Monetary Business cycles –
Lesson 3
Neo-Keynesian models – Imperfect
competition and nominal rigidities
Introduction to Neo-keynesian models
Theoretical attacks on keynesian models:
Absence of rational expectations and more generally, no optimal
individual behavior
Phillips curve should be « expectation-augmented »: Phelps and
Friedman (1968)
Consumption should be a function not only of current revenue (IS),
but also of expected future revenues (permanent revenue
hypothesis)
More generally, no optimal consumption/savings, leisure/labor choices…
Price rigidities: why wouldn’t firms adjust prices optimally?
Absent micro-foundations, this model cannot be a
basis for welfare and policy analysis
Introduction to Neo-keynesian models
Neo-Keynesian models constitute an answer to these
attacks:
Introduce rational expectation and more generally optimal
individual behavior
Price setting Neo-keynesian expectation-augmented Phillips curve
Optimal consumption/savings, leisure/labor choices…
Micro-foundations for price rigidities
Menu costs: small costs to adjusting prices
Imperfect competition: small gains from adjusting prices
Explains better economic fluctuations than neoclassical
model
Workhorse model for policy analysis
Introduction to Neo-keynesian models
Outline for Neo-Keynasian models:
Lesson 3: Imperfect competition and nominal
rigidities
Lesson 4: Price staggering
Lesson 5: Phillips curve
Lesson 6: A Neo-Keynesian model
Imbed imperfect competition and price staggering in an
otherwise standard dynamic model, as seen in lesson 1
(MIU model)
Effect of a monetary shock: empirical evaluation
Lesson 7: Implications (including policy)
Summary
Fixprice equilibria (PS3)
One particular equilibrium: Keynesian
unemployment
Excess supply: demand-driven supply
Effect of monetary policy
But:
No foundation for price rigidities
Why exclude the other regimes?
Summary
Solution: imperfect competition
Foundation for nominal rigidities
Menu costs: small costs to adjusting prices
Imperfect competition: small gains from adjusting prices
Demand-driven supply
Introduction - Outline
Imperfect competition and price rigidities
Static model with imperfect competition (BlanchardKiyotaki)
(1)
Price setting by households
(2)
Effect of a monetary shock without nominal rigidities?
(3)
Foundations of nominal rigidities
Partial equilibrium: do firms have incentives to adjust prices?
(4)
Effect of a monetary shock with nominal rigidities?
(5)
First pass at policy analysis
Introduction
Sources:
Olivier Blanchard, course materials for 14.452 Macroeconomic
Theory II, Spring 2007. MIT OpenCourseWare
(http://ocw.mit.edu/), Massachusetts Institute of Technology
Blanchard-Fisher, Chapter 8
Wickens, chapter 9
Romer, chapter 5
Blanchard-Kiyotaki model
Continuum of households-firms on [0,1], each
producing one differentiated good
Each household produces its good using its own labor
Utility of household i depends on the consumption
basket Ci, real money holdings Mi /P and labor Ni:
More precisely:
What is β?
Blanchard-Kiyotaki model
Ci depends on the consumption of all goods:
What is σ?
Nominal budget constraint:
Production function:
Blanchard-Kiyotaki model
4 steps:
(1)
(2)
(3)
(4)
Given resources devoted to consumption,
derivation of the demand for individual
goods
Given total resources, derivation of
resources devoted to consumption and
money
Derivation of the demand adressed to each
household, and resulting pricing and
production decisions
General equilibrium, with and without
nominal rigidities
Consumer
problem
(PS3)
Producer
problem
Step 1 - The demand for individual goods
Xi: nominal spendings devoted to consumption
How does the consumer allocate these spendings between
the different goods?
Household i ‘s objective:
Subject to:
This yields:
With
and
the general price index
Consumption of good j is then a function of the relative price
Pj /P and aggregate demand Ci:
Step 2 - The choice of money and
consumption
How does the household allocate his total resources between
consumption and money?
Household i’s objective:
Subject to:
Relationship between money holdings Mi and consumption Ci:
This yields:
Replacing in the utility, we get the indirect utility:
and
Step 3 - Pricing and production decisions
We now turn to the household’s pricing and
production decisions
Introduce imperfect competition
Step 3 - Pricing and production decisions
Households produce differentiated goods, they are pricemakers, so they take into account the effect of their price
on demand Yi
What is the demand for good i Yi?
Demand for good i by household j:
Aggregate demand for good i:
with
In equilibrium, demand for money=supply:
, so:
Step 3 - Pricing and production decisions
Household i maximizes
Subject to
Replacing Pi in the objective and solving the
maximization problem gives:
Step 3 - Pricing and production decisions
Indeed, by denoting
we can write profits as:
with
,
and
yields:
Marginal revenue
This yields the pricing equation
Marginal cost
Step 3 - Pricing and production decisions
Graph
Step 3 - Pricing and production decisions
Solving for Yi gives:
with
Discussion
Compare prices and quantities with perfect and
imperfect competition.
What about welfare?
Discussion
Compare the effect of an increase in demand
with perfect and imperfect competition with
fixed prices
Step 4: Effect of money with flexible prices
We first assume that prices are flexible:
households set their price optimally
Step 4: Effect of money with flexible prices
Partial equilibrium: an increase in
an increase in Pi /P and in Yi
leads to
Step 4: Effect of money with flexible prices
General equilibrium: all the firms reset their
price so P increases
Step 4: Effect of money with flexible prices
General equilibrium:
All firms have the same behavior Pi=P relative price Pi/P =1
So, output for each household must satisfy:
Is money neutral?
Step 4: Effect of money with flexible prices
Price level determination:
The price level must be such that the real money
stock generates the right level of demand:
Summary
Money is still neutral
Only differences with perfect competition:
Production and employment are lower than their
optimal level (second-best vs. first-best)
Presence of a mark-up on prices (P>MC)
Summary
However, these differences have non-negligible
consequences
Production and employment are lower than their
optimal level
Room for policy intervention
Presence of a mark-up on prices (P>MC)
Room for deviations from profit-maximizing prices
Room for price rigidities
Demand-driven supply
Foundations for price rigidities
Small costs of adjusting prices (« menu
costs », Akerlof and Mankiw)
Then why nominal rigidities?
Gains from adjusting prices are small too!
Foundations for price rigidities
2 arguments to justify that firms set their
prices at discrete intervals:
Small changes in prices have second-order effects
on profits
Small incentives to change prices
Even if the costs to change prices are small, firms do not
adjust prices (« menu costs », Akerlof and Mankiw)
However, first-order effect on production and welfare
« Real rigidities »: firms have even smaller incentives
to change prices if the marginal cost is flat (β close to 1)
Foundations for price rigidities – Secondorder gains
Formal argument for the second-order
gains from adjusting prices
Price currently set at Pi ≠ Pi*, with Pi* is the
optimal price for producer i
The gain from adjusting is П(Pi*)- П(Pi)
Taylor expansion of producer i’s profits П(Pi)
around Pi*:
П(Pi)- П(Pi*)= П’(Pi*) (Pi-Pi*)+ П’’(Pi*) (Pi-Pi*)2/2
= П’’(Pi*) (Pi-Pi*)2/2
Foundations for price rigidities – Secondorder gains
Start from an equilibrium with money supply
,
individual prices Pi and aggregate price level P
Money supply is increased to
But menu costs + second order gain from increasing
the price to Pi*
The individual prices stay at Pi
The aggregate price stays at P
New real money balances
*/P >
*
/P
Foundations for price rigidities – Secondorder gains
Effect on output and welfare?
Foundations for price rigidities – Secondorder gains
Effect on profits is second order while effect
on welfare and output is first order
For given menu costs, there are changes in
money supply that are small enough to prevent
price adjustment but still large enough to have
sizeable macroeconomic effects
Foundations for price rigidities – Real
rigidities
« Real rigidities »: Firms may have even smaller
incentives to change prices if marginal cost is
flat (β close to 1)
Indeed, we can show:
П(Pi)- П(Pi*)= П’’(Pi*) (Pi-Pi*)2/2
= П’’(Pi*) B(β-1)2(X-X*)2/2
with B a positive constant
Introducing price rigidities in the model
and Z are random
Prices are chosen before the realization of
productivity and money shocks
P and Pi are predetermined
Consumption -and thus demand- chosen
after realization of shocks
Step 4: Effect of money with sticky prices
General equilibrium:
All firms have the same behavior Pi=P relative price Pi/P =1
Output Y is given by:
(as long as MC<P)
And employment N by:
Is money neutral?
Implications of price rigidities
Empirical implications:
Unanticipated positive changes in money supply affect
positively consumption and output
Demand affects output: output is demand-determined
Normative implications:
Positive money shocks make output Y closer to the first-best
welfare goes up
Temptation to increase welfare through unanticipated money
growth. Is that a viable policy? Why?
Policy
2 types of distortions:
Imperfect competition
Nominal rigidities
Can monetary policy help alleviate the
consequences of these distortions?
Policy
First-best output (without any distortions):
Second-best output (with imperfect competition):
Actual output (with imperfect competition and
nominal rigidities):
Policy
In logs:
with
and
Policy
Can the Central Bank achieve the second-best output?
0
Increase in money supply in response to productivity
shocks in order to increase demand in line with supply
Policy
Can the Central Bank achieve the first-best output?
Contradiction: E(m)-E(m)>0
This policy cannot be implemented systematically
Indeed, agents anticipate it and set higher prices (time
inconsistency)
Summary – Model with imperfect
competition
Without nominal rigidities, money is still neutral
However, only small incentives to adjust prices
Justification for nominal rigidities
With nominal rigidities:
Money affects aggregate demand
Since firms still make profits, they can increase production: aggregate
demand affects aggregate supply
Money affects output and therefore welfare
Monetary policy can achieve the second-best output but not the firstbest
Next:
More realistic price setting
More dynamics