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What determines short-run equilibrium output? What determines output in the medium run and what in the long run? How can policy affect output in the short, the medium and the long run? Use the models that we have discussed throughout the module to answer this question. No algebra or graphs are needed; however, you should be able to describe the models and the mechanisms that drive the results. You should provide your answer in no more than 1,000 (one thousand) words.
We assume a representative household that lives for two periods. The household receives income as endowment in the first period, yi, and in the second period, y2. The household optimally decides how much to consume in the first period, c1, how much to save in the first period, s, and how much to consume in the second period, c2. The household would prefer to smooth consumption over time. In order to do that, the household can borrow and lend freely at the real interest rate, r. The household exits the world without debt. Household’s preferences are given by: 1 U(cl, c2) = log ci + — log C2, 1-Fp where p > 0 is the rate of time preference.
(i) Write down the representative household’s budget constraint for each period and derive the intertemporal budget constraint. What does this show? State formally the maximisation problem for the representative household.
(ii) State the equilibrium condition for the previous maximisation problem and derive the Euler equation. Explain your results.
(iii) Let us assume that the optimal choice of the representative household is described by the endowment point. What is the condition that should be satisfied in this case and what does this mean for household’s optimal choices for current consumption, future consumption and saving? Draw a graph with consumption in period 1 in the horizontal axis and consumption in period 2 in the vertical axis to depict household’s equilibrium.
(iv) Let a 20% decrease in second period’s income known at the beginning of period 1. Would this household continue to operate at the endowment point? If not, now the household
will be a lender or a borrower? Explain your answer and show this algebraically.
(v) Consider, instead, a household that lives forever (i.e., for an infinite horizon) and operates under the permanent income hypothesis. How will a temporary change in this household’s
future income (so, only in the next period) affect current and future consumption? What will happen if this is a permanent change? Assuming a change equal to x > 0, compute these
changes and explain your results.
Consider the following behavioural equations that describe the goods market in a closed economy:
C=C) + C1Yp
where C is consumption, Y, is disposable income, / is investment, r is the real policy rate, x defines the risk premium, cy > 0 is the autonomous part of consumption, a, > 0 the autonomous part of
investment, 0 < c, < 1 the marginal propensity to consume and 0 <a, < 1 the interest sensitivity of investment. Also assume that government spending, G, and taxes, 7, are both exogenous.
(i) Derive the IS relation. What is the value of the multiplier for a change in autonomous spending and what is the slope of the IS curve? What does the IS relation show?
(ii) Suppose the central bank chooses a real policy rate equal to r. Provide an interpretation of this policy rate. Draw the equilibrium for this economy using an IS-LM diagram and solve
for equilibrium output.
(iii) Provide an interpretation for the risk premium, x. Explain the effect of an increase in the risk premium on equilibrium output. By how much should the central bank change the real policy rate in order to keep output constant? Draw the necessary graph and explain your answer.
(iv) Explain possible limitations to the previous analysis (in question (iii)). Is there another way that the central bank can affect the borrowing rate; so, affect equilibrium output? Can,
instead, the fiscal authorities (i.e., the government) help out in the stabilisation process? Explain possible limitations to this analysis, too.
(v) Let now the risk premium to be also negatively affected by income; i.e., let x = x) —x,Y with x» > 0 and0 <x, <1. Provide an economic intuition for x, # 0, derive the IS relation and comment on the multiplier.