Solow’s Model of Unconditional Convergence

Development economics

Contents
1. Explain Solow’s model of unconditional convergence. Does empirical evidence
support unconditional convergence?......................................................................................3
2. What are the basic tenets of Sen’s “Cooperative-Conflict” model of the household?
How do ‘perceived biases’ affect women’s bargaining position in the family?....................4

1. Explain Solow’s model of unconditional convergence. Does empirical evidence
support unconditional convergence?
Solow model outline:
Model of the household and the firm
• Closed economy with a unique final good with discrete time
Large number of identical households
• Households do not have a preference function
• They save at a constant exogenous factor s ∈(0,1) of their disposable income,
regardless of what else happens
• Other important agent are the firms. Firms produce according to the production
function
Y =F ( K , L )
Firms maximize profit
• maxL ,K F ( K , L ) −rK−wL
• Where r is the amount that firm needs to pay to rent one unit of capital and w
is the wage the firm needs to pay one unit of labour.
• First order condition in a perfectly competitive market: wage rate equal to marginal
product of labour and rent equal to marginal product of capital
• w= ∂ F
∂ L ∧r = ∂ F
∂ K
• Cobb-Douglas production function:
• Y =F ( K , L ) =Kα∗L1−α ; 0< α <1
• We re-write the function in a more intensive form:
• Output per worker: y= Y
L =( K ¿¿ α∗L1−α)
L =¿ ¿
• k is the capital per worker
• Marginal productivity of capital MPK =α Kα −1∗L1−α
• Total amount paid out of capital: MPK . K
• Share of capital of total income: MPK . K
Y = α
• At steady state capital stock grows at the same rate as labour force.
∆ K
K =n