R.Mehra and E.C.Prescott,The equity premium 151 where x,.+1∈{入l,,入n}is the growth rate,.and Pr{x+1=入yix,=入}=中 (4) It is also assumed that the Markov chain is ergodic.The A,are all positive and yo>0.The random variable y,is observed at the beginning of the period,at which time dividend payments are made.All securities are traded ex-dividend. We also assume that the matrix A with elements a=for i,j= 1,...,n is stable;that is,lim A"as moo is zero.In Mehra and Prescott (1984)it is shown that this is necessary and sufficient for expected utility to exist if the stand-in household consumes y,every period.They also define and establish the existence of a Debreu(1954)competitive equilibrium with a price system having a dot product representation under this condition. Next we formulate expressions for the equilibrium time t price of the equity share and the risk-free bill.We follow the convention of pricing securities ex-dividend or ex-interest payments at time t,in terms of the time t consump- tion good.For any security with process {d}on payments,its price in period t is P=E,2g-U)da,/}: (5) =1+1 as equilibrium consumption is the process {y,and the equilibrium price system has a dot product representation. The dividend payment process for the equity share in this economy is {y,) Consequently,using the fact that U'(c)=c-, pe=pe(x,y (6) s=t+1 Variables x,and y,are sufficient relative to the entire history of shocks up to,and including,time t for predicting the subsequent evolution of the economy.They thus constitute legitimate state variables for the model.Since y,=y,'xz+l··,··xs,the price of the equity security is homogeneous of degree one in y,which is the current endowment of the consumption good.As the equilibrium values of the economies being studied are time invariant functions of the state (xy),the subscript t can be dropped.This is accomplished by redefining the state to be the pair (c,i),if y=c and x,=Ai.With this