How is present value different weights to income-consumption

Question

Assignment:

1. Show how taking a present value gives different weights to income and consumption in different years. Why is a unit of real income in the present more valuable than a unit of real income next year? Why is a unit of consumption next year cheaper than a unit this year?

2. Discuss the effects on this year's consumption, C₁, from the following changes:

a. An increase in the interest rate, i₁

b. A permanent increase in real wage income, (w/P) • L

c. An increase in current real wage income, (w/P)1 • L, but no change in future real wage incomes

3. Income effects

Consider again the household's multiyear budget constraint in equation (7.12). What are the income effects from the following:

a. An increase in the price level, P, for a household that has a positive value of initial nominal bonds, B₀. What if Bo is zero or negative?

b. An increase by 1% per year in every year's interest rate, i_t. Assume here that B₀ = 0.