Microeconomic Analysis: Farmer's Employment Decision and Roberto's Decision Making

Farmer's Employment Decision

Question 1

A farmer needs to decide, at the beginning of the planting season, whether to work on the farm for the planting season, or work in town. If the farmer works on the farm and  the yield that season is high, she will earn $120 for the season. The yield will be high  with probability 0.4. If she works on the farm and the yield that season is low, she will earn only $10 for the season. The yield will be low with probability 0.4. If she works on the farm and the yield that season is very low, she will earn nothing. Assume that the farmer must make her employment decision without any knowledge of whether the yield will be high or low. Alternatively, the farmer can choose to migrate to the town for this season. However, even urban employment is uncertain. If she gets a job in the urban formal sector (and there is a 50% chance that she will) then she will get a wage of $100
for the year. If she is unable to get a formal sector job, then she can always get an informal sector job, which pays $50.

Please answer all of the following questions about the farmer and her choices. Explain or show your calculations.

a)What is the expected value of working on the farm? What is the expected value of working in the town?

b)According to the Harris - Todaro model, will this farmer migrate to the town?

c)Suppose now that there is a “psychological” cost of $10 associated with moving to the city. This represents the money equivalent of the disutility to the farmer from having to move away from the village. Again, according to the Harris - Todaro model, will this farmer migrate to the town?

d)Still maintaining the “psychological” cost of $10 associated with moving to the city, suppose now that all formal sector jobs also come with medical benefits, which are worth $20 a year, in addition to the wage. Informal sector jobs do not carry any such benefits. Same question again: according to the Harris - Todaro model, will this farmer migrate to the town?

Question 2

Roberto lives in rural Venezuela and is finishing primary school. Roberto is deciding whether or not to go to secondary school. Roberto, like everyone else, lives only for two periods after primary school. In the first period, he could work on his family’s farm (without secondary school) for a salary of 300,000 Venezuelan Bolivars if crops were good or 100,000 Bolivars if crops were bad (Note, crops are good with 50% probability, and crops are bad with 50% probability).
Or, instead, Roberto could go to secondary school. If Roberto does go to secondary school in the first period, he’ll have to pay 60,000 Bolivars in fees (tuition and books)  but he also receives 20,000 Bolivars from waiting in a restaurant after school. In the second period, had he not gone to secondary school, Roberto would continue to work on the family farm and earn a salary of 300,000 Bolivars if crops were good or 100,000 Bolivars if crops were bad (Note, crops are good with 50% probability, and crops are  bad with 50% probability). With a secondary school degree in the first period, Roberto would earn 500,000 Bolivars (for sure) in the second period. Assume that the rate of interest at which Roberto can borrow or lend money is i.

a)What are Roberto’s costs (direct and indirect) of going to secondary school?

b)What are Roberto’s benefits of going to secondary school?

c)What are, the expected present value benefits and expected present value costs  of going to secondary costs? Based on your calculations, under what conditions will Roberto go to secondary school?

d)Recall that the internal rate of return to education is the interest rate i=r that makes the expected prevent value benefits equal to the expected present value costs. Calculate r.

e)Returning to your answer in c), explain what would happen to Roberto’s  decision if the rate of interest increased?

Roberto learned how to read and write in primary school. What, if anything, might you recommend to education policy makers in Venezuela in order to increase Roberto’s productivity on the farm?