ECON4019 Macroeconomic Analysis in course exam 2021-22

You must answer TWO questions from this section, using a separate white answer sheet for each question (all questions of equal weighting).

For two of the following, state whether you AGREE or DISAGREE and explain your reasoning.  Answers for which no reasoning is given will earn zero credit.

1. The Solow-Swan model predicts that convergence will occur more rapidly when decreasing returns to capital are slow to set in.                (15%)

2. Where the parameters are the same across countries, Romer’s model of ideas predicts sustained long-run cross-country variation in output-per-worker.         (15%)

3. If expectations were rational and the Lucas Phillips curve prevailed, then expected  inflation would be anchored by the inflation target and monetary policy would never be constrained by the zero lower bound.                              (15%)

4. Efficiency wages ensure that workers are paid according to their marginal product even when the goods market is imperfectly competitive.              (15%)

Section B

You must answer ONE question from this section, using a separate white answer sheet for each question (the weighting is noted against the sub question).

QUESTION FIVE

Consider Romer’s model of ideas with production given by Y(t) = K(t)a(A(t)Ly(t))1−a, 0 <

a < 1, where Y(t) is aggregate real output, K(t) is aggregate capital, A(t) is aggregate technology, and Ly(t) is the number of people working in the goods sector. Capital accumulates according to:

K(̇)(t) = SY(t) − δK(t),

where 0   < S < 1, and 0 < δ < 1. In the “ ideas” sector, new technology is produced according to:

A(̇)(t) = θA(t)φ LA(t),

where θ  > 0, and 0   < φ < 1 . The model is closed by assuming that the number of workers in the ideas sector, LA(t), is given by:

LA(t) = SAL(t),

where 0  < SA < 1 (all other workers work in the goods sector), and total population L(t) grows at rate n > 0 .

5.1. Provide an economic interpretation for the parameter θ . (5%)

5.2. If we define output-per-effective-person as:̃(y)(t) = , then derive an expression

for steady state output-per-effective-person that depends only on parameters and explain the effect that an increase in θ  has on this steady state.  Be sure to show all your working.  Explain what your steady state expression implies about absolute convergence. (40%)

5.3. Suppose that the economy begins from steady state when it experiences a one-time permanent increase in θ .  Using diagrams with time on the horizontal axis, show the effect that this increase in θ  has on the time-paths for log-output-per-effective- person and log-output-per-person. (25%)

(TOTAL 70%)

QUESTION SIX

Suppose the economy is described by the system:

y t − ye   = −a(Tt − Te),                                                                                               (2)

y t − ye  = −aλ(π t− πT ),                                                                                             (3)

where a >  0, a > 0, λ > 0, ye  represents equilibrium output, Te   represents the equilibrium real interest rate, and πT   represents the inflation target.

6.1. Suppose that the central bank’s loss function is given by:

Loss =  (y t −  ye)2  + λ(π t− πT )2  + μ(Tt − Te)2,

where λ >  0 and μ >  0 represent the relative weights assigned to stabilizing inflation (about its target) and the real interest rate (about its equilibrium level), respectively.  Explain why a  greater concern for interest rate stabilisation is equivalent to a greater concern for output stabilization and to a smaller value for λ . (10%)

6.2. The central bank wishes to conduct policy so as to minimise its loss function.

Solve for the optimal monetary policy and express the solution as a linear

relationship between the output gap and the deviation of inflation from target.  Be sure to show all your working.  Using a diagram with inflation on the vertical axis  and output on the horizontal axis, show how μ  >   0 affects the monetary policy rule. (30%)

6.3. Suppose that the economy is hit by an unanticipated temporary positive

aggregate demand shock that pushes inflation two percentage points above the inflation target.  If a  = 0.5, a  = 0.5, λ  = 2.0, and μ  = 0.4, then determine how many periods it is expected to take before inflation is less than half a percentage  point above target.  Explain whether greater concern for interest rate stabilization will increase or decrease the speed at which inflation returns to target. (30%)

(TOTAL 70%)