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Department of Economics, University of Toronto
Halina Kalita von dem Hagen
ECO 208Y: MACROECONOMIC THEORY
PROBLEM SET #2 – Solutions for Students
PART I:
1. Main points:
In ALL the models: 1. there is a positive relationship between output and employment in the
short run, and there is a negative relationship between employment and real wage. 2. Once MS
increases, LM shifts down, and AD shifts then to the right.
(a) Classical Model
perfect information, rational expectations, wage and price flexibility, they all cause an
INSTANTANEOUS adjustment of prices to equate again the shifted AD with the unchanged AS
(recall: classical AS is vertical at the full-employment level of income). Results: unchanged
output (hence: unchanged employment and real wage), prices increase, LM shifts back to its
original position.
In the classical model we cannot make distinction between (i) and (ii) above as it violates the
assumption of "perfect information".
(b) Imperfect information (New Classical) model
Case (i) is identical with (a) above.
Case (ii): draw a positively-sloped EAS curve. Assume: fixed expectations (hence EAS does
not shift) OR revised expectations (hence EAS does shift up but not as much as the AD shifted
since the extent of the shock is not fully known).
Either way, get the result: output deviates from its long-run level, prices increase. Since output
increases, employment increases, and this means that the real wage rate must have decreased.
( c) New Keynesian model
Irrelevant whether we deal with (i) or (ii) because due to the presence of contracts, agents cannot
act upon the new information regarding money supply, and hence it makes no difference (at least
for the time being) what they know about the shock. (Although one can also argue that the shock
may affect those contracts that are being re-negotiated NOW).
The short-run New Keynesian AS is flatter than the Lucas supply curve in (b) above because in
(b) wages do adjust somewhat as a result of increased demand for labour, whereas in (c) nominal
wage rate remains fixed. Hence in (c), output increases more than in (b), and so does
employment. Consequently, a decrease in the real wage in (c) will be larger than in (b).
Conclusions regarding the effectiveness of monetary policy
In the long-run:
1. all agents learn about the shock, and correctly revise their expectations;
2. all contracts may be re-negotiated.
Hence, in the long run, both (b) and (c) "collapse" into (a), which means: output returns to its
long-run equilibrium, and so do employment and real wage. The only lasting consequence of the
monetary expansion is an increase in the price level.
In the short-run:
monetary policy is most effective within the New Keynesian framework because of the nominal
wage rigidity. Its effectiveness within the New Classical model depends on the information held
by the agents regarding the shock. In the classical framework, monetary policy is neutral.
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PART II:
Evaluate the following statements. Carefully explain your reasoning:
1. Residential fixed investment is more sensitive to changes in r than the non-residential fixed
investment is. Lags in the investment process weaken further the link between investment and r.
Since MPI is higher in A than in B, the product-market multiplier in A is greater than in B. These
features of investment demand will make the IS curve in country A flatter than in country B.
Draw two differently sloped intersecting IS curves. Through their intersection point, draw the LM
curve. This is your original equilibrium, the same for country A and B.
The monetary policy shifts the LM curve. Mark the resulting equilibria for each country (i.e. the
intersection points between the shifted LM curve and the two IS curves). Compare them to the
original equilibrium. Conclude: The steeper IS, the smaller change in Y that results from the LM
shift.
It follows that the monetary policy is more effective in country A (i.e., with the flatter IS curve) –
this part of the statement is true.
The fiscal policy case is trickier.
Recall how the fiscal policy works within the model: for example, an increase in G expands
income. The money market is out of equilibrium, r has to increase to offset an increase in
demand for money triggered by higher income. However, higher r decreases investment,
triggering thus a fall in income. The decrease in income related to falling investment offsets the
initial increase in income related to increasing government spending. This is the essence of the
crowding-out effect.
The effectiveness of the fiscal policy will weaken therefore with a higher interest-rate elasticity of
investment. On this account, ceteris paribus, fiscal policy would be less effective in country A
(i.e., YI below will be high in A). However, the final effect of the fiscal policy is given by:
Ynet = ( YG - YI) * product-market multiplier
It follows that the higher the marginal propensity to invest (i.e., the higher the product-market
multiplier) the more effective, ceteris paribus, fiscal policy would be. On this account, fiscal
policy will work better in A.
On the basis of the original information it is impossible to conclude then in which country fiscal
policy would be more effective.
2. You can address this issue in ONE of the following ways:
A. State that the statement is false, and discuss the New Keynesian model to support your
argument. Conclude: the presence of contracts prevents agents from adjusting to policy changes
during the duration of contracts. Hence, even when economic agents do understand
consequences of the policy, and they correctly revise their expectations, they cannot act upon this
information, and hence output may deviate from its long-run level as a result of such policy
shocks introduced during the duration of contracts.
B. The above statement is certainly true in the imperfect-information models: whenever price
level deviates from its forecast AND whenever the changes in the firm's own price are only
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partially attributed to the changes in the general price level (i.e. b is smaller than 1), then output
will deviate from its natural level only as a result of expectational errors.
The above is true in some sense also within the New Keynesian framework: contracts are
conditioned on the expectations on the future policies. With no shocks, employment would
remain at its natural level during the duration of the contract, and hence the above statement
would be true. However, if contracts in the economy are staggered, there will be some inertia in
the wage-setting, and hence at least part of the output deviations could be explained on this basis.
Moreover, one can argue that the statement is false within the short-run New Keynesian
framework for the reasons discussed in A above.
3. This is a straightforward question on the New Classical model: assume perfectly flexible
prices and wages, and imperfect information. Firms observe immediately prices of their own
products, and only with some delay they learn about movements in the general price level. In the
meantime, they form expectations regarding this general price level. They change their output
only if their price changed IN RELATION TO other prices. Whenever their price rises, they
attribute part of this increase to the change in relative prices (and accordingly, they increase their
output), and part of it - to the unexpected change in the general price level (which does not affect
their production). If they make mistakes regarding the weigths attributed to the relative and
general price change, then their output (and hence the aggregate output) will deviate from its full
employment level.
Hence the statement is true ONLY IF we also assume perfect information (and rational
expectations). Otherwise, it is false.
4. In the classical model the aggregate supply curve is always vertical. Perfect information and
perfect price and wage flexibility ensure that the economy is always at the natural level of
employment and output. The slope (i.e. the elasticity) of the labour supply is irrelevant for the
slope of the AS.
In the New Keynesian model, the nominal wage rate is fixed by a contract. The labour supply
becomes then horizontal in the short-run at the contractual W (i.e. it is perfectly elastic). The
slope of the AS will therefore be determined only by the slope of the labour demand.
The New Classical case merits a consideration only if we assume mistaken expectations (since
otherwise the New Classical model is reduced to the Classical one). Draw two differently sloped
labour supply curves, initially intersecting labour demand at the same point. Assume fixed price
expectations by workers (so that the labour supply curves do not move). Shift then the labour
demand upward (or downward) as a result of higher (lower) than expected prices in product
markets. Show the new levels of employment as determined by the new labour demand curve
and the two labour supply curves. Note that the flatter (i.e. the more elastic) labour supply is, the
more level of employment changes. Given the production function, this means that the flatter the
labour supply, the more output changes for any given change in prices. Hence the statement is
true within the New Classical framework with mistaken price expectations.
(This also explains why the New Keynesian Aggregate Supply is always flatter than the New
Classical Aggregate Supply.)
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5. The increase in money supply shifts the LM curve to the right, and hence it shifts the
aggregate demand to the right. This will cause prices to increase in the long run, and since the
AD shift is partly anticipated, rational agents revise upwards their price expectations.
Consequently, the expectations-augmented aggregate supply shifts upward, but it shifts by less
than the AD shifted because the strength of the AD shift is underestimated. The new equilibrium
is determined by the intersection of the new AD and EAS curves (point A). The actual price level
increases, and so does the output. The increase in output implies a higher level of employment.
Since the higher level of employment reduces the marginal product of labour, and profitmaximization requires the equality of MPL with real wages, it follows that the real wage rate
decreases.
6. Draw the AD-AS graph, start with the long-run equilibrium at A, expected and actual prices
are PA.
Assume that the Aggregate Demand is expected to shift upwards. Due to this expectation, rational
agents will expect higher prices, let’s say: PB. This expectation leads workers to demand higher
nominal wages at each level of their working effort, to which firms concede as they expect that
their higher cost will be compensated by higher prices. As a result, the New Classical Aggregate
Supply (NCAS, EAS, Lucas’ supply curve) shifts upward.
However, by assumption – the rumours are unsubstantiated, i.e. the Aggregate Demand does not
shift. The short-run equilibrium is where the shifted EAS curve based on expected prices PB
intersects the actual (non-shifted) Aggregate Demand: at S.
Compare the equilibrium at S to the one at A.
At S, output Y is lower. Since output is lower, employment N is lower (assumption #1 of the
Aggregate Supply models). Lower employment implies higher Marginal Product of Labour MPL
(assumption #2 of the models). And given that the firms at all times equalize MPL with real
wages W/P (assumption #3 of the model), real wages are now higher.
Adjustments towards the long-run equilibrium
Note that at S actual prices are below the expected prices: PS < PB = Pe
Firms and workers therefore revise their expectations, in particular – they lower them. As long as
expectations are above PA, the actual prices will continue to be lower than expected prices, and
agents will continue revising their expectations downwards, towards A. Similarly, if they lower
their expectations below PA, the actual prices will be above the expected one, causing the agents
to revise their price expectations upward. As expectations are revised, the EAS curve will keep
shifting, reflecting the underlying changes in nominal wages established in the labour market.
Expectations stop being revised only once the “truth” is discovered, i.e. when expected prices will
equal PA again. Only at that level of prices, expectations are the same as the reality. This happens
in the long run. So, in the long run, we are back to the initial position at A = L.
Output returns to its initial (long-run, full-employment, natural) level, and so do employment,
marginal product of labour and real wages.
So: the statement is true in the short run (rumours, if credible, may have real effects on all the
variables listed) but not in the long run (the truth is discovered, and only the reality matters – and
not the rumours).
PART III:
Multiple choice answers
1C 2C 3C 4C 5D 6B 7C 8A 9D 10B 11D 12C 13D 14A 15C 16D
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