Obtain the demand functions for skilled and unskilled labor

Question

There are two types of labor in the economy: skilled labor LS and unskilled labor LU . Of course, skilled and unskilled labor earn di↵erent wages: WS /P and WU /P . The production function is given by

Y =Aln(LS)+ln(LU).

Parameter A reflects technology. Assume that skilled labor supply is increasing in the real wage of

skilled labor and unskilled labor supply is perfectly inelastic.

1. Determine if the production function satisfies the following properties: (1) diminishing marginal products, (2) marginal products & technology, (3) factor complementarity.
2. Obtain the demand functions for skilled and unskilled labor. Show the equilibrium graphically on two diagrams: market for skilled labor and market for unskilled labor.
3. What is the impact of technological progress (i.e. when A increases)? You need to discuss the effect on employment of skilled and unskilled labor, two real wages and output. Show the changes on the diagrams from part B.