Question

Consider a two-period model with a representative consumer whose Euler equation is:
1/c1 =E1β（1+r）（1/c2）
where ri is the return on any asset, Let β = 0.9. Suppose that c1 = 1 and how much of c2 you get depends on the state of the economy, as follows:
Good state with Probability = 0.5 Bad state with Probability = 0.5
a) Find the price q and the return r on an asset which pays c2 = 2 in good state and c2 = 0.5 in bad state in period 2.

Answer 1

Ans A)

(1/c1)=E(β(1+R)(1/c2)

c1=1 ; β=0.9

Good state probability=0.5=Bad State Probability

(1/1)=Probability of Good state*c2 in good state+Probability of Bad state* c2 in bad state

1=0.5*0.9*(1+R)(1/2)+0.5*0.9*(1+R)*(1/0.5)

1=0.45(1+R)(5/2)

1=0.45*2.5*(1+R)

(1/(0.45*2.5))=1+R

hence real interest rate is negative

R=-0.1111%

Risk neutral Price of an asset is Discounted expected vale of asset

Price of asset=Expected Value of Asset/(1+R)
q=0.5(2+0.5)/(1-0.111)=1.40607