Question 1
Consider the following behavioural equations that describe the goods market
in a closed economy:
? = ?0 + ?1??
?? = ? − ?
? = ?0 + ?1? − ?2
?
where ? is consumption, ?? is disposable income, ? is income, ? is
investment and ? is the interest rate. Also, assume that government
spending, ?, and taxes, ?, are both exogenous. The remaining parameters
are all positive and exogenous; in particular, ?0 defines the autonomous part
of consumption, 0 < ?1 < 1 the marginal propensity to consume, ?0 the autonomous part of investment, 0 < ?1 < 1 the impact of current output on investment, and ?2 the interest sensitivity of investment. (i) Derive and interpret the IS relation. What is the value of the multiplier for a change in autonomous spending, and what is the value of the slope of the IS relation? What is the condition that should be satisfied for the multiplier to be positive? [10 marks] (ii) Suppose the central bank chooses an interest rate of ? = ?. Solve ̅ for the short-run equilibrium output in this economy. Draw the IS-LM graph and depict the point that brings equilibrium in both the goods market and financial markets. Consider now an increase in the private sector’s confidence. Which are the implications for short-run equilibrium output? What should the central bank do in order to keep equilibrium output constant? Depict this case and the new equilibrium in the previous graph. [10 marks] See Next Page Created in Master PDF Editor 5QQMN937 Page 3 of 7 (iii) Let us assume that the demand for real money balances is given by: ? ? = ?1? − ?2 ?, where ? is money and ? is the general price level, and ?1 and ?2 are exogenously given positive parameters. Solve for the equilibrium level of the real money supply when ? = ?, so at the ̅ initial equilibrium. Then, compute the necessary change in the real money balances after the monetary authority’s response to the increase in the private sector’s confidence described in the previous question (question (ii)). Draw a graph that depicts equilibrium in the financial markets (i.e., the market for real money balances), before and after the monetary response. Explain the monetary policy response. [10 marks] (iv) Let us now assume that the consumption function is given by: ? = ?0 + ?1?? − ?2 ?, where ?2 > 0 is the impact of the interest rate on aggregate
consumption. What do you think can justify this assumption;
i.e., that consumption is negatively related to the interest rate?
What does this imply for households’ consumption behaviour?
Assume that ?0 and ?1
remain unchanged.
[10 marks]
(v) Derive and interpret the IS relation using the consumption
function in the previous question (question (iv)), and compare it
to the one you derived in question (i). Is the slope of the IS
curve now flatter or steeper? And what does this imply for
monetary policy effectiveness? Is now the change needed for
the monetary response described in questions (ii) and (iii) higher
or lower?
[10 marks]
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Question 2
Consider the Solow model in discrete time. The following system of equations
fully describe the economy:
?? = ?? + ??
?? = ???(??
, ??
) = ????
???
1−?
?? = ??
??+1 = (1 − ?)?? + ??
?? = ???
? defines income, ? defines consumption, ? investment, ? saving, ? the
capital stock, ? employment (or labour) and ? the state of technology; ? ∈
(0,1) is the rate of capital depreciation, ? ∈ (0,1) the saving rate and ? ∈
(0,1) is the capital elasticity of output. The previous equations describe a
closed economy with no government. We further assume no technological
progress, normalising for ?? = 1, and no population growth. We assume that
both the participation rate (labour force over population) and the
unemployment rate are constant, which means that the labour force is
constant; so, ?? = ?.
(i) Express the above equations in per worker form, defined by lowercase letters, and derive the fundamental law of motion of the
Solow model. What does this equation show?
[10 marks]
(ii) Explain how and why the economy starting from an initial quite low
level of capital, ?0
, will reach a steady state equilibrium. Compute
capital per worker, output per worker, investment per worker, and
consumption per worker in steady state equilibrium. What
determines output per worker in the long run? Draw a graph with
capital per worker at time ? on the horizontal axis and output per
worker at time ? on the vertical axis to depict a steady-state
equilibrium. Show also in the graph consumption per worker and
investment per worker.
[10 marks]
(iii) Assume an economy that is in steady-state equilibrium and
experiences an increase in the saving rate. Explain in words what
will happen to this economy initially, but also in the long run,
meaning the impact on both output per worker and its growth rate.
Show this in a graph (similar to the previous one). Should we
expect consumption per worker to rise in the long run? Explain your
answer.
[10 marks]
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(iv) Consider two economies, economy X and economy Z, which share
exactly the same attributes (i.e., characteristics), apart from the
saving rate; in particular, economy X has a higher saving rate. In
the steady state, which economy is going to have the higher output
per worker, the higher growth rate of output per worker, and
higher welfare for their citizens? Consider now, that they also
differ in their initial stock of capital; in particular, the economy Z
has a higher initial stock of capital. Does your answer now change,
and why? Consider now, instead, that economy Z invests more in
education than economy X. Does your answer now change, and
why?
[10 marks]
(v) Consider the discussion between innovation and imitation in
endogenous technological progress. Comment briefly on the
statement that poorer countries can grow largely by imitating. How
should governments design patent laws?
[10 marks]
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Question 3
Assume a central bank with preferences that are described from the
following loss function:
? = (?? − ??
)
2 + ?(?? − ?
?)
2
,
where ?? defines output at period ?, ?? defines medium-run equilibrium
output (given; exogenous), ??
is the inflation rate at period ?, ?
?
is the
inflation target (given; exogenous), and ? > 0 an exogenously given
parameter that defines the degree of central bank’s inflation aversion. The
supply-side of the economy is described by the following PC relation:
?? = ??
? + ?(?? − ??
),
where ??
? defines expected inflation at period ? and ? > 0 is an exogenously
given parameter that shows the responsiveness of inflation to changes in the
output gap. We further assume ??
? = (1 − ?)?
? + ???−1
, where 0 < ? < 1 is an exogenously given parameter that defines the degree of inflation persistence. The demand-side of the economy is described by the following IS curve: ?? = ? − ???−1 , where ??−1 defines the real policy rate set by the central bank, ? > 0 is the
interest sensitivity of aggregate demand and ? a positive constant. Both ?
and ? are exogenously given parameters. We assume that the real policy
rate affects aggregate demand with a lag.
(i) Explain the parameters ?, ?, and ?. What can affect those
parameters? Moreover, explain what determines the medium-run
equilibrium level of output, ??
, following equilibrium in the labour
market.
[10 marks]
(ii) Derive the central bank’s monetary rule (MR) in period 1, assuming
that the central bank faces a given inflation rate at period 0; so,
?0
. What does this rule show?
[10 marks]
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(iii) Solve for the inflation rate (as deviation from the target rate of
inflation) and output (as deviation from the equilibrium output) in
period 1, and for the real policy rate in period 0 (as deviation from
the medium-run equilibrium policy rate). Interpret your results.
Does it matter if the inflation rate at period 0 is different from the
target rate of inflation? What is the role of the degree of inflation
persistence?
[10 marks]
(iv) Draw the necessary graphs (IS-PC-MR), assuming adaptive
expectations, and briefly explain the adjustment of the economy to
the inflation shock; i.e., when ?0 > ?
?
.
[10 marks]
(v) Critically discuss the current state of the debate on the optimal
inflation rate (i.e., inflation target). Should central banks adopt a
higher (than a 2%) inflation target?
[10 marks]
Sample Solution