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Problem Set 6 - Solution

Problem Set 6 - Solution - Econ 313-1 TA Tian Liang...

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Econ 313-1 TA: Tian Liang Solutions to Problem Set 6 1. (a) i. If a consumer saved $1 in period 1, he would have $(1 + r ) in the following period. This interest on dollar amounts is called a nominal interest rate. ii. If the price of a good in period 1 is $1 ; and the price of a good in period 2 is $(1 + ° ) then we say that ° is the rate of in°ation. iii. If by giving up a unit of the consumption good in period 1, one can purchase (1 + ± ) units of consumption good in the next period then we say ± is the real interest rate. iv. Suppose the price of the good in period 1 is p 1 = 1 and the price of the good in period 2 is p 2 = (1 + ° ) ; and the interest on dollar amounts is r: By giving up one unit of consumption in period 1, the consumer will be able to save $ 1 in period 1, this saving will give him $(1 + r ) in period 2, which means that he will be able to by (1 + r ) = (1 + ° ) units of consumption good in period 2 at the price (1 + ° ) : Therefore, 1 + ± = 1 + r 1 + ° : (b) ± = r ° ° 1 + ° = 5% ° 2% 1 + 2% = 1 34 So the utility maximization problem is max c 1 ;c 2 u ( c 1 ; c 2 ) s.t. c 1 > 0 ; c 2 > 0 ° 1 + 1 34 ± c 1 + c 2 = ° 1 + 1 34 ± m 1 + m 2 (c) Approximated real interest rate: r ° ° = 5% ° 2% = 3% Exact real interest rate: r ° ° 1 + ° = 5% ° 2% 1 + 2% = 2 : 94% The approximated real interest rate is larger and easier to compute. 1
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2. (a) A bond is a debt security, in which the authorized issuer owes the holders a debt and is obliged to make interest payments (the coupons) and repay the principal (the face value) at a later date (the maturity date).
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