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Econ 30451: Topics in Development Economics

Midterm Exam 9th of November 2022

SECTION A: Answer Question 1 OR 2.

Briefly discuss ONE of the following statements. In your answer define or explain as precisely as possible any terms or concepts which are underlined, with reference to the context in which they are being used. The text for each answer should be no longer than 2 pages, but you could include diagrams or examples where appropriate. They have equal value.

1. Consider the role of permanent rights in the paper by Banerjee-Gertler-Ghatak, (JPE, 2002). How do the incentives for tenant (TT) and landlord (LL) change compared to a short-term sharecropping contract? [50 Marks]

2. Discuss the role of insurance in a developing country context and its problems. Compare the pros and cons of individual versus group insurance. [50 Marks]

SECTION  B: Answer Problem 1 OR 2.

For each problem in section B, make sure that when providing answer, you refer to the general framework of PA theory.

Problem 1    [50 Marks]

Consider a street vendor who is meeting clients on behalf of his boss: depending on how hard the street vendor works, no sale (revenues equal to zero), good sale (revenues equal to 100) and excellent sale (revenues equal to 400) are likely according to the following probabilities:

{0     with prob. 0.1; {0     with prob. 0.6;

Works hard {100 with prob. 0.3;       Does not work hard  {100 with prob. 0.3;

{400 with prob. 0.6; {400 with prob. 0.1;

Assume that working hard has a cost of effort of 25 for the street vendor; also assume that the street vendor has another job opportunity, which involves no risk and pays 81 (so that he will never accept a contract that gives him expected utility less than 81).

a) Compute the expected profits for the boss if the street vendor puts in a high level of effort;                   [12,5 Marks]

b) Compute the expected profits for the boss if the street vendor puts in a low level of effort;          [12,5 Marks]

c) Is there any contract that the boss will be happy to sign that could induce the street vendor to put in a low level of effort?      [12,5 Marks]

d) Suppose the boss proposes to the street vendor “if you make no sale, you pay me 164. If you make a good sale, you pay me 64. If you make an excellent sale, you will be paid 236 pounds”. Will the street vendor sign such a contract and which level of effort will he choose?                                  [12,5 Marks]

Problem 2     [50 Marks]

Fred owns a local grocery shop and hires a salesperson for his shop. For simplicity, assume that the daily revenue can be either XH = 60 (if ‘the project is a success’) or

XL = 20 (if the project ‘fails’). The revenues depend on two things: demand and salesperson’s effort. Salesperson can work hard e = 1 or be lazy e = 0. If he works hard the probability of success is 0.80; if he is lazy the probability of success is 0.25. Fred, who is the principal, is risk-neutral and maximizes his (expected) profits πP = X − w, where w is the wage he will pay to the salesperson. The salesperson (agent) is risk-averse and has payoff πA = (√ w) −e (notice that this is his utility of wealth net of the cost of exerting the effort). Instead of working in the grocery shop the salesperson could be a fisherman for £16 a day which does not involve much effort, so his reservation utility is U = (√ 16) = 4.

a) Suppose that the effort is observable. Find the profit-maximizing wage if (i) Fred wants the salesperson to be lazy (ii) Fred wants salesperson to work hard. Which level of effort would Fred choose? [25 Marks]

b) Now assume that the effort is unobservable. Fred can no longer make wage contingent on effort, so he realizes that to create incentive for the salesperson to work hard he has to give him a bonus in case the sales turn out to be high. Suppose the bonus scheme in this case works as follows: if sales are low, he will pay the salesperson wL as you calculated in part (a) for high effort. If sales are high, salesperson will receive wH = wL + B, where B is the bonus. Calculate the lowest bonus that will induce e = 1. Will Fred choose the salesperson to work hard now? [25 Marks]

Fred owns a local grocery shop and hires a salesperson for his shop. For simplicity assume that the daily revenue can be either XH = 60 (if ‘the project is a success’) or XL = 20 (if the project ‘fails’). The revenue depends on two things: demand and salesperson’s effort. Salesperson can work hard e = 1 or be lazy e = 0. If he works hard the probability of success is 0.8; if he is lazy the probability of success is 0.25. Fred, who is the principal, is risk-neutral and maximizes his (expected) profits πP = X − w, where w is the wage, he pays to the salesperson. The salesperson (agent) is risk-averse and has payoff πA = √ w −e (notice that this is his utility of wealth net of the cost of exerting the effort). Instead of working in the grocery shop the salesperson could be a fisherman for 16 dollars a day which does not involve much effort, so his reservation utility is U = √ 16 = 4.

c) Suppose that the effort is observable. Find the profit-maximizing wage if (i) Fred wants the salesperson to be lazy (ii) Fred wants salesperson to work hard. Which level of effort would Fred choose?

If P wants A to be lazy, she just needs to pay him $16, which results in payoff of 4, same as what he’ll get being a fisherman. If she wants him to work hard, then she needs to satisfy

√ w − 1 = 4, so w = 25 (that is provided he works hard, which she can verify, and pay him nothing otherwise). P wants to max her profits, so she’ll choose the level of effort that results in higher expected profits for her. If she contracts the agent to exert low effort level, her expected payoff is πP (e = 0) =0.25 · 60 + 0.75 · 20 − 16 = 30 − 16 = 14. If she contracts the agent to exert high effort level, her expected payoff is πP (e = 1) = 0.8 · 60 + 0.2 · 20 − 25 = 52 − 25 = 27. P will prefer Agent to work hard

d)  Now assume that the effort is unobservable. Fred can no longer make wage contingent on effort, so he realizes that to create incentive for the salesperson to work hard he has to give him a bonus in case the sales turn out to be high. Suppose the bonus scheme in this case works as follows: if sales are low, he will pay the salesperson wL as you calculated in part (a) for high effort. If sales are high, salesperson will receive wH = wL + B, where B is the bonus. Calculate the lowest bonus that will induce e = 1. Will Fred choose the salesperson to work hard now?

The size of the bonus B should be such that A’s Best Response is to choose e = 1. Mathematically, 0.8 √ 25 + B + 0.2 √ 25 − 1 ≥ 0.25√ 25 + B + 0.75√ 25, rearrange to obtain 0.55√ 25 + B ≥ 3.75 resulting in B ≥ 21.5. Since P wants to max her profits, she’ll offer the lowest acceptable bonus.

In this specific case, given the wording of this question, when P chooses low effort level, her expected profits are exactly the same as in part (a). If P decides to offer the bonus scheme to make A work hard, her expected profits are 0.8 · (60 − 46.5) + 0.2 · (20 − 25) = 9.8. So for her it does not make sense to encourage A to work hard even though it is efficient to do so.