Project #91337 - Economics problems on topic: less-developed regions



1. Structural Transformation Theory


Consider the economy of Lewisville, which is just beginning to industrialize. The economy was

entirely reliant on corn production until now. There are 100 identical families each farming their

own land. Each family has 6 members who participate equally in farm work and share the output.

Each farm has a small land area and can employ up to 3 full time workers, each of whom produce 1

unit of corn. Beyond 3 workers, additional workers generate no additional farm output. Hence farm

output c=min{3,x} where x is the number of workers on the farm.


In response to an industrialization policy adopted by the government, new factories have recently

started opening up in Lewisville. Each new factory produces shirts using labor, and the marginal

product of labor in each factory is 10-y, where y is the number of workers. Workers are free to move

between farm and factory with no migration or transport costs.


Factories are owned by entrepreneurs who maximize profits. They save 10% of their profits and

invest these profits to build new factories, which start the following year. Each new factory requires

a set up cost equal to 32 shirts.


Lewisville trades with the rest of the world and is too small to affect world prices. Hence, shirt and

corn prices are fixed: the price of corn relative to shirts is 4, and each shirt can thus be sold at a

price of 0.25 units of corn.


(a) Before the factories, what is the average product of labor (corn output/worker) in each farm?

What is the marginal product of labor? What proportion of the economy’s labor force is



(b) In year 1, 20 new factories arrive. With wages in agriculture set to the average product of

labor and free mobility between sectors, what will the wage rate in the industrial sector be in

units of shirts? How many workers will each factory employ in year 1?

[Hint: WI = APLA * PA (where PA is price of corn relative to shirts).]


(c) What is total employment in industry in year 1?


(d) Will there be surplus labor in agriculture in year 1?


(e) How many factories will there be in year 2 given that each factory earns of a profit of 32

(=1/2*y(10 - WI)) in year 1? 


(f) Will there be surplus labor in agriculture in year 2?


(g) Suppose the government introduces a tax credit that increases the savings rate to 0.45. How

many more years will it take for all surplus labor to transition out of agriculture?



2. Structural Transformation Trends


Using the WDI, download the full historical time series on the urban population share and the share

of employment in agriculture in your country. Using excel or Stata, plot the two variables on the

same graph with the year on the x-axis. Also calculate the correlation between the two. Briefly

describe the trends and patterns.



3. Sharecropping, Fixed Rents, and Risk Aversion


Consider the decision-making of farmers in a poor rain-fed agricultural area of India. Suppose that

there are two possible outcomes at the end of each growing season depending on the amount of

rainfall: the good outcome generates revenue of $100, the bad outcome generates $50. Due to

historical reasons associated with the British colonizers’ treatment of wealthy landowners, fixed

rent contracts are $30 in region A and $20 in region B. Suppose that all land sizes are identical and

the only input to production is labor, and the cost of labor (inclusive of opportunity costs) is fixed at



(a) Suppose that there is a 70% chance of good rainfall. What is the expected income under fixed

rent contracts for a tenant in region A? in region B? What about expected profits?


(b) Now suppose that there has been a dramatic increase in factory jobs in nearby towns leading to

an increase in the (opportunity) cost of labor on the farm to $60. Will tenants in region A still accept

the fixed rent contracts? in region B? What is the maximum fixed rent rate that tenants will accept

in each region?


(c) Going back to the original assumptions, what sharecropping rule (i.e., what value of α) will

make landlords indifferent between fixed rent and sharecropping contracts? Use the resulting α* to

show that tenants will prefer fixed rent instead of sharecropping in the case of good rainfall but

sharecropping in the case of bad rainfall.


(d) Going back to the original assumptions, now suppose that irrigation canals are widely available

and reduce farmers’ dependence on rainfall. Conceptually, this lowers the chance of a bad outcome

by 10%. How would your answers to (a) and (b) change? Discuss the intuition for this result.


(e) Going back to the original assumptions, suppose that landlords adopt a small dose of altruism

and decide to offer limited liability contracts in which they will return 50% of the rental payment at

the end of a bad rainfall season. What is the new expected income under fixed rent contracts for a

tenant in region A? in region B? What are the implications for contract choices?




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