Consider the two-period intertemporal model of a consumer. Incomes in the two pe
ID: 1116753 • Letter: C
Question
Consider the two-period intertemporal model of a consumer. Incomes in the two periods, y and y, are exogenous, and there no taxes and no government consumption. Assume that the consumer can borrow or save at the interest rate r.
(a) Graphically represent the optimal choice of consumption and saving. Explain the conditions that characterize this choice.
(b) What are the three assumptions we typically make regarding con- sumer’s preferences over different goods? What do they imply in terms of the shape of the indifference curves/response to pure income changes?
Explanation / Answer
a) The consumer's budget constraint for the current period:
c + s = y - ts, where ts= taxes in all the constraints given
b) The consumer's budget constraint for the future period:
c' = (1+r)s + y' - ts'
c' = (1+r)(1-t) + y' - ts'
c) One lifetime budget constraint:
s = c' - y' + ts'/ (1+r)
d) consumer problem occurs when he has to decide whether to choose present consumption or future consumption. The optimal point occurs where in the graph, the slope of the highest attained indifference curve is equivalent to the slope of the budget constraint.