Seminar 4

I. Inequality and growth with incomplete credit markets

Consider a simple economy with two agents L and H with initial endowment a_L and a_H (a_L <a_H). Time is discrete and for simplicity both agents save a constant share s of their earnings for the next period.

1. Both agents has a production technology y=f(k) where k is capital invested (they always work one unit of labor), and the production function has standard properties f’>0, f’’<0.
   Consider first the case where there is a credit market. If both agents try to maximize current period production, show that L would want to borrow from H and how this would improve efficiency.
2. Assume now that there are frictions in the credit market. For simplicity, we simply say that borrowing and lending is impossible. Show that this reduces current period aggregate production and aggregate savings relative to what you could derive in question 1). What happens to next period’s production and savings relative to the scenario in question 1)?
3. Show that there is a steady state equilibrium, and explain how it depends on the initial endowment a_L and a_H.
4. Consider finally a case where production can be done using two different technologies. In a “traditional” sector, production is f_t(k)=ak. The “modern” sector is more productive but requires a fixed cost F: f_m(k)=bk-F where a<b.
   Study the effect of inequality, i.e. the differential between a_L and a_H, and how it depends on the value of F and whether a<1/s or not.

II. Natural resources and development

1. Consider the theoretical model considered by Mehlum et al. (2006). Explain the role of their parameter λ, and discuss whether this captures “good institutions” in a good way.
2. Explain how they model the productive sector and why the productive sector becomes more profitable the more entrepreneurs are in the productive sector.
3. Explain how good development depends on the interplay between the amount of resources R and institutional quality λ.
4. Explain first how Mehlum et al. test their theory empirically. Discuss:
   1. Whether it is a proper test of the predictions of their model
   2. The empirical validity of their approach more generally.
5. Discuss how we empirically can distinguish between resources induced by Dutch disease and bad politics/rent seeking.