Problem $2$: Skill$-$Biased Technological Change and

Wage Inequality $(65$ Points$)$

A firm produces output Y using unskilled labor L and skilled labor H$.$ The

production function is given by:

Y $=$

h

$($AU L$)$ $1$

$+($AS H$)$ $1$

i

$1$

Parameters:

$$ AU : Technology parameter for unskilled labor productivity.

$$ AS : Technology parameter for skilled labor productivity.

$1$

$$ $>0$: Elasticity of substitution between unskilled and skilled labor.

$$ L: Quantity of unskilled labor employed.

$$ H: Quantity of skilled labor employed.

Assumptions:

$$ The firm operates in a competitive market.

$$ It aims to maximize profit by choosing optimal levels of L and H$.$

$$ Wages are determined by the marginal products of labor.