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(SOSC186)Answers+SOSC+186+Quiz+4+Fall+2008.pdf
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Answers to Quiz 4 (November 18, 2008) SOSC 186
a)
With perfect competition we know that the two wages have to be equal. Since the demand function is the same in either sector, it is easy to see that in a perfectly competitive economy, each sector will employ the same number of workers (50 each) and the wage will be (112-50)/5 = 12.4.
b)
If urban wages are fixed at 15, urban demand will be Durban = (112-5*15) = 37. Since no unemployment is allowed, all the remaining 63 workers must be absorbed in the rural sector. With 63 workers, the marginal productivity and hence the wage of the rural workers wr will be (112-63)/5 = 9.8.
Note that the fixed urban wage is binding since 15 are greater than the perfect competition wage of 12.4.
c)
If we allow for urban unemployment, we know that the equilibrium condition is
Expected Urban Wage = Rural Wage
Or, Urban Wage * Probability of getting an Urban Job = Rural Wage (1)
Now the probability of getting an urban job is E/L, or E/(E + U) C where E is the urban labor demand and L is the urban labour force (which equals the sum of urban employment and the urban unemployed). U is the number of unemployed people in the urban sector.
Here the urban wage is fixed at 15 C so that urban employment (E) equals 37. Thus the LHS of equation (1) is 15*37/(37 + U).
To get the RHS of (1), note that now there are (100-L) people in the rural sector, or (100-37-U). The wage rate therefore in the rural sector is
wr = [112 C(100-L)]/5 = [112-(100-37-U)]/5 = (112-63+U)/5 = (49+U)/5 . (2)
Now just equate equation (2) to 15*37/(37+U). This will give a quadratic equation in U, which will be something like
U2 + 86U C 962 = 0.
Solve this, you get two solutions, only one of which will be positive. This will be about 10.
Thus U equals 10 C so that the urban labour force (L = E+U) is 37+10 = 47; the rural labour force is 100-47 = 53, so the rural wage is (112-53)/5 = 11.8.
The rural wage is higher than in part (b) because now some of the people who do not get a job in the urban sector still decide to stay there. This restricts the supply of labor to the rural sector, which in turn pushes up wages.
Urban Rural
wages wages
Urban Labor Rural Labor
Dd curve Dd curve
15
A
12.4