The name is absent

assume that the size of the education budget is exogenously determined. We
normalize to unity the cost of providing an agent with the medium level of
education and denote by c the cost of providing an agent with the high level
of education.¹⁴ We impose the following restrictions on the parameters of
the model:

Condition 1 y > V > 2

Condition 2 b < c

The first condition implies that investment in the high level of educa-
tion is efficient.¹⁵ The second condition implies that the government cannot
provide all agents with the high level of education, however, it does not
necessarily imply that the government is financially constrained. As long
as both goods are consumed in equilibrium then it is inefficient to provide
agents employed in the Y sector with the high level of education. A suf-
ficient condition for a financially constrained government is that b = 1 as
either some agents employed in the X sector will be type m or some agents
employed in the Y sector will be type I.

Let θ_i (i = l,m, h~) denote the proportion of type i agents. The govern-
ment’s choice of θ_i^,s must satisfy the following two constraints:

θι + θ_m + θh = ^{1                          (1)}

and

b ≥ θ_m + cθ_h                            (2)

where the second constraint states that government spending on education
cannot exceed the budget.

All agents have identical Cobb-Douglas preferences specified as:

U_i = (X_iY_i) I    i = l,m,h                   (3)

where Xi and Y_i denote a type i’s worker consumption of the high-tech
product and primary commodity, respectively.

¹⁴Given that the size of the budget is exogenous what matters is the size of the budget
relative to the cost of education.

¹⁵Notive that if v < 2 it is never optimal to employ agents with medium level of
education at the primary sector.

<<   7   8   9   10   11   12   13   >>

More intriguing information