In the questions in this section, we will use the Romer model (with a modest modification below), described by equations Y = ALyt BE (0,1] AAtti = EAtLat Lyt + Lat = L Lat = IL with a given initial value Ap. Assume that the real interest rate (discount rate) in the econ- omy is R, and this interest rate stays constant irrespective of the changes in the economy. Question 1.1 /5 points/ What is the growth rate of the stock of ideas, expressed using the parameters of the model? What is the growth rate of output per capita? For the following questions, the formula for the geometric sum will be useful: 1 - 9 Question 1.2 /10 points) Let pdv (Y) denote the present discounted value of total future output, defined as pdu (Y) = Yt 1 = 0 (1 + R) Rewrite the expression for pdv (Y) in terms of output Yo, the interest rate R and the growth rate of output. What is the restriction on the parameters of the model to assure that pdu (Y) is well-defined (i.e., that the present discounted value of output is finite)? Question 1.3 /5 points/ Using the formula for the geometric sum, calculate the present discounted value of output pdu (Y)