Question $2.$ Wage Differentials $($Benjamin et al$.,$ Chapter $10)$

Consider an economy of only two industries, one high wage and the other low wage. Each employs the same number of workers, equally divided between two occupational groups: skilled and unskilled. Skilled workers are identical with each other in the two industries, and so are the unskilled.

The low$-$wage industry pays its skilled labour $$21$ an hour and its unskilled labo $$6,$ during both a recession and an expansion; that is$,$ it has a rigid wage structure.

The high$-$wage industry pays its skilled labour $$33$ per hour in both a recession and an expansion, but it pays its unskilled workers $$6$ during recession and $$25$ during expansion; that is$,$ only its skilled wages are rigid over the business cycle.

Assume that there is a barrier to mobility between the two industries, preventing worker migration between the two industries.

Please express all wage differentials in terms of percentage difference $($e$.$g$.80\%).$

$1$

a$)$ For the whole economy, calculate the inter$-$occupational wage differential $($ratio of skilled to unskilled wages$)$ in both the recession and the expansion.

b$)$ Calculate the inter$-$industry wage differential $($ratio of high$-$to low$-$wage industries$)$ for both skilled and unskilled workers in both the recession and the expansion.

c$)$ Does the inter$-$occupational wage differential narrow or widen in the expansion and recession? Why?