Statistic Problems
Answer both questions
1. Consider the two-period Real Business Cycle (RBC) model without uncertainty presented in the lecture slides (also Romer, 2019, ch.5), but with one modification, Now assume that the instantaneous utility function for households takes the form:
4-9 (1 — e t)i_y = +b 1 — 0 1 — y
where ci is consumption at time t and (1-Pr) is leisure time at time t. Given that the time endowment is normalised to 1, it follows that ft is hours worked at time t. Finally, 0>0, h>0 and y>0 are parameters.
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, ci is consumption in the present period and C2 is consumption in the next period. Remember, 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).
Answer the following questions:
Present the Lagrangian (constrained maximisation) problem for the household under this modified specification. [10%]
Derive the first order conditions for the household in this case. [Hint: the household chooses ci, C2, Pi and P2]. [10%]
Use the first order conditions for -Pi and P2 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 (141]/(142). Explain how an increase in the relative wage (w2/w/) affects the household’s decision about how much leisure to enjoy in each period. [10%]
Show that the intertemporal elasticity of substitution between period 1 and period 2 leisure time is y-1 in this case.
Explain how the magnitude of y1 influences the household’s decision-making in the model, [10%]
Labour economists (e.g. Altonji. 198) typically estimate that the intertemporal elasticity of substitution for leisure is low; specifically, 0<y-1<1. Why is this finding problematic for our RBC model when comparing the predictions of the theory to relevant empirical evidence for the US or the UK? [10%]
Q2, Outline the major shortcomings of Real Business Cycle theory as a framework for understanding short-run economic fluctuations (i.e. business cycles), How does the ‘canonical New Keynesian model’ seek to address these shortcomings? [50%]
Word limit; 750 +10% (word limit excludes the list of references; use the Harvard system of referencing for this question).
