Lecture: The Covid Lockdown
Due to covid the GDP in each country in the world dropped since the outbreak, Households cut
spending by 1/3, enormous increase in personal savings rate, a mild deflation.
What does a lockdown do?
• A deep recession caused by an exogenous health shock. ⇒ A lockdown is the economic
equivalent of a medically induced coma: fall in GDP is necessary counterpart of containment.
• Huge increase in personal savings, but only mild deflation. ⇒ A lockdown is not just a fall in
demand, like in a normal recession or in a recession caused by a financial crisis (Ch. 15).
• Deflation rather than inflation. ⇒ A lockdown is not just a supply shock, like the oil crises of
the1970’s (Ch. 15).
• How to explain deflation resulting from a supply shock?⇒We need a model with multiple
sectors.
Two sectors and a lockdown:
Consider an economy that consists of two sectors:
1. Will be shut down in a lockdown because it is contact-intensive and non-essential.
2. Will not be shut down, either because it is not contact-intensive, or because it is essential
(e.g. healthcare or food supply).
Output in the economy is the sum of output in each sector: Y= Y1 + Y2
• What does a lockdown do? → a supply shock of size once shutdown, output of sector 2
cannot be delivered anymore → this part of economy will completely disappear
A negative supply shock:
Blue = before lockdown, LRAS = Y. LRAS moves
to the left because sector 1 is shut down, so the
output that’s left is the output of sector 2. As
long as people don’t have perfect foreside, SRAS
moves together with LRAS from A to B
What will happen to aggregate demand (AD)? → ANSWERED IN THIS LECTURE
This lecture:
, 1. Will the sector that is not shut down also suffer?
2. Can we control the damage to this sector by giving transfers?
3. What are the government spending and tax multipliers?
- should we have a large-scale stimulus program from the government?
4. What is the multiplier on transfers to workers employed in either sector?
- Is a lockdown the time for a basic income, or should we target transfers to workers in the
sector that is shut down?
5. Will aggregate income fall by more than a fraction φ?
- Does it matter whether we shut down only one sector of size φ, or both sectors for a
fraction φ?
6. How effective is monetary policy?
7. Can we explain deflation from a supply shock?
THE MODEL:
Aggregate income Y:
• Focus on a closed economy.
• Focus on equilibrium: income equals planned or aggregate expenditure, Y=PE.
• Planned or aggregate expenditure PE consists of
- consumption C ,
- investment I,
- government expenditure G, excluding transfers.
• T denotes aggregate taxes net of transfers.
- When T<0, people receive more transfers than they pay taxes.
• Spending is income: Y= C + I + G.
• Assume investment and government spending are exogenous.
A concave consumption function:
If disposable income Y – T
is lower than C^bar, than
people consume their full
disposable income Y – T. If
disposable income Y – T is
higher than C^bar, than
they consume C^bar +
something else (→ but
then they will not spend
their full disposable
income). C^bar is the level
at which consumers start
saving. So when their
disposable income is below
C^bar they might want to consume more, but they cannot because they are constraint by their
disposable income. But as soon as their disposable income hits C^bar, they will first spend C^bar, but
from the remainder of their disposable income and C^bar they will spend a fraction c = their MPC
when they are not liquidity constraint (= wealthy). Equivalent formulation: we have minimum of
C^bar and disposable income → so when disposable income is smaller than C^bar, we will spend
everything because we don’t have more. But as soon as C^bar is greater than disposable income,
,we will consume that + something else = MPC * disposable income minus C^bar. We have a
concave function because MPC = 1 when disposable income is low (we’ll spend everything) → but as
soon as we hit C^bar MPC falls from 1 to C → so function becomes flatter at C^bar
The Keynesian Cross with liquidity constraints:
This is how it would look like if we add I and G.
we have autonomous expenditure, which is
intersect of the graph (I + G – T). at some point
we hit that Y = C^bar + T (so disposable income is
equal to C^bar). At this point people start saving
and that’s why the graph flattens, they only
spend fraction c. so at this point the PE curve
becomes flatter and it crosses the 45 degree line
somewhere → here Y = PE
assume that autonomous
expenditure (I + G – T) is
always larger or equal than
C^bar so that disposable
income is always larger than C^bar. As a result of that people will always save something. People
always spend C^bar and on top of that they consume a fraction of the remaining disposable income
Remember two sectors:
• The economy that consists of two sectors:
- Will be shut down
- Will not be shut down
Consumption by workers in each sector:
People in sector 1 start saving
at phi*Cbar and people in
sector two start saving at (1-
phi)*C^bar
,Consumption on each sector:
For simplicity, assume that
- all consumption up to the liquidity constraint is spent in sector 2, the essential sector.
- marginal propensities to consume in each sector are fixed: c1+c2 = c<1 (together they are c and c is
<1)
Sector 1: Remainder of a
fraction c1 of disposable
income of workers in sector
1 + remainder of a fraction
of c1 of disposable income
of workers in sector 2
Sector 2: consists of the
consumption up to liquidity constraint C^bar. If workers in sector 1 are relatively poor they will spend
everything in sector 2, if they have slightly more disposable income than C^bar, than they have a
fraction left and they spend c2 times disposable income minus C^bar in sector 2 (similarly for people
working in sector 2)
Before the Lockdown:
No workers are liquidity
constraint = all people
start saving a bit
The last equation =
needed!!!!!
, THE LOCKDOWN
Tax holiday: people who
work(ed) in sector 1 do
not have to pay taxes
anymore, and we assume
that they do not receive
transfers (yet). They are
liquidity constraint
because they now have
no disposable income →
they want to borrow but
they cannot
Question 1: What will happen to income earned in sector 2, 𝒀′𝟐
→ will the sector that is not shut down also suffer from the lockdown?
YES!
Intuition:
The lockdown does not only stop consumption on sector 1, but also consumption in sector 2 by
workers (that used to be) employed in sector 1 .
Income in sector 2:
The red part denotes the fact
that people working in sector 2
contribute to the income in
sector 2
Both because people form
sector 1 even cannot buy their
necessities anymore, and they
have no disposable income
