The budget constraint facing an individual planning his or her consumption over two periods is an intertemporal one in which the present value of consumption expenditures must equal the present value of incomes in the two periods:

C_1+C_2/(1+r)=m_1+m_2/(1+r)..............(A)

where m and C represent income and consumption respectively and r is the interest rate, the subscripts represent the two time periods.

1. Draw the intertemporal budget constraint in the C₂-C₁-plane. (as given in the lecture slide)
2. Explain the meaning of this constraint.
3. If m₁ > C₁, this individual is saving in period 1. Why does this imply that m₂ < C₂?
4. If this individual is saving in period 1, why is m₁ - C₁ less than C₂ - m₂?

Now suppose the individual's utility function is given by

U(C_1,C_2)= C_1,C_2...................(B)

And m₁= m₂= $1000 and r = 0.1 or 10%

1. Suppose individual decide to consume m1 = , or (no saving/borrowing). Calculate individual's utility at this point using the utility function given in 'B'.
2. Draw the graph in the C2-C1-plane and mark the individual's optimal consumption point (C₁, C₂). (NOTE: at optimal point marginal rate of substitution (MRS) is equal to (1 + r). Calculate individual's utility at the optimal consumption point. Compare the individual's optimal utility with the utility obtained in part 'e'.
3. Now assume that interest rate is reduced to 5%. Calculate individual's utility at the new optimal consumption point. Compare the individual's utility with the utility obtained in part 'e' and part 'f'.
4. Now assume that interest rate is increased to 20%. Repeat part 'e' and part 'f'
5. Now assume that inflation rate is 3%. Repeat part 'e' and part 'f'.
6. Now assume that m1 = $2000, and m2 = 0, r= 0.1 (10%). Repeat part 'f'
7. Now assume that m1 = 0, and m2 = $2000, r= 0.1 (10%). Repeat part 'f'
8. Explain your findings.