Consider the technology revolutions model of Section 4.2, and in partic- ular the method of calculating the frequency of technology revolutions explained in Section 4.2.4. Suppose now that consumer population is no longer constant over time and is growing with time so that = t for every t = 1, 2,.... Suppose that technology was last replaced in period to, and that technology g+1 is about to replace technology g in period te+1. Answer the following questions.

(a) Write down the technology g + 1 adoption condition similar to (4.6), taking into consideration that population grows with time.

(b) Calculate the date t+1 of the adoption of technology g+1 as a function of adoption date of technology g (tg).

(c) Let A=2, n=1, and assume that technology g = 1 was adopted in period t = 2. Calculate the adoption date of technology 9 = 2 (12), the adoption date of technology g = 3 (13), and the adoption date of technology g = 4 (t4).