Coursework Questions:

1. We incorporate geography in the sharecropping contract model in Lecture 1, in particular the special case with CE utility function, linear compensation rule and risk neutral principal (Holmstrom-Milgrom 1991). Suppose there are two countries: cold country (I = 0) and hot country (I = 1). Assume people dislike hot climate, and we modify the agent's utility function as u(w) = -exp(-r-(w-1)).

a. Show that the new CE = μ - g(e) - r/2 s² - I

b. What are the maximization problems faced by the agent and the principal in the extended model? Apply the Nash equilibrium concept to solve for the optimal contract.

c. From the above results, comment on the statement: "In the hot country, high-powered incentives should be provided to maximize the joint surplus in the society. Ultimately, the cold country enjoys a higher output level."

d. From Acemoglu-Johnson (2005) and Acemoglu-Johnson-Robinson (2002)*, within 800 words, provide empirical evidence that contribute to the debate on the geography hypothesis versus the institutions hypothesis.

* Acemoglu, Daron, Simon Johnson and James A. Robinson. 2002. Reversal of Fortune: Geography and Institutions in the Making of the Modern World Income Distribution. Quarterly Journal of Economics 117(4):1231-1294.

2. We consider asymmetric payoff in the regional experimentation model in Lecture 6. Suppose with a successful new experiment, current-period payoff for the two units in U-from is (i + G + 1)R, where G ≥ 1. Correspondingly, the success payoff in M-from full scale and small scale experimentation would be (i + G +s) and (i + G + s)R/2 + (i + s)R/2 - δc/2 respectively. The payoffs without experiment and with experiment failure remain the same.

AssumingGR/(1-δ) > C, follow the notations in Qian-Roland-Xu (2006):

a. State the recursive formula for V_i^UF and V_i^MF, and solve p^UF and P^MF in the extended model.

b. State the recursive formula for V_i^MS and Solve V_i^MF, and solve p^* and P^MF in the extended model.

c. Solve p^~ in the extended model. How do Figure 3 and Figure 4 in Qian-Roland-Xu (2006) (G = 1 case) change when we consider the G > 1 case?

d. Chinese land reform in 1978-1984 was one successful regional experiment that spread nationwide. From McMillan-Whalley-Zhu (1989) and Lin (1992), within 500 words, provide evidence that land reform has improved Chinese agricultural productivity.

3. Within 1200 words, explain the institutional conditions that are respectively essential for Chinese regional competition and regional experiments since 1978.