This exercise asks you to endogenize innovation decisions in the model of Section 19.5. Assume that new goods are created by technology firms in the North as in the model in Section 13.4 in Chapter 13, and these firms are monopolist suppliers until the good they have invented is copied by the South. The technology of production is the same as before, and assume that new goods can be produced by using final goods with the technology N(t) ? = ηZ(t), where Z(t) is final good spending. Imitation is still exogenous and takes place at the rate ι. Once a good is imitated, it can be produced competitively in the South.
(a) Show that for a good that is not copied by the South, the equilibrium price is
(b) Characterize the static equilibrium for given levels of Nn(t) and No(t).
(c) Compute the net present value of a new product for a Northern firm. Why does it differ from (13.8) in Section 13.4?
(d) Impose the free-entry condition, and derive the equilibrium rate of technological change for the world economy. Compute the world growth rate.
(e) What is the effect of an increase in ι on the equilibrium? Can an increase in ι make the South worse off? Explain the intuition for this result.