariffs, Bertrand, game theory)
Topic 1 - Asymmetric Information — insurance & moral hazard (Q2–Q3)
Topic 2 - Equilibrium in Different Market Structures — bundling, price discrimination, two-part tariffs, Cournot/Bertrand (Q1, Q4, Q6, Open Q1–Q2)
Topic 3 - Game Theory — Battle of the Sexes, dominant strategies, mixed NE (Q5, Open Q2D)
Topic 4 - Price Competition with Complementary Goods — substitutes vs complements, best-response functions (Q4, Open Q2)
Exercise 5 - Solutions — price discrimination & two-part tariffs (Open Q1)
Exercise 8 - Solutions — Cournot & Stackelberg quantity competition (Open Q2)
Microeconomics — subject hub

Firm 1 / Firm 2	Quantity	Price
Quantity
Price

Sample Exam 2 — Worked Solutions

Sample Exam 2 — Worked Solutions

What this paper tests

One-page recap

Related Notes