ECON239: Development Economics
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ECON239: Development Economics
Midterm —— Answer Guide
2021
Section B: Multi-part Questions
B1. Household Fertility Choice
Q16: The budget constraint can be written as
C = 20(100 一 10N) 一 400N + 3000
C = 5000 一 600N
Q17: The budget constraint implies the following feasible combinations of C and N :
|
Number of Children |
2 3 4 5 |
6 7 8 |
|
Consumption |
3800 3200 2600 2000 |
1400 800 200 |
Given that the household chooses C = $2000 and has preferences represented by convex indi§er- ence curves, its optimal choice of N is 5.
Q18: The budget constraint can now be written as
C = 20(100 一 10N) 一 400N + 4000
C = 6000 一 600N
Q19: The budget constraint implies the following feasible combinations of C and N :
|
Number of Children |
2 3 4 5 |
6 7 8 |
|
Consumption |
5800 4200 3600 3000 |
2400 1800 1200 |
Given that the household chooses C = $2400 and has preferences represented by convex indi§er- ence curves, its optimal choice of N is 6.
Q20: The budget constraint can now be written as
C = 30(100 一 10N) 一 400N + 3000
C = 6000 一 700N
Q21: The budget constraint implies the following feasible combinations of C and N :
|
Number of Children |
2 3 4 5 |
6 7 8 |
|
Consumption |
4600 3900 3200 2500 |
1800 1100 4 00 |
Given that the household chooses C = $3200 and has preferences represented by convex indi§er- ence curves, its optimal choice of N is 4.
Q22: The answers to these questions suggest that the householdís preferences are such that (1) children are a normal good and (2) the substitution e§ect of an increase in Parent Aís wage outweighs the income e§ect.
B2. The Harris-Todaro Model
Q23: In a competitive, áexible wage equilibrium, the marginal products would be equated across the two sectors so that
40 一 4LF = 30 一 LA :
Suppose no one works in the informal sector, LF + LA = 10; and so we can write
40 一 40 + 4LA = 30 一 LA :
It follows that
5LA(*) = 30
LA(*) = 6:
Consequently LF(*) = 4 and the wage is equal to the MP of labour in both sectors: w* = 30 一 6 = 24:
No one would choose to work in the informal sector, LI(*) = 0, given this equilibrium wage, so this conÖrms the supposition above.
Q24: Given w = 32, the demand for workers in the formal sector satisÖes
32 = 40 一 4LF
If migration is not allowed, it follows that LI = 2.
Q25: The probability that a worker in the city gets a job in the formal sector is given by
LF 2
LF + LI 4
It follows that the expected wage in the urban sector is
we = (0:5 X 32) + (0:5 X 20) = 26
Q26: The probability that a worker in the city gets a job in the formal sector is given by
LF 2
LF + LI 10 一 LA
Q27: First note that LF = 2: The expected wage in the urban sector can be expressed as
we = pw + (1 一 p)wI
we = 10 24一LA + 20
In this equilibrium the rural and urban labour forces adjust so that the agricultural wage equal the expected urban wage. That is
wA = we
30 一 LA = 10 24一LA + 20
(10 一 LA)2 = 24
Taking the square root of both sides yields
10 一 LA = 4:9
LA = 5:1
It follows that LI = 10 一 2 一 5:1 = 2:9.
Q28: The implied agricultural wage is given by
wA = 30 一 5:1 = 24:9:
As noted above, in the Harris-Todaro equilibrium, the expected wage must also equal this value.
2022-04-11