Skill-biased technological change is a change in the production technology that favors skilled (more educated, more experienced) labor over unskilled labor by increasing its relative productivity. Suppose that there are two types of workers in the economy: skilled labor N1 and unskilled labor N2 and that firms uses both types of labor to produce output. The representative labor firm's production function is F(z1. z2,K, N1, N2)=K^α(z1N1+z2N2)^(1-α) ,where z1,z2 are the specific productivity levels for skilled labor and unskilled labor respectively.
a) Write the firm's profit maximization problem and derive the two equations that characterize the firm's labor demand.
b) Define the wage premium as the ratio of skilled labor wage rate over unskilled labor wage rate,w1/w2. Suppose that z1=z2, What is the wage premium? Now suppose that z2 remains unchanged, but that z1 increases to a new value z1'=1.5z1. What is the new wage premium? What does it imply for the evolution of inequality?
c) Suppose that the government imposes a tax and subsidy system. In particular, suppose that the government taxes skilled workers (who earn the higher wage) at a rate t and uses the proceeds to subsidize the unskilled workers (who earn the lower wage) at the rate s. What is the effect of this program on the labor market equilibrium and on average productivity in the economy, defined as total output divided by the total number of workers, skilled + unskilled?