ECON6002 · Macroeconomic Analysis
Nominal Rigidities & the New Keynesian Model
In ECON6002 Macroeconomic Analysis at the University of Sydney, Topic 7 is the hinge of the whole unit: it breaks the money-neutrality of the Real Business Cycle model by adding two frictions — monopolistic competition (a real markup) and Calvo price stickiness (a nominal rigidity). The canonical New Keynesian (NK) model then has three blocks: an optimising household whose Euler equation log-linearises into the dynamic IS curve, monopolistically competitive firms that set prices à la Calvo (giving the NKPC in the next topic), and a central bank following a Taylor rule. Master the objects introduced here — the CES markup ε/(ε−1), natural (flexible-price) output, Calvo duration 1/(1−θ), the output gap, and the dynamic IS curve — because every mark on the 55% closed-book final (Topics 7–10) is built on them.
What this chapter covers
- 011. Why RBC is not enough — money non-neutrality, demand shocks, and sticky-price evidence (Bils–Klenow, ~7–12 month price durations)
- 022. The three building blocks — household ⊕ monopolistic firms ⊕ central bank, keeping RBC's rational expectations
- 033. The household block — objective, labour-supply FOC, and the NK Euler equation with nominal variables
- 044. Monopolistic competition and CES (Dixit–Stiglitz) demand — the downward-sloping demand curve each firm faces
- 055. The constant markup μ = ε/(ε−1) over marginal cost, and its competitive limit as ε → ∞
- 066. Natural (flexible-price) output — the policy-independent benchmark the output gap is measured against
- 077. Calvo pricing — random constant-probability resetting and expected price duration 1/(1−θ)
- 088. The output gap and the dynamic IS curve — log-linearising the Euler equation, closed by the Taylor rule
Optimal markup pricing and natural output
- +2(a) Write profit as [P(i) − V]·P(i)^(−ε)·P^ε·C. Differentiate with respect to P(i) and set to zero: (1−ε)·P(i)^(−ε) + ε·V·P(i)^(−ε−1) = 0.
- +2Multiply through by P(i)^(ε+1)/(P^ε·C) to collect terms: (1−ε)·P(i) + ε·V = 0, so P(i) = [ε/(ε−1)]·V.
- +2Compute the markup μ = ε/(ε−1) = 6/5 = 1.20 — a 20% markup over marginal cost. All firms are identical, so P_t = 1.20·V_t and real marginal cost = V_t/P_t = 1/μ = 5/6 ≈ 0.833.
- +2(b) Because real marginal cost is fixed at 1/μ, combining it with the household labour-supply condition and the production function Y_t = A_t·N_t pins a unique natural output ŷ_t^n — the flexible-price level, independent of monetary policy.
- +2The productivity pass-through is ŷ_t^n = [(1+φ)/(σ+φ)]·â_t = [(1+1)/(2+1)]·â_t = (2/3)·â_t.
- +2Apply the shock: â_t = +3% gives ŷ_t^n = (2/3)(3%) = +2%. Natural output rises by 2%, less than one-for-one because a wealthier household takes part of the productivity gain as extra leisure (σ > 1).
Key terms
- Nominal rigidity
- Prices (or wages) that do not adjust instantly to shocks. In the New Keynesian model the rigidity is sticky prices, and it is what gives monetary policy a real, non-neutral effect on output.
- Monopolistic competition
- A market of many firms each producing a differentiated variety, so every firm faces a downward-sloping demand curve and has the pricing power to set a markup over marginal cost — the real friction that makes a chosen (and holdable) price meaningful.
- CES / Dixit–Stiglitz aggregator
- The consumption aggregator that combines differentiated varieties with a constant elasticity of substitution ε > 1, delivering the demand curve C_t(i) = (P_t(i)/P_t)^(−ε)·C_t that each firm faces.
- Markup μ = ε/(ε−1)
- The constant factor by which a flexible-price monopolistic competitor's price exceeds marginal cost. It rises as market power grows (smaller ε) and tends to 1 in the competitive limit ε → ∞; its reciprocal 1/μ is real marginal cost.
- Calvo pricing
- A tractable sticky-price mechanism in which each firm may reset its price only with a constant probability 1−θ per period (θ = probability the price stays fixed), giving an expected price duration of 1/(1−θ). Higher θ means stickier prices and larger monetary real effects.
- Natural / potential output
- The level of output the economy would produce with fully flexible prices, ŷ_t^n = [(1+φ)/(σ+φ)]·â_t. It depends on productivity, preferences and the markup but not on monetary policy, and is the benchmark the output gap is measured against.
- Output gap (ỹ_t)
- Actual minus natural output in logs, ỹ_t = ŷ_t − ŷ_t^n. It is the real-activity variable in the dynamic IS curve and the New Keynesian Phillips Curve, and a target of stabilisation policy.
- Dynamic IS curve
- The log-linearised consumption Euler equation written in gap form, ỹ_t = E_t ỹ_{t+1} − (1/σ)(r̂_t − E_t π̂_{t+1}) + ε_t. It is the NK aggregate-demand block and, because it contains nominal variables (the nominal rate and expected inflation), the point of departure from RBC.
Nominal Rigidities & the New Keynesian Model FAQ
Can AI help me with nominal rigidities and the New Keynesian model?
Yes — ask Sia to walk through any nominal-rigidities or New Keynesian model problem or concept step by step, the way University of Sydney tests it. Sia is an AI tutor that explains the derivation — the CES markup, Calvo duration, natural output, or the dynamic IS curve — building your understanding rather than handing over answers, so you can reproduce it yourself in a closed-book exam.
What is the difference between θ and 1−θ in Calvo pricing?
In ECON6002, θ is the probability a firm keeps its price fixed in a given period, so 1−θ is the fraction of firms that reset. The expected duration of a price is therefore 1/(1−θ) — for example θ = 0.8 gives 1/0.2 = 5 quarters. A higher θ means stickier prices, a flatter aggregate-supply curve and larger real effects of monetary policy. Some textbooks define the letter the other way round, so always state the convention you are using.
Why does the New Keynesian model add frictions to the RBC model?
Because RBC implies money is neutral — nominal shocks leave real variables unchanged — but the data show otherwise: identified monetary-policy shocks move output and hours, and micro price data (Bils–Klenow, Nakamura–Steinsson) show individual prices are fixed for roughly 4–11 months (incl.-sales vs regular-price measures). Adding just two frictions, monopolistic competition (real) and Calvo sticky prices (nominal), gives monetary policy a real role while keeping the rest of the RBC engine.
What is natural output and why does it matter?
Natural (or potential) output is what the economy would produce if prices were fully flexible, ŷ_t^n = [(1+φ)/(σ+φ)]·â_t. It depends on productivity, preferences and the markup but not on monetary policy, so it is a benchmark rather than a policy target. Its importance is that the output gap — actual minus natural output — is the variable that drives inflation in the New Keynesian Phillips Curve and that policy tries to stabilise.
How is Topic 7 examined in ECON6002?
Topic 7 is part of the 55% closed-book final exam, which covers Topics 7–10 and provides a standard log-linearised NK formula sheet. Because the equations are given, the marks come from deriving results (for example the markup from the CES first-order condition), naming mechanisms, and stating assumptions — not from recall. Any Topic-7 idea can also appear in the final's True/False/Uncertain short-answer question, where the explanation carries almost all the marks. Practice comes from Tutorials 7–10.
Is Calvo pricing realistic, and should I mention its limitations?
No, Calvo is chosen for tractability rather than realism, and a strong exam answer says so. Its constant-hazard assumption is empirically wrong: the frequency of price change is not constant, it rises with inflation, and real pricing is partly state-dependent (menu-cost timing). The reason it is used anyway is that its memoryless resetting aggregates cleanly into the micro-founded New Keynesian Phillips Curve. State both the failing and the payoff to earn full marks.
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Exam move
Treat Topic 7 as the vocabulary list for the entire New Keynesian half of ECON6002: if the markup ε/(ε−1), natural output, Calvo duration 1/(1−θ), the output gap and the dynamic IS curve are second nature, then Topics 8 (the NKPC) and 9 (Monetary Policy) — which carry the two big extended-response questions on the final — become mechanical. Start from the unit outline on Canvas to confirm topic weights, then work Tutorials 7–10 by hand, because they are the only official practice for the final and it is built almost verbatim on them. Since the exam is closed-book (with a provided log-linearised NK formula sheet), rehearse each derivation until you can reproduce it cold: derive the markup from the CES first-order condition rather than quoting it, and always state the θ convention before doing Calvo comparative statics. Practise the True/False/Uncertain format in full — the marks are in the mechanism plus one boundary case that qualifies the verdict. Ask Sia to generate fresh Topic-7 practice questions and to check each step of your working as you go.
