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Sample Exam 1 (practice) · Ido Eisdorfer · worked-solution

Sample Exam 1 — Worked Solutions

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Sample Exam 1 — Worked Solutions

Part of: Microeconomics Sample Exam 1 (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, Actuarially Fair Premium, Price Discrimination, Two-Part Tariff, Bertrand Competition, Nash Equilibrium, Mixed Strategy, Perfect Competition

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This practice paper came without an answer key, so every answer below is solved from scratch and the arithmetic checked programmatically. Where the wording leaves room for interpretation (Q2-b "free coffees", Q2-d cost across days) the assumption is flagged in a callout. Treat the letter answers as well-reasoned, not gospel.

What this paper tests

One paper, the whole course

The six MC questions and two open questions sweep all four topics. The single most useful framing for revision:

  1. Q1, Q4, Open Q2 — monopoly pricing tools: bundling vs separate sales, price discrimination, the two-part tariff. Always start from MR = MC in each segment.
  2. Q2, Q3 — insurance under moral hazard: an uninsured consumer pays P=MCP = MC; a fully insured one pays P=0P = 0 and over-consumes. Every number falls out of that one idea.
  3. Q5, Open Q1c–d — game theory: dominant strategies, Nash equilibrium (pure and mixed), and reading a 2×2 payoff matrix.
  4. Q6, Open Q1 — Bertrand price competition, homogeneous (Q6) and differentiated (Open Q1).
  1. Q1 — Bundling vs. separate sales

    A profit-maximizing firm sells computers and screens. The marginal cost of a computer is $1,000 and the marginal cost of a screen is $300. The willingness to pay for computers is:

    Customer Computer
    1 900
    2 1,100
    3 1,300
    4 1,500

    If the firm sells computers separately, what price maximizes profit from computers?
  2. Q2 — Expected medical expenditure when uninsured

    The probabilities of the health states are:

    Pr(Mild-1)=12,Pr(Moderate-2)=13,Pr(Severe-3)=16\begin{gathered} Pr(\text{Mild-1}) = \frac{1}{2},\quad Pr(\text{Moderate-2}) = \frac{1}{3}, \\ Pr(\text{Severe-3}) = \frac{1}{6} \end{gathered}

    The demand functions for medical services are: Q1=5−PQ1 = 5 - P, Q2=15−PQ2 = 15 - P, Q3=20Q3 = 20. The marginal cost of medical treatment is MC=2MC = 2. What is the individual's expected medical expenditure if he is uninsured?
  3. Q3 — Will a risk-averse person buy full insurance?

    Continuing with the data from the previous question, suppose the individual is offered full insurance at the actuarially fair premium. Which of the following statements is correct?

    (The original paper's wording is truncated here — "…, the actuarially fair premium for full insurance." — this is the intended reading.)
  4. Q4 — Price discrimination: public vs. government

    The public demand curve for the monopolist's product is: P=100−XP = 100 - X. The marginal cost of producing the product is: MC=XMC = X. The government is willing to buy up to 10 units from the monopolist at a price of 50 per unit. Assume the monopolist can price discriminate between the public and the government.

    How much will the monopolist sell?
  5. Q5 — "Odd or even" game

    Two players, A and B, play an "odd or even" game. Each player chooses a number. If the sum of the numbers is even, Player A wins. If the sum is odd, Player B wins. Which statement is correct?
  6. Q6 — Bertrand with asymmetric costs

    In market XX, two producers, A and B, compete in prices à la Bertrand. Producer A has a higher marginal cost than Producer B. Which statement is correct?
  7. Open 1a — Equilibrium before the standard

    Two firms, 1 and 2, produce differentiated products and compete by simultaneously setting prices p1p_{1} and p2p_{2}. Both firms have the same constant marginal cost: c=6c = 6 and no fixed costs.

    Demand is given by:

    q1=29−p1+14p2,q2=29−p2+14p1.q_{1} = 29 - p_{1} + \tfrac{1}{4}p_{2}, \qquad q_{2} = 29 - p_{2} + \tfrac{1}{4}p_{1}.

    a. Find the equilibrium prices, quantities, and profits of each firm.
  8. Open 1b — Equilibrium with the standard

    Now, the firms may jointly adopt a common product standard that makes products easier to compare and substitute. Demand becomes:

    q1=27−2p1+p2,q2=27−2p2+p1.q_{1} = 27 - 2p_{1} + p_{2}, \qquad q_{2} = 27 - 2p_{2} + p_{1}.

    Adopting the standard requires each firm to incur a fixed cost: K=30K = 30. The standard is adopted only if both firms agree.

    b. Assume both firms adopt the standard. Find equilibrium prices, quantities, and profits after subtracting the adoption cost. Compare prices, quantities, and profits with part (a).
  9. Open 1c — Will both firms adopt?

    c. Suppose firms simultaneously decide whether to adopt the standard. Is there an equilibrium in which both firms adopt?
  10. Open 1d — For which K is adoption guaranteed?

    d. For which values of KK is adoption by both firms guaranteed in equilibrium? (Hint: KK may be also a subsidy, i.e., negative values.)
  11. Open 2a — Industry supply & competitive equilibrium

    Four coffee carts operate in a perfectly competitive market.

    Each cart has cost: TC(qi)=qi2+64TC(q_{i}) = q_{i}^{2} + 64. Market demand: Q=440−20pQ = 440 - 20p.

    a. Find the industry supply function and the short-run equilibrium.
  12. Open 2b — Merger to monopoly + coffee card

    b. Suppose the four carts merge into a monopoly with: TC=0.25Q2TC = 0.25Q^{2}. The monopoly sells a coffee card at price TT that includes several free coffees. Find TT.
  13. Open 2c — One uniform price, two groups

    c. MBA demand: QM=220−10pQ_{M} = 220 - 10p, Other students: QR=220−20pQ_{R} = 220 - 20p. The monopoly cannot price discriminate. Find the monopoly price.
  14. Open 2d — Price discrimination across days

    d. Now MBA students attend only on Fridays, and all other students attend only during weekdays. The monopoly can price discriminate. Find the prices.

One-page recap

Q Topic Tool Answer
MC1 Bundling Uniform price over WTP ladder C — $1,300 (profit 600)
MC2 Insurance Uninsured ⟹ P=MC=2P=MC=2 A — 18.33
MC3 Moral hazard Fair premium 21.67 > 18.33 (loss 1.67) C — ambiguous
MC4 Price discrimination Fill govt cap, MRpub=MC=QMR_{\text{pub}}=MC=Q C — 10@50 (govt), 30@70 (public)
MC5 Game theory Matching pennies C — no dominant strat., unique mixed NE
MC6 Bertrand (asym.) Limit price at MCAMC_A or pBmp_B^m E — B and C both correct
Open 1a Diff. Bertrand MR=MCMR=MC, symmetry p=20, q=14, π=196p=20,\ q=14,\ \pi=196
Open 1b Diff. Bertrand tougher demand, −K-K p=13, q=14, πnet=68p=13,\ q=14,\ \pi^{\text{net}}=68
Open 1c Adoption game "Don't" dominant No adoption equilibrium
Open 1d Adoption game 98−K≥19698-K \ge 196 K≤−98K \le -98 (subsidy ≥ 98)
Open 2a Perfect comp. P=MCP=MC, sum supplies Qs=2p, p=20, Q=40Q_s=2p,\ p=20,\ Q=40
Open 2b Two-part tariff p=MCp=MC, T=CST=CS p=20, T=40p=20,\ T=40
Open 2c Uniform monopoly MBAs only, MR=MCMR=MC p=132/7≈18.86p=132/7\approx 18.86
Open 2d 3rd-degree PD MRi=MCiMR_i=MC_i per day pM≈18.86, pR≈10.08p_M\approx 18.86,\ p_R\approx 10.08
Exam reflexes
  • "Sold separately / single price" → walk the WTP ladder; profit =n(p−MC)= n(p-MC).
  • "Uninsured" → P=MCP=MC. "Fully insured" → P=0P=0, over-consumption, fair premium computed on the insured quantities.
  • Price discrimination / government buyer → treat each channel's MRMR separately; with rising MCMC, MCMC depends on total output.
  • "Two-part tariff / membership card" → p=MCp=MC, fixed fee =CS=CS; never literally price the good at zero when MCMC rises.
  • Matching-pennies wording → no pure NE, unique mixed NE; "no Nash equilibrium" is the trap.
  • Asymmetric Bertrand → efficient firm limit-prices at the rival's MCMC (or its own monopoly price, whichever is lower).