Please help me with the last subquestion which is the fifth one. Thanks a lot! P

Question

Please help me with the last subquestion which is the fifth one. Thanks a lot!

Problem 1: Elasticity and the Consumption/Savings Decision (50 points) Suppose that you have a function f(r). The elasticity of f is defined as d in f(z) d Inr e(z) = Notice that for any 1 close to r d in f(r) In f(11) ~ In f(z) % change in f % change in x E(T) ~ In 1 Inr so the definition of elasticity that you are taught in Econ 1101 is actually jus t an approximation of the definition of e(x) above i.) Show that ! HINT: Notice that In f(x) In f(en). Take the derivative of this expression with respect to Inr.) Now, consider a version of our simple model of the household's sav- ings/consumption decision. The household derives utility from con- sumption today c and consumption tomorrow d'. It's utility function is given

Explanation / Answer

draw the graph and regress. The slope of graph is 1/coefficient of relative risk aversion as described in the previous part. Essentially we are trying to find the value of sigma ( coefficient of relative risk Aversion) which would give us the required equity premium in the economy. If you will calculate it will come out to be very small. That is people are not risk averse so the question is then why would they invest in stock which have higher return (~5%). This is the puzzle. if we look it in the other way around and insert some meaningfull value for sigma which is around 2 then we fail to get the observed premium in the stocks.Thus in the simple terms data does not support the equity premium hypothesis. In macroeconomics people call it puzzle but its just a non conformity with the actual data. The stock returns calculated using the consumption growth model does not conform to data.

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