2102 Tutorial 7

Econ2102 Macroeconomics 2 Tutorial 7 (Week 5 May – 9 May) All students are required to submit a written answer to Question 5* at the beginning of the tutorial. The answers to starred questions will be discussed in the following week’s tutorial. Q1 One of the fundamental equations of modern macroeconomics (and modern finance) is the consumption Euler equation. Q2 shows how to formally derive the Euler equation, but here we can try and derive it by economic reasoning. We can use the no-arbitrage reasoning that we used for investment. Suppose that you have $1 and your options are to spend the money on some additional consumption today (period 1) or some additional consumption tomorrow (period 2). There is no uncertainty and no inflation. (i)If you spend the money on additional consumption today how do you value that additional consumption? (Hint. Think about valuing consumption in terms of utility). The above is option 1. Now for option 2. You save the $1 and use it increase your consumption in period 2. (ii)If you save the $1 what will be your gross return in period 2. (Hint. The net real interest rate is r). How much consumption will your $1 from period 1 buy you in period 2? (iii)If you buy consumption in period 2, how do you value that additional consumption? (Hint. See part (i)). (iv)Multiply the answers to parts (ii) and (iii) together. This is basically the return to option 2, except that the return occurs in period 2 and we would like to compare it to a return in period 1. Normally we would just discount the period 2 return by the real interest rate. But since we are valuing consumption in terms of utility, we apply a subject discount factor to the period 2 consumption return. (Hint: Use as the discount factor). (v)Equate the returns from the two options and you have the Euler equation. (vi)Express in words what the Euler equation implies. Q2 Suppose that a household has a utility function of the form; ( ) ( ) ( ) where

(i)Explain the meaning of the β...