In the questions in this section, we will use the Romer model (with a modest modification below), described by equations

Yt=AtLyt(0,1] At+1=zAtLat

Lyt+Lat=LLat=lL

with a given initial valueA0. Assume that the real interest rate (discount rate) in the econ- omy isR, and this interest rate stays constant irrespective of the changes in the economy.

Letpdv(Y) denote the present discounted value of total future output, defined as

pdv(Y)=????Yt.t=0(1+R)t

Rewrite the expression forpdv(Y) in terms of outputY0, the interest rateRand the growth rate of output. What is the restriction on the parameters of the model to assure thatpdv(Y) is well-defined (i.e., that the present discounted value of output is finite)?