Chapter 8: Business Cycles

Evidence suggest that Nominal Rigidity and the New Keynesian Model

Nominal rigidity: prices are slow to adjust to achieve market clearing. In contrast to models
featuring 'market clearing' where prices are flexible and adjust so that demand and supply are
equalized.

● This can lead to inefficient outcomes(supply of output is always below the efficient
level when all the markets are perfectly competitive) and excessive GDP fluctuations
when shocks occur, potentially creating a role for central banks or governments to
improve outcomes.

New Keynesian model builds on the dynamic macroeconomic model but incorporates
nominal rigidity.

● In this framework, the goods market features sticky prices and imperfect competition.
We begin with a simplified version where all prices are fixed and then it adds partial
price adjustment to analyze inflation later on(Ch 9).
● While nominal wages are considered fully flexible, the model can also incorporate
efficiency wages.

This is one of the frameworks for understanding how the economy fluctuates during business
cycles.

Demand Shocks

● According to the New Keynesian model, a negative demand shock leads to declines in
GDP, consumption, and investment. Prices and inflation remain unchanged due to the
fixed prices. Employment declines, and real wages fall. If wages are rigid due to
efficiency wages, unemployment rises.
● The model predicts that consumption and investment are procyclical (moving in the
same direction as real GDP), employment is procyclical, and average labor productivity
is countercyclical.

Monetary Policy Shocks

● Business cycles can be triggered by shifts in monetary policy stances.

● For example, if a central bank increases interest rates, consumption and investment fall,
leading to a decline in real GDP.(Shifts of the MM line)
● Employment and real wages decrease, while unemployment rises if wages are rigid.

New Keynesian model is broadly consistent with the business-cycle stylized facts when the
business cycle is caused by demand shocks, including shifts in monetary policy.
The Natural Rate of Interest

● It is useful to analyze the hypothetical case of fully flexible prices even in the short
run to understand the different predictions the model makes for the short run and the
long run and to provide guidance on how monetary policy should be conducted.
● It assumes the goods market is imperfectly competitive to allow for sticky prices and
considers how imperfectly competitive firms would set prices if they were always free to
adjust them.
● In the long run, the New Keynesian model predicts that the real interest rate and output
coincide with their 'natural' levels and all variables will tend to their respective natural
levels in the long run absent any further changes or shocks to the economy.

Real Business Cycle Theory

● Real business cycle (RBC) theory argues that business cycles are efficient
responses to variations in the economy’s ability to produce, driven by supply
shocks.
● In this view, policy intervention is seen as counterproductive.
● RBC approach analyzes how supply shocks affect equilibrium in the goods, labor, and
money markets.
● RBC theory identifies exogenous shocks to total factor productivity (TFP) as the
primary source of business cycles. While technological progress drives permanent
increases in TFP in economic growth, RBC theory considers supply shocks as increases
or decreases in TFP that are eventually reversed(temporary change in z).

Coordination Failure Model

● Coordination failure model states that business cycles are driven by self-fulfilling
changes in optimism or pessimism, even without fundamental shocks.
● This model suggests that the economy has multiple equilibria, and shifts between
these states of optimism and pessimism can cause business cycles, even when the
economy’s fundamentals remain unchanged.
● The model depends on strategic complementarity in firms’ employment decisions,
arising from a positive ‘spillover’ effect from aggregate employment to individual firm
productivity.
Sample Question 1

Event: Dismal News => fall in expected future income => cutting consumption and increase
labour supply
Part a)
● Reduced consumption demand shifts output demand to the left.
● With sticky prices, output is not determined by the intersection of output demand and
output supply, but by output demand together with the real interest rate determined by
the central bank’s monetary policy.
● With no change in interest rates, output falls.
● Firms with sticky prices will accommodate demand for output.
● Lower output demand implies that fewer workers are needed to produce (movement
along the production function), so the (vertical) labour demand curve shifts to the left.
Employment falls.
● Output falls by as much as the horizontal shift in output demand, which is the change in
consumption. The fall in output is thus identical to the fall in consumption, so total
(national) saving S = Y − C − G is unchanged.

● The (hypothetical) flexible-price output supply curve shifts to the right because of the
rightward shift of labour supply.
● Together with the leftward shift of output demand, the market-clearing interest rate
(“natural rate of interest”) is decreased.

● From the diagram in part (a), it can be seen that the real wage has fallen and the
marginal product of labour has risen.
● Since the marginal rate of substitution between leisure and consumption moves in line
with the real wage, the gap between MPN and MRSl,C has increased.
● Thus, it makes sense to try to raise employment and output since the valuation of
households’ leisure time falls below their valuation of the goods that could be produced
with that time.
● Cutting the nominal interest rate to the new natural interest rate would raise output,
moving down the output demand curve.

● Since we know Y = C + I + G, saving S = Y − C − G must be equal to investment I.

 ● The lower interest rate increases investment and thus saving as well (with sticky prices,
the extra demand generates the extra income that finances the extra saving).

● If expected inflation is zero, the nominal interest rate is equal to the real interest rate.
● Since money can be stored and does not depreciate, the nominal interest rate cannot fall
below zero assuming no shortage cost of money.
● Hence it is not possible to achieve the required negative real interest rate.

i.
● An increase in government spending shifts output demand to the right.
● Since the increase is temporary, the rise in the tax burden spread over a long period of
time is small, so the leftward shift owing to lower consumption does not offset the
direct effect.
● This means that a government spending increase of an appropriate size can deliver the
same level of output as in part (c).
● Note that this is a simple event where the fall in output demand is caused by a loss in
confidence in future expected income, so the temporary fiscal stimulus can help.
ii
● A (credible) reduction in future government spending generates a positive wealth effect
on households since they face a lower lifetime tax burden.
● If the reduction is expected to be sufficiently large and long lasting, and the public
believe that the government will actually implement what the policymaker promise today,
the wealth effect on consumption demand can shift the output demand curve far enough
to the right to achieve the target level of output.

This is the case of a permanent reduction in government spending.

● The direct effect is to shift output demand to the left by an amount equal to the cut in
spending.
● A permanent change in spending leads to positive wealth effects on consumption and
leisure demand.
● But the rise in consumption will be smaller than the cut in government spending because
the rise in leisure demand reduces labour supply (which will have an impact on income
in the long run when prices are flexible).
● Consequently, the output demand shifts to the left overall, which induces a fall in output
in the short run.
Sample Question 2

Part a)
Productivity spill-over effect
● Profit-maximizing labour demand is where the real wage equals the marginal product
of labour. If the marginal product of labour is increasing in aggregate employment
then labour demand is upward sloping, not downward sloping as usual.
● The output supply curve is derived by varying the real interest rate and tracing out the
effects of variation in desired labour supply on equilibrium employment, and thus firms’
supply of output. A higher real interest rate shifts labour supply to the right.
● If labour demand is steeper than labour supply (if the spillover effect is sufficiently
strong), this means equilibrium employment falls as the real interest rate rises. This
implies the output supply curve can be downward sloping, not upward sloping as
usual.

● If both output demand (unchanged) and output supply curves are downward sloping, it is
possible that they have more than one intersection point.
● Any intersection point is an equilibrium of the economy, so multiple equilibria are
possible.
● There is no fundamental reason why the economy has to be at one equilibrium rather
than the other. Given the spillover, different equilibria are self-justifying:
○ high output and employment imply high productivity, which rationalizes firms’
choice of high employment, but
○ low output and employment imply low productivity, which equally well justifies a
choice of low employment.
● In this situation, there is strategic complementarity: firms would like to take actions
similar to those of other firms. It then matters whether firms are optimistic or
pessimistic about the employment and output plans of others.
● A widely read news story could act as a trigger to switch from optimism to pessimism
given that firms know others have seen the story and are thinking similar thoughts.
● The news story acts as a ‘sunspot’ variable. Even if it reveals no information about the
economy’s fundamentals, its predictions can create the conditions that justify those
predictions.
● Given that there are effectively increasing returns to labour at the aggregate level, a fall
in employment will lower productivity. This is consistent with the cyclical
behaviour of productivity on average.

● If one firm acts alone, there is no benefit of the spillover from other firms. In this case,
the marginal product of labour is diminishing at the level of individual firms.
● So if one firm were to expand employment, extra workers would be hired at a real
wage above their marginal product. This would mean the firm is making less profits.
● It can be collectively rational for all firms to expand employment, but individually
irrational unless others are expected to follow.
● The research commissioned by the firms may reveal information about the economy’s
fundamentals, but this is NOT necessarily what matters for optimism in the
coordination failure model.
● It is essential that the managers of a firm expect others also to be optimistic.
● The research differs from the news story because the former is private while the latter
is public information.
● The private information does not necessarily lead to a self-fulfilling prophecy
because it does not help managers to know what other managers are thinking.
Sample Question 3 (combining Chapter 4 and 8)

Assumptions
● Prices of goods and services are completely sticky goods prices.
● Wages are flexible and adjust so that demand equals supply in the labour
market.(Alternative assumption: Efficiency wages theory with real wages above the
equilibrium level)
● Representative household with consumption demand that depends negatively on the
real interest rate r according to optimality condition MRSc,c’ = 1+r.
● Firms must borrow to finance investment at interest rate rl (insufficient internal funds to
finance the marginal investment), investment is determined by MPk’ - d = rl.
● Interest rate spread x = rl - r > 0, reflecting the imperfection of the financial market.
● r is the interest rate received by the saver.

Event: A financial crisis leads lenders to expect a higher fraction of bad loans in the future,
which results in a higher interest-rate spread x.

(a)
What is the effect of higher x on the output demand curve Yd?
Assuming the stance of monetary policy remains unchanged(a horizontal MM line with a
constant nominal and real interest rate r0)
What happens to real GDP Y and employment N?

● Given rl = x + r, a higher x leads to a higher interest rate rl on a firm's borrowing for each
and every interest rate r received by the saver. => reduction in investment demand Id,
shifting the output demand curve Yd to the left.
● Note that there is no change in r and no direct impact on consumption demand.
● With no change in the stance of monetary policy, the real interest rate remains at r0 on
the same horizontal MM line.
● Y falls from Y1 to Y2, which reduces firms’ need for workers given they cannot sell as
much output with prices remaining fixed, so employment N will also fall.
Part b)
● From part a, the model predicts a negative impact on GDP.
● Central Bank objective is to stabilize the output at the natural level Y*, which is
determined by the intersection of the output demand curve Yd and a hypothetical
output supply curve Ys.
● Natural level of GDP declines from Y1* to Y2*.
● Actual real GDP Y2 with a constant real interest rate declines by more
● Opening up a negative output gap(Y2 - Y2*<0).
● Central bank needs to lower the nominal and real interest rate from r1* to r2*, shifting
down the MM line to close the output gap.

Overall effects with the rise in x and the monetary policy response.
● Output Y falls because the natural level of output declines.
● Consumption increases because a lower r.
● Investment falls overall because the real GDP is lower.
○ This implies rl remains higher overall even when the central bank cutting the
interest rate r.
Part c) Yes.
● At the natural level of output, MRPN = MRSl,c, and MRPN < MPN due to the existence
of market power.(MPN > MRSl,c at Y*).
● For output and employment further below Y*, MPN rises because of diminishing returns
to labour, and MRSl,c falls because people have more leisure when employment
declines. The gap between MPN and MRSl,c is widening as output decreases.
● MPN represents the economy's ability to produce output, while the MRSl,C reflects the value
people place on their leisure time in terms of consumption.
○ This means the economy's capacity to produce is worth more than what individuals
value their leisure time.
● It is optimal to increase employment and output.
● Monetary policy response in part (b) moves the economy closer to a point where
MPN=MRS, which is in the interests of the representative household.

● Efficient resource allocation conditions

○ MPk' - d = r for investment
○ MRSc’,c = 1+r for consumption.
● With the interest rate spread, the investment demand equation MPk’ - d = rl and x = rl - r
imply
○ MPk’ - d = r + x.
● Consumption demand equation MRSc,c’ = 1+r implies r = MRSc’c -1, and therefore:
○ MPk’ - d = (MRSc,c’ -1) + x.
● A rise in the spread x increases the wedge between the two sides of the efficiency
condition.
● Monetary policy response alleviates the inefficiently low level of production and
employment, it does not correct the misallocation of resources between
consumption and investment.
○ Investment demand would be lower than the efficient level due to the spread
 ○ Consumption demand is higher due to the monetary policy response lowering the
interest rate r.
● Lower investment I raises the left-hand side of the efficiency condition, while higher C
lowers the right-hand side.
Sample Question 4

Event: Temporary reduction in total factor productivity z.(assume wealth effect is small)

Part a) RBC => implications for employment, real wages, and the real interest rate.(the dynamic
general equilibrium model in ch3)

Output Supply
● Lower TFP z =(reduce)> MPN => Nd curve shifts to the left.
● Lower TFP z together with the fall in labour demand(Nd) leads to a leftwards shift of
the output supply curve Ys.
Output demand
● Negative wealth effect on consumption demand Cd
● Negative shock will be short-lived, so the reduction in consumption demand is less than
the direct impact of the shock on people's incomes.
● Another way to cope with the shock and mitigate the effect on consumption is to
increase labour supply Ns, which offsets some of the leftward shift of Ys. However,
these wealth effects are relatively small.
● Effects on investment demand Id is small because productivity is expected to
recover.
● Yd shifts to the left, however, the shifts are small relative to the effects of the shock on
the supply curve, so the real interest rate rises to clear the goods market.

● In the labour market, Nd shifts left and Ns shifts to the right, first from N1*(r1) to N2*(r1)
because households are worse off and supply more labour to compensate, and second
from N2*(r1) to N2*(r2) as the rise of the real interest rate increases the incentive to build
up savings by working more.
● As Nd shifts to the left but Nd shifts to the right, the real wage w necessarily declines,
but the overall impact on employment N is ambiguous.
● Note that this is not in contradiction to the decline in real GDP Y because lower
productivity means that more work might be needed even though output declines.
The diagram illustrates the case where the effect on Nd is dominant and employment
falls.

● Fiscal policy response: Temporary increase in public expenditure G.

● Ricardian equivalence holds
Goods Market
● Higher G shifts the output demand curve to the right.
● It also increases the tax burden of households, which has two effects.
● First, it causes a reduction in consumption demand due to a negative wealth effect, but
this is smaller in magnitude than the change in G because the increase in G is only
temporary. So, the output demand curve shifts to the right overall.
● Second, the tax burden also increases labour supply, shifting the output supply curve to
the right.
● Real GDP Y must increase.
● The effect on Ys through labour supply should be smaller than the shift of Yd, so the real
interest rate rises.
● Higher r reduces consumption demand, so along with the negative wealth effect,
consumption must fall.
Labour Market
● Ns shifts to the right because of the wealth effect.
● No shifts of the labour demand from higher G itself.
● Hence, employment N rises.
Whether the households are better off or worse off?
● Consumption falls because of higher tax burden and higher interest rate.
● Supplying more labour which reduces leisure.
● Households are worse off if they value both consumption and leisure.
● It does not make sense for the government to choose higher G because of the shock
that caused the recession.
Part c)
Event: Permanent productivity shock

● It has larger effects on consumption and investment demand.

● It is possible that the real interest rate will decline.
● However, the shift of the labour demand curve is the same because this depends only
on the current level of productivity z.
● The larger wealth effect on Ns makes it more likely that employment rises overall rather
than declines, and increases the size of the fall in the real wage.
● If permanent productivity shocks were driving business cycles in the RBC model,
employment would be less procyclical or even countercyclical, and real wages would be
more procyclical.
● Since the empirical evidence on business-cycle fluctuations shows that employment is
strongly procyclical while real wages are only weakly procyclical, the RBC model fits
the empirical evidence best for temporary supply shocks.
Simple Question 5

Part a)
● Event: Temporary increase in G
● Prices are flexible and markets are perfectly competitive.
● Crowding out of private consumption and investment
● GDP will rise by less than public spending.
Event: Temporary increase in G
● Higher G shifts the output demand curve Yd to the right.
● It also increases the tax burden of households, which has two effects.
○ First, it causes a reduction in consumption demand due to a negative wealth
effect, but this is smaller in magnitude than the change in G because the
increase in G is only temporary. So, the output demand curve shifts to the right
overall.
○ Second, the tax burden also increases labour supply, shifting the output supply
curve to the right.
● Real GDP Y must increase.(both Ys and Yd shifts to the right)
● The effect on Ys through labour supply should be smaller than the shift of Yd, so the real
interest rate rises.
● Higher r reduces consumption demand, so along with the negative wealth effect,
consumption must fall.
● With the investment demand equation, MPk’ - d = r, higher r also reduces the investment
demand.
● Since both consumption and investment unambiguously fall, there is crowding out and
GDP rises by less than the increase in public spending.
Labour Market
● Ns shifts to the right because of the wealth effect.
● No shifts of the labour demand from higher G itself.
● Hence, employment N rises.
Part b)

Event: increase in future total factor productivity z’

● Increase in z’ would lead to a rise in marginal product of capital in the future period MPk’.
● MPk’ - d = r=> the demand for investment increases=> Yd shifts to the right.
● The increase in future productivity also raises future income creating a positive wealth
effect. Positive wealth effect => raises consumption and leisure(reduces Ns).
○ Yd shifts to the right and Ys shifts to the left.
● The overall rightward shift of output demand is now greater than the change in public
spending.
● However, GDP can increase by more or less than the previous level because output
supply is upward sloping and shifting to the left.
● Crowding out can still occur through higher interest rates.
Part c)
i. CB keeps the nominal and real interest rate constant.

● The MM line is horizontal and there would be no change in real interest rate in this case.
Since output demand shifts to the right by more than G, the overall change in Y is now
larger than G. There is no crowding out effect on consumption and investment.
ii) CB set the nominal interest rate equal to the natural rate of interest
● The MM line shifts upward.
● The outcome would be exactly the same as in part (b)