Introduction to Modern Economic Growth (1) Denote the unskilled wage by w (t) and the skilled wage by v (t) Show that, as long as v (t) is sufficiently larger than w (t), the instantaneous profits of a monopolist producing skill-intensive and labor-intensive goods are v (t) H 1 w (t) L and πl (t) = π h (t) = ε − n (t) − m (t) ε − m (t) where L is the total supply of unskilled labor and H is the total supply of skilled labor Interpret these equations Why is the condition that v (t) is sufficiently larger than w (t) necessary? (2) Define a balanced growth path equilibrium as an allocation where n and m grow at the same rate g (and output and wages grow at the rate g/ (ε − 1)) Assume moreover that a firm that undertakes R&D to replace the skill- intensive good has an equal probability of replacing any of the existing n − m skill-intensive goods Show that the balanced growth path has to satisfy the following condition wL vH = (1 − µ) (r + λ − (1 − µ) λ/µ) (r − (1 − µ) λ/µ) µ where µ ≡ m/n and λ ≡ m/ ˙ (n − m) = gµ/ (1 − µ) [Hint: Note that a monopolist producing a labor-intensive good will never be replaced, and its profits will grow at the rate g (because equilibrium wages are growing) A monopolist producing a skill-intensive good faces a constant flow rate of being replaced, and while it survives, its profits grow at the rate g.] (3) Using consumer demands over varieties (i.e., the fact that y (ν, t) /y (ν , t) = (p (ν, t) /p (ν , t))−1/ε ), characterize the balanced growth path level of µ What is the effect of an increase in H/L on µ? Interpret 704