comparative statistics in the 2 period model

Question 1

what is the effect of changes in income on the two period framework?

Answer 1

as a result of growth in the current income:
- consumption in both periods increase
agents act to smooth their consumption over time
- savings increase as the consumption in next period has increased due to higher savings

Question 2

what is the effect of an increase in the interest rate?

Answer 2

a rise in the interest rate makes current consumption relatively more expensive and future consumption relatively cheaper so there will be a substitution effect to the future consumption
a rise in r will make household worse of as an increase in cost of borrowing reduces future income which leads a reduction in both current and future consumption according to the income effect. both the income and substitution effect reduce current consumption but the effect on future consumption is ambigous