Pim and her three sisters own a small farm in the agricultural sector of the land of Grim. They

work equally hard, and the value of their output measured in the local currency, nice, is 4,000 nice,

which they divide equally. The urban sector of Grim has two kinds of jobs. There are informal jobs

which anybody can get, which pay 500 nice, and there are formal jobs which pay 1,200 nice. The

probability of getting these jobs depends on the proportion of such jobs to the urban labor force,

exactly as in the Harris-Todaro model.

(a) Assume that Pim compares her own expected returns in the two sectors and there are no costs of

migration. Calculate the threshold proportion of formal jobs to urban labor force that will just deter

Pim from migrating.

(b) The full production function on Pirn's farm is given in the following table.

Number working on farm Output (in nice)

One sister 1,500

Two sisters 2,500

Three sisters 3,300

Four sisters 4,000

Suppose that Pim and her sisters seek to maximize their total family income, instead of Pim simply

acting to maximize her own. Assume that the threshold proportion that you derived in (a) actually

does prevails in the urban sector. Now prove that Pim will migrate.

(c) Will any of Pirn's sisters also wish to migrate?