Economic growth and economic development 717

Introduction to Modern Economic Growth also acquire skills Conclude from this that there exists a cutoff level of ¯ not get education ¯ such that all Kx > K talent, K, (2) Show that, along BGP relative supplies take the form: ¯ Γ(K) H = ¯ L − Γ(K) Explain why such a simple expression would not hold away from the BGP ¯ [Hint: agent with talent K ¯ has to be indif(3) How would you determine K? ferent between acquiring skills and not] Show that the relative supply of skills as a function of the skill premium must satisfy Γ (ln ω/ (r∗ + υ − g ∗ )) H = , L − Γ (ln ω/ (r∗ + υ − g∗ )) where r∗ and g ∗ refer to the BGP interest-rate and growth rate (4) Determine the BGP skill premium by combining this equation with (15.27) and (15.30) Can there be multiple equilibria? Explain the intuition Exercise 15.29 * Consider an economy with a constant population and risk neutral consumers discounting the future at the rate r Utility is defined over the final good, which is produced as Y (t) = ∙Z n y (ν, t) ε−1 ε dν ε ¸ ε−1 where ε > and intermediate y (ν, t) can be produced using either skilled or unskilled labor In particular, when a new intermediate is invented, it is first produced using skilled labor only, with the production function y (ν, t) = h (ν, t), and eventually, another firm may find a way to produce this good using unskilled labor with the production function y (ν, t) = l (ν, t) Assume that when there exist n goods in the economy and m goods can be produced using unskilled labor, we have ˙ (t) = bm Xm (t) n˙ (t) = bn Xn (t) and m where Xn (t) and Xm (t) are expenditures on R&D to invent new goods and to transform existing goods to be produced by unskilled labor A firm that invents a new good becomes the monopolist producer, but can be displaced by a new monopolist who finds a way of producing the good using unskilled labor 703