Exercise 2

Consider the following discrete-time multiple period economy with a single repre-sentative agent. There is no terminal period so the economy continues forever. The agent is endowed with one unit of an asset paying dividends Dt which follows from the recursion

lnDt+t =lnDt +t+ tt+t, (1)

where , are constants and the noise terms t+t have a mean of zero, a variance of 1, and are mutually independent for all t, and hence independent of Dt. All other assets are in zero-net supply.

The agents preferences are characterized by the utility function u(c) = c¹ / 1 - , with > 0

and for = 1 she has log utility. In addition she has time-additive expected utility with a time preference parameter .

1. (a) Argue that in equilibrium, the agents optimal consumption must be equal to the dividend of the asset, i.e. Ct = Dt for all t.

Exercise 2 Consider the following discrete-time multiple period economy with a single repre- sentative agent. There is no terminal period so the economy continues forever. The agent is endowed with one unit of an asset paying dividends Dt which follows from the recursion In Dt+at = In Dt +uAt+ov Atet+at, (1) where h, o are constants and the noise terms Et+At have a mean of zero, a variance of 1, and are mutually independent for all t, and hence independent of Dt. All other assets are in zero-net supply. The agent's preferences are characterized by the utility function u(c) :, with y > 0 1-7 and for y=1 she has log utility. In addition she has time-additive expected utility with a time preference parameter 8. (a) Argue that in equilibrium, the agent's optimal consumption must be equal to the dividend of the asset, i.e. Ct = Dt for all t. = Exercise 2 Consider the following discrete-time multiple period economy with a single repre- sentative agent. There is no terminal period so the economy continues forever. The agent is endowed with one unit of an asset paying dividends Dt which follows from the recursion In Dt+at = In Dt +uAt+ov Atet+at, (1) where h, o are constants and the noise terms Et+At have a mean of zero, a variance of 1, and are mutually independent for all t, and hence independent of Dt. All other assets are in zero-net supply. The agent's preferences are characterized by the utility function u(c) :, with y > 0 1-7 and for y=1 she has log utility. In addition she has time-additive expected utility with a time preference parameter 8. (a) Argue that in equilibrium, the agent's optimal consumption must be equal to the dividend of the asset, i.e. Ct = Dt for all t. =