(Solved): B1 (25 marks). Consider an economy which has only two regions - urban and rural. There are a total o ...

B1 (25 marks). Consider an economy which has only two regions - urban and rural. There are a total of 100 workers in the economy and they are all identical and risk-neutral. Assume there are no moving costs and that workers only take into consideration their wages when making location decisions. The marginal product of labour in the formal urban manufacturing sector is given by \[ M P_{F}=90-L_{F} \] where \( L_{F} \) denotes the number of workers employed in that sector. Similarly, the marginal product of labour in the rural agricultural sector is given by \[ M P_{A}=80-2 L_{A} . \] where \( L_{A} \) denotes the number of workers employed in agriculture. Employers in both sectors act competitively taking the wage in their sector as given. In the urban area there is also an informal sector in which workers can earn \( w_{I}=10 \). Let \( L_{I} \) denote the number of workers (in millions) employed in the informal urban sector. (a) In a competitive, flexible wage equilibrium how many workers will be employed in the agricultural, formal urban manufacturing and informal urban sectors and what will their wages be? (b) Suppose the formal sector wage is exogenously set at \( \underline{w}=30 \). What is the expected wage in the urban sector as a function of \( L_{A} \) (i.e. the expected wage curve). (c) In a Harris-Todaro long-run equilibrium how many workers will be employed in the agricultural, formal urban and informal urban sectors and what will their wages be? (d) Now suppose the government imposes migration restrictions such that only those workers with a formal sector job are allowed to move in to the urban area. How many workers will be employed in the agricultural, formal urban and informal urban sectors and what will their wages be now? (e) Explain why the policy in (d) results in an inefficient allocation of workers across the rural agricultural and urban manufacturing sectors. How could a more efficient allocation be achieved, assuming the formal sector wage cannot be reduced?