Consider the following variation of the Romer model.
Yt = Aα t ·Lyt, 0 < α < 1 (1)
?At+1 = z·At ·Lat (2)
L = Lyt + Lat (3)
Lat = `·L (4)
The only di?erence is the exponent on At, α.
a. Provide an economic interpretation for each equation.
b. Demonstrate that 0 < α < 1 means there is a diminishing marginal product to ideas in this economy.
c. Show that there are still increasing returns to scale (ideas and labour) in this economy.
d. What is the growth rate of knowledge in this economy?
e. What is the growth rate of output per capita in this economy? (Hint: if y(t) = x(t)a then the growth rates are related as follows gy(t) = agx(t).)
f. Solve for the level of output per capita at each point in time.