Assignment Remit

This is a 50% assignment in total, split in two parts (Questions 1 and 2 i.e. Q1 and Q2) which are equally weighted. This part is Q1 which is a written assignment.

Q2 is a video submission which is in a different submission box. The deadline for both partsQ1 and Q2 is 19th  December.

Module Learning Outcomes:

This assignment is designed to assess the following module learning outcomes. Your submission will be marked using the Grading Criteria given below.

•   Analyse the theoretical models of modern macroeconomics research to discuss the main issues relating to business cycles and long-run growth;

•   Analyse issues relating to business cycles and long-run growth both in the UK and in the wider international economy;

•   Appraiseselected papers from professional journals.

Q1. Consider the two-period Real Business Cycle (RBC) model without uncertainty presented in the lecture slides (also Romer, 2019, ch.5) but now assume that u(•), for households, takes the form.

where ct  is  consumption at time t and (1–{t) is leisure time at time t. Given that the time endowment is normalised to  1, it follows that ℓt  is hours worked at time  t.  Note that ut contains three parameters: θ>0, b>0 and γ>0.

All households in the economy are assumed to be identical; we can therefore consider a ‘representative household’ (henceforth ‘the household’). Set t=1 for the present period and set t=2 for the next period. For example, c1  is consumption in the present period and c2  is consumption in the next period. This is a two-period model so there are no time periods prior to t=1 and there are no time periods after t=2. Assume that the household begins and ends life  with  no  accumulated  wealth  and  that  the  real  interest  rate  is  r  (where  r>0).  The intertemporal budget constraint is therefore:

Answer the following questions:

a)    Present   the    Lagrangian    problem   for   the   household   under   this   model specification. Briefly explain why we need to use the Lagrangian technique.         [10%]

b) Derive the first order conditions for the household in this case.                            [10%]

c)  Use  the  first  order  conditions  for  ℓ1    and  ℓ2    to  derive  an  expression  for  the relative amount of leisure time chosen by the household over the two periods, i.e. derive  an  expression  for   (1–ℓ1)/(1–ℓ2).  Explain  how  an  increase  in  the  relative wage  (w2/w1) affects the household’s decision about how much leisure to take in each period.                      [10%]

d)  Calculate  the  intertemporal  elasticity  of  substitution  between   period  1  and period 2 leisure time in this case.                                        [10%]

e) Labour economists typically estimate that the intertemporal elasticity of

substitution  for  leisure  is  small   empirically.  Why  is  this  problematic  for  the RBC  model  considered  here  when  comparing  the   predictions  of  the  theory   to relevant empirical evidence for the US or the UK?         [10%]

f) Aside from the issue considered in part (e), outline two other shortcomings of Real Business Cycle theory as a framework for understanding short-run economic fluctuations (i.e. business cycles) for an economically developed country such as the  US or the UK.                                                                                                                              [50%]

For Parts (a) to (e): there is no word limit and referencing is not required.

For Part (f): you should conduct your own wider reading/research; the word limit for   this sub-part is 500 words (+10% tolerance) and you should reference according to the Harvard system.