ECON 222 Lecture Notes - Lecture 12: Farad, Consumption Smoothing
ECON 222 Full Course Notes
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consider the following two-period model. The consumer has preferences given by: u(c,c')=ln c + Ã ln c' where c is current consumption, c' is future consumption, and Ã >0 is a discount factor. The consumer receives exogenous income y u tge current period and y' in the future period. The consumer pays proportional tax ts on savyings (i.e. the consumer saves s in the current period but only gets (1-ts) tomorrow). The consumer can save at the interest rate r.
a) Write down the consumer's budget constraint for the current period.
b) Write down the consumer's budget constraint for the future period.
c) Combine the two budget constraints above into one lifetime budget constraint
d) Solve the consumer's optimization problem for c and c'
e) Write down the tax revenue the government receives then imposing the tax on savings.
Consider the two-period intertemporal model that we studied in class.
(a) (5 marks) Discuss the similarities and differences between the drivers of consumption predicted by this model compared to those suggested by the traditional KeynesianconsumptionfunctionC=C(Y âT).
(b) (10 marks) Explain why this model predicts that consumption in the present and future will increase in response to either a rise in current income, or, a rise in future income. What happens to savings in each case?
(c) (15 marks) On a C1 vs. C2 diagram, sketch an indifference curve and budget constraint showing the optimal choice for a borrower. Now show the impact of an increase in the real interest rate r on the borrower, sketching two different cases: (i) where the increase in r results in a rise in period 2 consumption, and (ii) where the increase in r results in a fall in period two consumption. How can the model account for these two different cases? Discuss, what assumption must hold in each case.